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Regionalism, majority government and the electoral system in Canada : the case for two-seat constituencies Sutherland, Neil John 1988

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REGIONALISM, MAJORITY GOVERNMENT AND THE ELECTORAL SYSTEM IN CANADA: THE CASE FOR TWO-SEAT CONSTITUENCIES By N e i l John S u t h e r l a n d B . S c , Western Washington U n i v e r s i t y , 1982 B.A., U n i v e r s i t y o f B r i t i s h Columbia, 1986 A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF ARTS i n THE FACULTY OF GRADUATE STUDIES (Department o f P o l i t i c a l Science) We accept t h i s t h e s i s as conforming t o the r e q u i r e d standard THE UNIVERSITY OF BRITISH COLUMBIA J u l y 1988 (c) N e i l John Sutherland, 1988 In p r e s e n t i n g this thesis in part ia l f u l f i lmen t o f t h e requ i remen ts fo r an advanced deg ree at t h e Univers i ty o f Bri t ish C o l u m b i a , I agree that t h e Library shall m a k e it f ree ly avai lable fo r re ference and s tudy . I fu r ther agree that permiss ion fo r ex tens ive c o p y i n g o f th is thesis fo r scholar ly p u r p o s e s may b e g r a n t e d by the head o f m y d e p a r t m e n t o r b y his o r he r representa t ives. It is u n d e r s t o o d that c o p y i n g o r pub l i ca t ion o f th is thesis fo r f inancia l gain shall n o t b e a l l o w e d w i t h o u t m y w r i t t e n pe rm iss ion . D e p a r t m e n t The Univers i ty o f Brit ish C o l u m b i a 1956 M a i n Ma l l Vancouve r , Canada V 6 T 1Y3 Date / L ^ r / 5 7 l*)T? DE-6(3 /81) ABSTRACT A continual problem i n Canadian p o l i t i c s i s regional c o n f l i c t . There are several reasons why the major issues i n Canadian p o l i t i c s are r e g i o n a l l y - d e f i n e d . Some o f the socio-economic v a r i a b l e s include e t h n i c i t y and economic bases, which are reinforced by geography. Some of the p o l i t i c a l variables include the d i v i s i o n of powers between the cen t r a l and p r o v i n c i a l governments, and the regional concentration of party representation i n the central government l e g i s l a t u r e . At t h e l e v e l o f the electorate, Canada's national p o l i t i c a l p a r t i e s a c t u a l l y receive multi-regional support. Thus, introducing an e l e c t o r a l system that translates votes i n t o seats more proportionately than the present system should increase the multiregional representation of Canada's p o l i t i c a l p a r t i e s at the l e v e l of seats i n the l e g i s l a t u r e . However, introducing a more proportional e l e c t o r a l system would p r o b a b l y decrease t h e l i k e l i h o o d o f a p a r t y forming a m a j o r i t y government. Consequently,. i f Canada's l e g i s l a t o r s f e l t that executive s t a b i l i t y through majority government was a more important normative c r i t e r i o n (along with whatever vested int e r e s t s they might have) than a government with multiregional representation, then proposals f o r a more proportional e l e c t o r a l system w i l l remain an academic exercise. i i The objective of t h i s study was t o f i n d an a l t e r n a t i v e e l e c t o r a l system which s a t i s f i e s both the c r i t e r i a of majority government and multiregional representation. Based on the premise t h a t the most s i g n i f i c a n t independent variables a f f e c t i n g majority government and multiregional representation are d i s t r i c t magnitude and geographical d i s t r i b u t i o n of partisan support, i t was hypothesized that Increasing the d i s t r i c t magnitude from one t o two, or from one t o three, would maintain the bias i n favour of and increase the multiregional representation of a large, d i f f u s e party. The r e s u l t s of the study show that a d i s t r i c t magnitude of two would provide a large d i f f u s e party with a majority of seats f o r the same voter support as the present system does. In addition, DM2 rewards t h i s large d i f f u s e party with the seats necessary t o form a minority government at a much lower voter support l e v e l than does the e x i s t i n g system. Thus, DM2 solves the problem of underrepresentation of regions i n the government party, and i s at the same time even more advantageous t o a large d i f f u s e party than i s the present e l e c t o r a l system. i i i CONTENTS Chapter Page Abstract i i Tables and Figures v i 1. Introduction The Problem 1 Methodology 3 2. The Variables The E l e c t o r a l System, Federalism, and Regionalism 6 The E l e c t o r a l System, Majority Government, and S t a b i l i t y 8 The E l e c t o r a l System, Regionalism, and I n s t a b i l i t y 10 The Two C r i t e r i a that an Alt e r n a t i v e E l e c t o r a l System Must Meet 12 Proportional Representation E l e c t o r a l Systems 13 The Largest Remainder Formula 14 The Highest Average Formula 15 Highest Average and Largest Remainder Formulae Compared 17 Variables A f f e c t i n g Proportionality 18 The Objectives of t h i s Study 31 3. Methodology Co l l e c t i o n of Data 33 C l a s s i f i c a t i o n of Data 35 4. Analysis of National Data Results of the 1953 E l e c t i o n 39 The 1957 E l e c t i o n 41 The 1962 E l e c t i o n 42 The 1963 E l e c t i o n 43 The 1965 E l e c t i o n 46 Ef f e c t s of D i s t r i c t Magnitude on L i b e r a l Seat Shares 47 Eff e c t s of D i s t r i c t Magnitude on Conservative Vote Shares 53 5. Analysis of Regional Data The Liberals i n the West 58 The Liberals i n Quebec 61 The Results For the Li b e r a l s i n Quebec and i n the West Compared 63 The Conservatives i n Quebec 64 6. Conclusions Summary of Findings 67 Psychological E f f e c t s 68 Alternative Proposals 70 C l a r i f i c a t i o n 71 Present-Day Relevance 73 Further Study 74 i v Chapter Page Appendices A. E l e c t i o n Results f o r a l l Parties i n a l l the Elections f o r a l l D i s t r i c t Magrdtudes 75 B. Regional Results f o r the Liberals i n the West and Quebec, and f o r the Conservatives i n Quebec 76 C. P r c p o r t i o n a l i t y as a function of D i s t r i c t Magnitude 77 D. Regression Coefficients 78 Endnotes 79 Bibliography 1. E l e c t o r a l Systems 2. General and Theoretical Works 3. Canada 4. Data Analysis 5. Sources of Data 81 83 84 86 86 v TABLES AND FIGURES Table Page 4.1 L i b e r a l Vote Shares and Seat Shares using DM1, DM2, DM3, DM6 and DM-PROV f o r the 1953, 1957, 1962, 1963 and 1965 Elections 40 4.2 L i b e r a l Vote Shares and Seat Shares using FPP from 1935 t o 1980, and Seat Shares using DM2 f o r the 1953, 1957, 1962, 1963 and 1965 Elections 49 4.3: Conservative Votes Shares and Seat Shares using FPP from 1935 t o 1980, and Seats Shares using DM2 and DM3 fo r the 1953, 1957, 1962, 1963, and 1965 Elections 54 Figure Page 2.1 The Relation Between Proportionality and D i s t r i c t Magnitude 16 4.1 L i b e r a l Seat Shares using DM1, DM2, LTD, DM6 and DM-PROV 48 4.2 L i b e r a l Seat Shares using FPP and DM2, where scatter— p l o t equals FPP r e s u l t s from 1935 t o 1980 50 4.3 Conservative Seat Shares using FPP, DM2, and DM3, where scatt e r p l o t equals FPP re s u l t s from 1935 t o 1980 55 v i CHAPTER 1 INTRDDQCTIGN The Problem What s t r u c t u r a l changes can be made to the Canadian p o l i t i c a l system, so that regional concerns can be more e f f e c t i v e l y a r t i c u l a t e d , and r e g i o n a l c o n f l i c t s more e a s i l y resolved by accommodation? Various c o n f l i c t - r e s o l u t i o n mechanisms are possible. However, only those that do not threaten the s e l f - i n t e r e s t of the beneficiaries of the e x i s t i n g system have a r e a l i s t i c chance of being implemented. The lower chamber would have rKDthing t o gain, and probably much t o lose, i f there were an elected second chamber. And replacing the e x i s t i n g e l e c t o r a l system with a more p r o p o r t i o n a l e l e c t o r a l system may do more than j u s t i n c r e a s e m u l t i - r e g i o n a l r e p r e s e n t a t i o n w i t h i n the n a t i o n a l p o l i t i c a l party caucuses; i t may also decrease the l i k e l i h o o d that any one of them can form a one-party government. I s i t possible, then, t o a l t e r the Canadian e l e c t o r a l system i n such a way as t o increase the multi-regional representation of the largest party without s u b s t a n t i a l l y decreasing i t s t o t a l number of seats i n the leg i s l a t u r e ? This hypothetical and p r a c t i c a l question provides the focus of the t h e s i s . I t w i l l be argued that regional a l i e n a t i o n i n Canada i s at le a s t p a r t i a l l y the r e s u l t of underrepresentation of d i f f e r e n t regions i n the central government; so that increased representation of a region i n the party forming the national government would decrease that region's sense o f a l i e n a t i o n . I t w i l l a l s o be argued t h a t the e x i s t i n g First-Past-the-Post (FPP) e l e c t o r a l system d i s t o r t s the t r a n s l a t i o n of votes i n t o seats, e s p e c i a l l y at the regional l e v e l . Consequently, i f an e l e c t o r a l system that i s more proportional than FPP causes l e s s d i s t o r t i o n of votes i n t o seats at the regional l e v e l , i t should decrease regional a l i e n a t i o n . The f i r s t question, whether a more proportional e l e c t o r a l system would decrease the degree of underrepresentation of various parties i n various regions, i s therefore more or l e s s taken f o r granted t o be i n the affirmative. The more inte r e s t i n g question, and the question whose answer i s more d i f f i c u l t t o predict, i s whether the largest party - and thus the government party - w i l l have i t s loss of seats i n regions where i t i s overrepresented more than compensated f o r or l e s s than compensated f o r by i t s gain of seats i n regions where i t i s underrepresented, under a more proportional e l e c t o r a l system. I f the largest party's loss of seats i n one region i s i n fa c t at l e a s t compensated f o r by i t s gain of seats i n another region, under a more proportional e l e c t o r a l system, then we w i l l have found an e l e c t o r a l system that may increase the multi-regional representation of the largest party's caucus, without decreasing i t s chances of forming a one-party government. A major problem i n Canadian p o l i t i c s , then, i s regional c o n f l i c t . This problem i s further i n t e n s i f i e d by a d i v i s i o n of powers between l e v e l s of government, by the absence of a d i v i s i o n of powers within the central government - i n p a r t i c u l a r , the absence of an elected second chamber based 2 on representation by region - and by the FPP e l e c t o r a l system that d i s t o r t s the r e g i o n a l support of n a t i o n a l p o l i t i c a l p a r t i e s when translated from the l e v e l of the electorate t o the l e v e l of l e g i s l a t i v e seats. Hence, our focus i s on a r e a l - l i f e problematic s i t u a t i o n , and the questions that focus our investigation are whether a more proportional e l e c t o r a l system would increase the multiregional representation of the national p o l i t i c a l p a r t i e s , and whether such an e l e c t o r a l system would be i n the best interests of the major be n e f i c i a r i e s of the e x i s t i n g system. Methodology We want to c o l l e c t data of a quantifiable v a r i a b l e that appears t o s i g n i f i c a n t l y a f f e c t the relationship between representation, regionalism, and federalism. We must also take i n t o consideration the a v a i l a b i l i t y of data. The FPP e l e c t o r a l system provides a l i n k between representation and r e g i o n a l i s m ; and the t r a n s l a t i o n o f votes i n t o seats i s s t r i c t l y quantitative. Also, the number of votes cast f o r each candidate i n each constituency i s published by the government. The e l e c t i o n r e s u l t s of 1953 t o 1965 national elections have been chosen because the constituency boundaries remained unchanged during t h i s s i x - e l e c t i o n period, thereby providing us with a r e l a t i v e l y large sample s i z e , and because the smaller p a r t i e s d i d not undergo any h i s t o r i c a l decline i n t o t a l vote support during most of t h i s period. The proposed methodology i s as follows. A f t e r c o l l e c t i n g e l e c t i o n r e s u l t s from the 1953 t o the 1965 national elections, hypothetical 3 c o n s t i t u e n c i e s of two, three, and s i x seats, as w e l l as "regional" constituencies based on various d e f i n i t i o n s of "region" w i l l be created. This approach permits an examination of regionalism i n Canada from the perspective of regional representation i n the executive ( i n the government party, and therefore i n the cabinet) and regional representation i n the le g i s l a t u r e . In order t o create these hypothetical constituencies, the number of v a l i d votes cast i n one constituency w i l l be added t o those of contiguous constituencies, which are o r i g i n a l l y ordered alphabetically. However, because constituencies are not the same s i z e or shape, they cannot be added contiguously ad infiriitum. Some attention must also be paid t o regional urban centers, and d i f f e r e n t i a t i o n made between urban and r u r a l areas. With each i n c r e a s e i n d i s t r i c t magnitude (the s i z e of the cxanstituencies, i n terms of seats), two trends w i l l be noted: f i r s t , the increase or decrease i n regional representation of each national p o l i t i c a l party w i l l be recorded; second, the increase or decrease i n the number of seats held by each party i n the l e g i s l a t u r e w i l l be recorded. Because of the small sample s i z e - number of elections, n, = 5, - i t w i l l be d i f f i c u l t t o formulate a l i n e a r r e l a t i o n s h i p between the number of seats per constituency ( d i s t r i c t magnitude) and the proportionality of votes translated i n t o seats. However, these r e s u l t s can be transposed on t o a graph showing the rel a t i o n s h i p between votes and seats f o r elections between 1937 and 1984. Such a transposition w i l l allow us to observe whether increased d i s t r i c t magnitudes w i l l increase or decrease the bias (the amount by which a large party's seat share exceeds i t s vote share) i n favour of either or both large p a r t i e s . 4 Besides v a r i a t i o n i n s i z e and shape of contiguous constituencies, there are other methodological d i f f i c u l t i e s . F i r s t , the 1958 election, when the Conservative party won a majority of the seats i n the province of Quebec, represents an anomaly i n our data set, and w i l l therefore be omitted. Second, not every p o l i t i c a l party contested every seat i n every el e c t i o n . This problem w i l l be dealt with by t r e a t i n g a l l instances where a party ran a candidate i n one constituency, but not i n the constituency contiguous t o i t , as single-seat constituencies. A l s o , time and s t r a t e g i c voting must be treated as c e t e r i s paribus. There i s much evidence t o support the argument that the spectre of the 'wasted vote' i n an FPP e l e c t o r a l system decreases the e l e c t o r a l support of smaller p a r t i e s , and that t h i s e f f e c t i s s e l f - r e i n f o r c i n g over time; consequently, the introduction of a more proportional e l e c t o r a l system c o u l d i n theory i n c r e a s e the e l e c t o r a l support f o r smaller p a r t i e s . For our study t o attempt t o take into account such factors as a l t e r n a t i v e forms of s t r a t e g i c voting would be pure speculation - even with hindsight - and so we must assume that the wasted vote factor had a minimal impact during the 1953-1965 period. F i n a l l y , i f we are to assume that t h i s study has present-day relevance, then we must also assume that the national p o l i t i c a l p a r t i e s s t i l l have the same regional strongholds of partisan support, and that Canada s t i l l has the same sources of regional c o n f l i c t . Both of these assumptions are admittedly i n doubt at the moment. I t w i l l , however, be argued that we are presently i n a period of p o l i t i c a l uncertainty; so that s i m i l a r patterns of regional support and sources of c o n f l i c t may re-emerge i n the future. 5 CHAPTER 2 THE VARIABLES T h e E l e c t o r a l System. Federalism, and Regionalism The First-Past-the-Post (FPP) e l e c t o r a l system vised i n Canada t o e l e c t members of the lower chamber i s a s i g n i f i c a n t determinant of several aspects of the Canadian p o l i t i c a l system. For example, i t has a greater tendency t o produce one-party m a j o r i t y governments than do more proportional e l e c t o r a l systems. Also, FPP has a greater tendency than Proportional Representation (PR) e l e c t o r a l systems t o produce two dominant pa r t i e s at the constituency l e v e l . However, between constituencies i t i s not always the same two parties that dcndnate; cxariseguently, at the national l e v e l there may be more than two large parties. Having more than two large p a r t i e s decreases the l i k e l i h o o d of one-party majority gcvernment; and i n a p o l i t i c a l system with a t r a d i t i o n of one-party government, a one-party minority gcvernment i s more probable than a c o a l i t i o n government. Having more than two large parties competing i n an FPP system also increases the l i k e l i h o o d that each party w i l l have t h e i r s t r o n g e s t bases o f support amongst geographically-concentrated sectional i n t e r e s t s . Thus, there i s a high p r o b a b i l i t y that an FPP e l e c t o r a l system w i l l produce a one-party majority or minority government with l i t t l e or no representation of one or more regions i n i t s caucus. 6 The preceding hypothesis assumes that there i s a fusion of the executive and l e g i s l a t i v e branches, and that the l e g i s l a t u r e i s i n e f f e c t unicameral. I f the l e g i s l a t u r e was bicameral, with members of the second chamber e l e c t e d on some b a s i s other than p o p u l a t i o n , t h a t i s , representation by region, then at le a s t one source of regional c o n f l i c t -highly-populated regions c ^ - ^ o t i n g lesser populated regions - would be a l l e v i a t e d . A second elected l e g i s l a t i v e chamber based cn representation by region would also mean a formal forum f o r expressing regional i n t e r e s t s a t the c e n t r a l government l e v e l . However, where no second elected l e g i s l a t i v e chamber e x i s t s , some a l t e r n a t i v e means of a r t i c u l a t i n g regional concerns must be found. In a unitary, e f f e c t i v e l y unicameral, FPP system, such as B r i t a i n , r e g i o n a l a s p i r a t i o n s and f r u s t r a t i o n s may be expressed through ' n a t i o n a l i s t ' movements running and e l e c t i n g candidates i n ce n t r a l government elections. However, the influence of these n a t i o n a l i s t p a r t i e s i s a function of t h e i r parliamentary strength, which i s inconsistent over time. In contrast, where a federal system d i v i d i n g powers between a central government and l o c a l governments has been transplanted on t o a system where the executive and l e g i s l a t u r e are fused, and the l e g i s l a t u r e i s e f f e c t i v e l y unicameral and elected using the FPP system, the l o c a l governments can be expected t o take on the r o l e of constant defenders of regional i n t e r e s t s . However, the experiences of the Canadian p o l i t i c a l system have shown that p r o v i n c i a l government a r t i c u l a t i o n of regional concerns i s j u s t as l i k e l y t o exacerbate as t o resolve regional c o n f l i c t s . 7 The Electoral System. Majority GcMernment, and St a b i l i t y The seminal a r t i c l e r e l a t i n g regional c o n f l i c t i n Canada t o the party system, and the party system t o the FPP e l e c t o r a l system, was writt e n by Alan Cairns i n 1968 1. In t h i s and l a t e r papers 2, Cairns begins by comparing the normative values of FPP and more proportional e l e c t o r a l systems. Cairns l i s t s the d i s t o r t i o n of votes when translated i n t o seats as the p r i n c i p a l f a u l t of the FPP system, from the point of view of democratic theory 3. However, i t i s u n l i k e l y that the advocates of FPP would deny that as a mechanical device f o r t r a n s l a t i n g votes i n t o seats FPP i s imccurate and i n e f f i c i e n t . Rather, FPP advocates argue that s t a b i l i t y i s a more important normative c r i t e r i o n than the procedural n i c e t i e s of fairness and consistency. They then go on t o l i n k s t a b i l i t y with single-party majority government, and note that single-party majority government occurs more frequently where FPP i s used. Edmond Morgan argues that a l l governments r e s t on opinion, and the opinions they r e s t on are generally " f i c t i o n s " ; that i s , propositions widely accepted even though known t o be ccritrary t o f a c t 4 . Cairns bypasses the argument between advocates of FPP and advocates of more proportional e l e c t o r a l systems over the primacy of d i f f e r e n t normative c r i t e r i a . Instead, he accepts, f o r the sake of argument, the FPP advocates' c r i t e r i o n of s t a b i l i t y . As we s h a l l see, he then proceeds t o argue that the occurrence of majority government where FPP i s used i s less frequent than i t i s often generalized t o be, and that the l i n k between 8 executive s t a b i l i t y and the o v e r a l l s t a b i l i t y of a p o l i t i c a l system i s generally a f i c t i o n . F i r s t , regarding the tendency of FPP t o manufacture an a r t i f i c i a l majority of seats f o r the party with the most, but l e s s than h a l f , of the votes. Cairns points out that i n Canadian national elections from 1921 t o 1965, FPP helped t o transform a minority of votes i n t o a majority of seats only s i x out of twelve times - a 50 percent success r a t e 5 . In h i s 1979 paper, Cairns also notes the "perverse capacity" of FPP t o sometimes award the party with the most votes with the second largest amount of seats; thus denying the l a r g e s t party, i n terms of votes, of having the cpportunity t o even form a single-party minority government6. Hence, i n our quest t o f i n d a more appealing e l e c t o r a l system than FPP, we do not need t o f i n d one with a 100% success rate at awarding the party with the most votes with a majority of the seats. In fact, f o r the f i v e elections we w i l l be l o o k i n g at, only the 1953 e l e c t i o n produced a majority government; while two others, the 1957 and 1962 elections, awarded the Conservative party more seats than the L i b e r a l s even though they received a lower percent of the popular vote 7. Regarding the l i n k between single-party majority government and o v e r a l l s t a b i l i t y , there are two factors that have t o be taken i n t o account. One i s whether or not empirical evidence substantiates the l i n k . The other i s the assumption that majority government i s the most or only s i g n i f i c a n t v a r i a b l e a f f e c t i n g s t a b i l i t y . As Cairns argues, the l i n k i s e m p i r i c a l l y i n v a l i d , and the assumption i s f a l s e 8 . 9 U n t i l the 1960's, the most caramon generalization when comparing FPP to systems of proportional representation was that p o l i t i c a l systems that used FPP were stable, while systems that used PR were p o l i t i c a l l y unstable. The most commonly c i t e d examples of p o l i t i c a l i n s t a b i l i t y associated with PR e l e c t o r a l systems were the German Weimar Republic and the French Fourth Republic. This generalization ignored the h i s t o r i c a l , c u l t u r a l , economic and other factors that affected p o l i t i c s i n Germany and France during these periods. I t also ignored counter-examples of r e l a t i v e s t a b i l i t y i n Scandinavian countries, the Benelux countries, and the Alpine countries of Europe, a l l of which use PR e l e c t o r a l systems. I t further ignored several examples of p o l i t i c a l i n s t a b i l i t y occurring i n countries which use the FPP e l e c t o r a l system. The E l e c t o r a l System. Regional ism, and I n s t a b i l i t y The point i s that there are other factors that are much more important t o maintaining the s t a b i l i t y of a p o l i t i c a l system than whether a single-party majority government i s formed, or a minority or c o a l i t i o n government must be sustained. In Canada, the most important factor a f f e c t i n g the s t a b i l i t y of the p o l i t i c a l system i s regional c o n f l i c t . Deductive reasoning therefore leads us t o argue that i t i s essential t o have a s t r u c t u r a l mechanism within the central government apparatus f o r resolving regional c o n f l i c t . And observation leads us t o conclude that the e x i s t i n g Canadian national government lacks such a mechanism. 10 I t was argued i n the introduction that a second chamber elected on the basis of representation by region was p o l i t i c a l l y inexpedient from the point of view of the largest party, which governs by means of i t s control of the lower chamber. Yet i f the lower chamber i s t o f u l f i l l a regional c o n f l i c t r e s o l u t i o n function, i t w i l l have t o be elected using an e l e c t o r a l system other than FPP; which manufactures a government party a r t i f i c i a l l y underrepresented i n one or more regions j u s t as frequently as i t manufactures a government party with an a r t i f i c i a l majority. In order f o r the central government t o be viewed as a neutral a r b i t e r of regional c o n f l i c t , i t must be able t o present i t s e l f t o the c i t i z e n s of every province as a spokesman f o r regional interests equal i n legitimacy t o that of the p r o v i n c i a l governments. I t hardly seems l i k e l y that the c i t i z e n s of a province would perceive a central government with few or no representatives from that province i n i t s party caucus or i n the cabinet, as a defender of the province's interests i n situations where they run contrary t o the i n t e r e s t s of provinces i n another region with substantial representation w i t h i n the central government party's caucus. Of c o u r s e t h e c e n t r a l government may w e l l be a c t i n g i n the underrepresented province or region's best i n t e r e s t s ; but t h e i r perception of biased decision-making may s t i l l p e r s i s t . Furthermore, i t i s i n the p r o v i n c i a l p o l i t i c i a n s ' s e l f - i n t e r e s t t o e x p l o i t any opportunity t o appear as the legitimate defender of p r o v i n c i a l in t e r e s t s . Consequently, i t i s t o the p r o v i n c i a l p o l i t i c i a n ' s maximum p o l i t i c a l advantage t o make the central government appear t o be a h o s t i l e foreign power; and nothing gives him more ammunition than t o be seated across the negotiating table from a central government lacking i n representation from that province. 11 I f the above assumptions are correct, then increasing the power of p r o v i n c i a l governments cannot be expected t o a l l e v i a t e regional c o n f l i c t . Rather, the s t a b i l i t y of the Canadian p o l i t i c a l system depends upon the c e n t r a l government being perceived as a neutral a r b i t e r of c o n f l i c t i n g regional i n t e r e s t s . I t can only do t h i s i f the government party has multi-regional representation. The Two C r i t e r i a t h a t an Alternative E l e c t o r a l System Must Meet In Canada, then, there i s indeed a l i n k between s t a b i l i t y and the e l e c t o r a l system; but t h i s l i n k has l e s s t o do with s t a b i l i t y associated with one-party majority government, than with s t a b i l i t y associated with central government legitimacy as a resolver of regional c o n f l i c t . Thus, t o s a t i s f y the normative c r i t e r i o n of s t a b i l i t y i n the Canadian p o l i t i c a l system, the e l e c t o r a l system must achieve two goals, single-party majority government and multi-regional representation within the government party. These two goals may or may not be r e a l i z a b l e under a single e l e c t o r a l formula. I t has already been noted that the FPP system has had a 50 percent success rate at producing majority governments i n Canada; and that a l l of Canada's national p o l i t i c a l p a r t ies, including the largest party, have had t h e i r s t r o n g e s t bases of support amongst geographically concentrated sectional i n t e r e s t s . We must therefore inquire into the a b i l i t i e s of a l t e r n a t i v e e l e c t o r a l systems t o produce a bias i n favour of the largest 12 party/ comparable t o that produced by FPP, and at the same time, t o provide a greater incentive f o r large parties t o broaden the geographical base of t h e i r support, than does FPP. Proportional Representation E l e c t o r a l Systems There are l i t e r a l l y dozens o f d i f f e r e n t e l e c t o r a l systems presently i n use i n various countries around the world. However, with the exception of B r i t a i n , a l l the countries of Western Europe use what are commonly r e f e r r e d t o as P r o p o r t i o n a l Representation (PR) e l e c t o r a l systems. There are three properties that a l l PR systems share, which are a l l r e l ated t o d i s t r i c t magnitude. F i r s t , as the name suggests, the tr a n s l a t i o n of votes i n t o seats i s l i k e l y t o be more proportional under PR systems; and, more s p e c i f i c a l l y , there should be a p o s i t i v e relationship between pro p o r t i o n a l i t y and d i s t r i c t magnitude. According t o Douglas Rae, t h i s r e l a t i o n s h i p i s c u r v i l i n e a r and asymptotic: "as d i s t r i c t magnitude i n c r e a s e s , the p r o p o r t i o n a l i t y of outcome increases at a decreasing rate... .When d i s t r i c t magnitudes are raised substantially beyond twenty, a "plateau" e f f e c t seems t o take place." 9 Figure 2.1 i l l u s t r a t e s t h i s r e l a t i o n s h i p . A l o g i c a l extension of t h i s i s that since FPP i s biased i n favour of the largest party or two largest parties, as d i s t r i c t magnitude increases, the bias i n favour of the largest party decreases. F i n a l l y , as d i s t r i c t magnitude increases, the p a r t i e s 1 shares of a l l the votes are le s s affected by how geographically concentrated or d i f f u s e t h e i r voter support i s . 13 The Largest Remainder Formula Amongst PR systems, some of the most cxanmonly used axe referred t o as " l a r g e s t remainder" systems. In i t s simplest form, the largest remainder formula works as follows: each voter uses one vote t o e l e c t more than one representative per constituency. Votes are then translated i n t o seats using a "quota", which i s calculated by d i v i d i n g the number of v a l i d votes i n a constituency by the number of seats i n the constituency; or, i n terms of percentages, a quota i s equivalent to (l/# of seats) * 100 percent. To see how the largest remainder formula works i n theory, consider an example where there i s a ten-seat constituency (from now on the number of seats i n a c o n s t i t u e n c y w i l l be r e f e r r e d t o as the " d i s t r i c t magnitude") and four p a r t i e s are competing. The quota i s therefore (1/10) * 100 = 10 percent. Each party i s then awarded i t s share of the seats by d i v i d i n g i t s share of the votes by the quota. So i f party A received 40 percent of the votes, party B received 30 percent of the votes, party C received 20 percent, and party D 10 percent, then party A would be awarded 40 percent/10 percent = 4 seats, party B 30/10 = 3 seats, party C 20/10 = 2 seats, and party D 10/10 = 1 seat. Compare t h i s t o FPP, with the h y p o t h e t i c a l t e n - s e a t c o n s t i t u e n c y broken up i n t o t e n one-seat constituencies, and with the d i s t r i b u t i o n of party support amongst voters constant across the ten constituencies. In such a scenario, party A, with f o r t y percent of the votes, would be awarded a l l ten seats. 14 In the above example, a l l the seats i n the constituency were conveniently allocated by use of the quota. But what i f instead of whole integers, the four p a r t i e s had a few l e s s votes or more votes than necessary f o r a quota? What i f party A received 42 percent of the votes, party B 28 percent, party C 24 percent, and party D 6 percent? Under t h i s scenario, only eight of the ten seats could be allocated by use of the quota. The largest remainder formula solves t h i s problem by awarding the p a r t i e s with the "largest remainders" of votes with the remaining two seats. In our example, the remaining seats would be awarded t o party B, with a remainder of 8 percent, and party D, with a remainder of 6 percent. Because of i t s r e l a t i v e s i m p l i c i t y , the largest remainder formula w i l l be used i n the analysis of our data; except that instead of a quota base on # of votes/# of seats, the "Droop quota", # of votes/(# of seats + 1), w i l l be used. For example, f o r a two-seat constituency, instead of the quota being (1/2) * 100 = 50 percent, the Droop quota would be (1/3 * 100 = 33.4 percent. Using the Droop quota allows us t o a l l o c a t e more seats on the basis of quotas than on the basis of largest remainders, f o r constituencies with d i s t r i c t magnitudes of 2 or 3. I t i s presumed that t h i s w i l l make our calculations much simpler. The Highest Average Formula Along with largest remainder, the most commonly used PR formulas are referred t o as "highest average". The simplest form of the highest 15 j F I G U R E *.1 ! P R O P O R T I O N A L I T Y ! 1 .OQ_ P M > P O R T I O N A U T Y O P V O T I S T K A M . H A T B D I N T O A S A F U N C T I O N O P D I S T f l l C T M A Q N I T U O E - 9 9 _ - 9 8 _ . 9 7 . . 9 6 _ - 9 4 _ . 9 3 . . 2 0 . P r o p o r t i o n a l i t y l a b a n d o n t h * a v a r a g * d e v i a t i o n b e t w e e n v o t e a n d s e a t s h a r e s . P r o p o r t i o n a l i t y I n c r e a s e s a t a d e c r e a s i n g r a t e a s d i s t r i c t m a g n l i u d * I n c r e a s e s . P r o p o r t i o n a l i t y a p p r o a c h e s , b u t n e v e r r e a c h e s , 1 0 0 % (%) H 1 r -I 1 h H 1 h 5 . 0 1 O . 0 DISTRICT M A G N I T U D E 1 5 . 0 2 0 . 0 average formula i s the d'Hondt. Under t h i s procedure, r a t i o s of votes t o seats are calculated f o r each party, and the f i r s t seat i s awarded t o the party with the highest r a t i o . Beginning with number of seats held by each party/ n, equal t o zero, the r a t i o s are calculated using the equation party's votes/n + 1 = party's votes/1. So a f t e r the largest party has been awarded the f i r s t seat, i t s new r a t i o w i l l be party's votes/(n + 1) = party's votes/2. Highest Average and large s t Remainder Formulae Compared To see why larger parties would consider highest average t o be a f a i r e r system than largest remainder, r e c a l l the second h a l f of our e a r l i e r example. Using largest remainder, party A was awarded 4 seats and party D 1 seat. Yet party A received 42% of the votes, compared to party D's 6%. Party A could therefore r i g h t l y claim that since i t received seven times as many votes as party D, i t i s e n t i t l e d t o seven times as many seats. Using the d'Hondt highest average formula, the seats would be allocated as follows: party A would be awarded 5 seats, party B, 3 seats, party C, 2 seats, and party D would receive no seats. This example i l l u s t r a t e s a general difference between highest average and largest remainder; highest average tends t o be more biased i n favour of larger p a r t i e s and more bi a s e d a g a i n s t smaller parties than does largest remainder. The equations used by largest remainder and highest average formulae can be and have been adjusted such that the above tendencies are 17 reversed. However, as noted by Rae, the most powerful determinant of p r o p o r t i o n a l i t y i s d i s t r i c t magnitude. 1 0 Thus, i f a p o l i t i c a l system wished t o increase the proportionality of i t s e l e c t o r a l outcome, i t would be simpler and more e f f i c i e n t to increase the average d i s t r i c t magnitude rather than switch t o another PR formula. In the analysis of our data, then, we w i l l assume that the impact on our r e s u l t s , had we used an a l t e r n a t i v e formula, would be minimal. We w i l l assume that comparing the e f f e c t of d i f f e r e n t d i s t r i c t magnitudes on the t r a n s l a t i o n of votes into seats i s much more revealing. Based on these assumptions, we w i l l use the equation which makes our r e s u l t s simplest to calculate - the Droop quota. Variables A f f e c t i n g Prctxxrtlonality Based on the hypothesis that there i s a p o s i t i v e c u r v i l i n e a r asymptotic re l a t i o n s h i p between proportionality and d i s t r i c t magnitude, we would assume t h a t by i n c r e a s i n g the d i s t r i c t magnitude from the single-member constituency used by FPP to a d i s t r i c t magnitude of two, there would be a dramatic increase i n proportionality; i n other words, we would expect the largest party t o s u f f e r a dramatic decrease i n seats. I f t h i s i s the case, then our f i r s t objective, executive s t a b i l i t y through majority government, w i l l became v i r t u a l l y unobtainable. And i f our f i r s t c r i t e r i o n f a i l s , our second c r i t e r i o n , s t a b i l i t y of the p o l i t i c a l system as-a-whole through multiregional representation i n government, i s not worth pxirsuing i n p r a c t i c a l terms. However, i t i s p r e c i s e l y because the two c r i t e r i a are i n t r i c a t e l y related that the p o s s i b i l i t y e x i s t s f o r a large party with multiregional support at the l e v e l of the electorate to 18 gain j u s t as many seats with a d i s t r i c t magnitude of two as with a d i s t r i c t magnitude of one. The degree t o which a party's loss of seats i n one region i s compensated f o r by a gain i n seats i n another region under a more proportional e l e c t o r a l system i s a function of three factors: the party's t o t a l share of votes, the d i s t r i b u t i o n of i t s vote share, and the number of p a r t i e s competing i n each region. These three variables int e r a c t d i f f e r e n t l y depending on the d i s t r i c t magnitude. To i l l u s t r a t e how these variables would interact using an FPP system, l e t us use the example of a country with two "regions" of equal population and four p o l i t i c a l p a r t i e s . Party A receives 40 percent of the t o t a l vote, Party B receives 30 percent, Party C 20 percent, and Party D 10 percent. I f voter support f o r each party i s constant throughout the country, then under FPP, Party A w i l l be awarded a l l the seats i n the l e g i s l a t u r e . However, i f Party B receives 45 percent of voter support throughout one region, and only 15 percent i n the other region, then Party B w i l l receive h a l f the seats. In other words, there i s more p o l i t i c a l "pay-off", i n terms of seats, f o r the second largest party i n an FPP system t o seek reg i o n a l l y concentrated voter support. At the same time, i t i s t o neither the advantage nor the disadvantage of Party A t o seek more r e g i o n a l l y concentrated support, since doing so would neither increase nor decrease i t s t o t a l number of seats i n the l e g i s l a t u r e . Meanwhile, Party A finds i t s e l f i n a s i t u a t i o n where i t represents only one region i n the l e g i s l a t u r e , even though i t i s supported by 40 percent of the voters i n the other region. 19 The above example i s imaginary, but not u n r e a l i s t i c of how the FPP system a c t u a l l y operates. Describing the tendencies of the FPP system with i n the Canadian p o l i t i c a l system, Cairns made the observation that FPP i s biased against the N.D.P., a small party with r e l a t i v e l y d i f f u s e support, and biased i n favour of the Soc i a l Credit party, a small party w i t h q u i t e concentrated regional support 1 1. As a r e s u l t , a party representing i n t e r e s t s that cut across regional boundaries i s continuously underrepresented i n the central government l e g i s l a t u r e , while a party symbolic o f r e g i o n a l p r o t e s t i s overrepresented i n the Canadian l e g i s l a t u r e . In an a r t i c l e written i n 1977, Richard Johnston and Janet Ballantyne made the additional observation that f o r large p a r t i e s i n the Canadian p o l i t i c a l system, the FPP e l e c t o r a l system i s biased i n favour of a large party with d i f f u s e support more so than a large party with re g i o n a l l y concentrated support 1 2. However, i n the previous example we saw that while FPP was biased i n favour o f both large parties, i t rewarded the large party with re g i o n a l l y concentrated support the most. The explanation i s that voter support f o r the two large parties i n the Canadian p o l i t i c a l system i s neither as d i f f u s e nor as concentrated as that f o r the two largest partie s i n the example. To pro v i d e an even more extreme example of how powerful a determinant o f e l e c t o r a l outcome geographical d i s t r i b u t i o n of voter support can be, consider the following case. Party C, with 20 percent of voter support, receives a l l of i t s support i n one region. Party A 20 receives 35 percent of voter support i n one region, and 45 percent i n the other, while Party B receives 25 percent i n one region, and 35 percent i n the other. I f voter support f o r each party i s constant w i t h i n each region, then the FPP system w i l l award Party C, with 20 percent of t o t a l votes, with h a l f the t o t a l seats. Meanwhile, Party B receives no seats. The example of the ef f e c t of geographical d i s t r i b u t i o n of party support on the t r a n s l a t i o n of votes into seats when the FPP system i s used also provides an i l l u s t r a t i o n of how the term "wasted vote" can be used. The most caramon usage of the term "wasted vote", t o r e f e r t o a s i t u a t i o n where voters f e e l that t h e i r votes are wasted when they vote f o r a party that f i n i s h e s t h i r d and out of the race, w i l l be dealt with at a l a t e r point. For now, we want t o confine ourselves t o situations where pa r t i e s gain more or l e s s votes than necessary t o gain a constituency s e a t . 1 3 Referring t o the previous example, i n one region Party A received 35 percent of the votes and no seats. Since Party A has nothing t o show f o r the 35 percent of voter support i t received, i n e f f e c t those 35 percent of votes were wasted. Meanwhile, i n the other region, Party A received 45 percent of the votes, when a l l i t needed to receive i n order t o win a l l the seats was 35.1 percent. In ef f e c t , the 10 percent of the votes Party A received above what i t needed t o win a l l the seats i n the region ( i t s "margin of victory") were wasted. Understanding the d i s t r i b u t i o n of voter support f o r p o l i t i c a l p a r t i e s i n terms of wasted votes and margin of v i c t o r y gives us a better idea of how propor t i o n a l i t y w i l l be affected when d i s t r i c t magnitude i s i n c r e a s e d . I f a simple b i v a r i a t e r e l a t i o n s h i p e x i s t e d between 21 p r o p o r t i o n a l i t y and d i s t r i c t magnitude, t h e n we would expect propor t i o n a l i t y to increase when d i s t r i c t magnitude was increased from one (FPP) t o two. S i m i l a r l y , increasing d i s t r i c t magnitude t o two would be expected t o decrease the bias i n favour of the largest party. However, as the next example i l l u s t r a t e s , i f the largest party has r e l a t i v e l y d i f f u s e support, and t h e r e are one o r more p a r t i e s w i t h more regionally concentrated voter support, then when d i s t r i c t magnitude i s increased to two, the number of wasted votes of the largest party may decrease. Hence, the bias i n favour of the largest party may a c t u a l l y increase. This of course i s the f i r s t c r i t e r i o n that the a l t e r n a t i v e e l e c t o r a l system must meet. In t h i s next example, there are three regions of equal population, and voter support i s constant within each region. Region One i s inhabited by an ethnic minority. The largest party i n Region One i s the N a t i o n a l i s t Party/ which receives 51 percent of the vote. Regions Two and Three are i n h a b i t e d by the e t h n i c m a j o r i t y , and Region Two i s the economic metropolis of the country, while Region Three i s an economic hinterland. The largest party i n Region Three i s the Anti-Establishment Party, which receives 51 percent of the vote. The Accommodation Party receives the remaining 49 percent of the vote i n Region One, 70 percent of the vote i n Region Two, and 30 percent of the vote i n Region Three. The Alternative Party receives the remainder of the votes. We thus have a s i t u a t i o n where two p a r t i e s are confined t o single regions and a t h i r d party has voter support ranging from 30 percent t o 70 percent across regions. 22 Using the FPP system, there w i l l be the following outcome. In Region One, the Nati o n a l i s t Party's margin of v i c t o r y i s 2 percent. In Region Two, the Aocxammodation Party's margin of v i c t o r y i s 40 percent. In Region Three, the Anti-Establishment Party's margin of v i c t o r y i s 20 percent. Assuming that a p o l i t i c a l party has l i m i t e d resources with which t o compete i n an ele c t i o n campaign, the Accommodation Party has a cushion of 40 percent i n Region Two, which i n terms of p o l i t i c a l pay-off i n the way of votes, would be better spent i n seeking more voter support i n other regions. As i t stands now, the AcccnrnxxJation Party has wasted the excess 40 percent of the votes i t received i n Region Two, j u s t as i t has wasted the 49 percent i n Region One and the 30 percent i n Region Three which resulted i n no seats. In fact, i f we add the three margins of v i c t o r y together with the percentage of votes of a l l the l o s i n g p a r t i e s i n each region, we f i n d that on average 64 percent of the votes were wasted. I f proportionality i s measured i n terms of votes translated i n t o seats, the outcome i s equally distorted. The Anti-Establishment Party and the N a t i o n a l i s t Party, each with one-sixth of the t o t a l votes, receive one-third each of the t o t a l seats. Meanwhile, the Alternative Party, also with one-sixth of the t o t a l votes, but with l e s s regionally concentrated support, receives no seats. The other party with d i f f u s e support, the Accommodation Party, received one-half of the t o t a l votes, but only one-third of the t o t a l seats. 23 I t was noted e a r l i e r that i n Canada the FPP system has been biased i n favour of a large party with d i f f u s e support. However, t h i s example i s not meant t o be a r e f l e c t i o n of how the FPP system has a c t u a l l y operated wit h i n the context of the Canadian p o l i t i c a l system. Rather, i t i s intended t o i l l u s t r a t e that geographical d i s t r i b u t i o n of partisan support i s an independent v a r i a b l e t h a t can s i g n i f i c a n t l y a f f e c t the proportionality of e l e c t o r a l outcome. We are therefore predicting that as d i s t r i c t magnitude increases, two trends w i l l occur. F i r s t , p roportionality w i l l increase, and with i t a decrease i n the bias i n favour of large part i e s . Also, the bias i n favour of p a r t i e s with regionally cxsncentrated support w i l l decrease as d i s t r i c t magnitude increases. With respect to i n d i v i d u a l p a r t i e s , four trends are predicted. Small p a r t i e s with d i f f u s e support are expected t o gain more seats as d i s t r i c t magnitude i s increased. Conversely, large parties with concentrated support are expected to lose seats. However, i n the case o f s m a l l p a r t i e s w i t h concentrated support, we have a t^ro-predictor equation where the sign of one slope i s p o s i t i v e and the sign of the other slope i s negative; so that whether small regionally concentrated p a r t i e s gain or lose seats when d i s t r i c t magnitude i s increased w i l l vary depending on t h e i r i n d i v i d u a l s i z e and corcentration. The e f f e c t of d i s t r i c t magnitude on large parties with d i f f u s e support i s also represented by a two-predictor equation with one p o s i t i v e slope and one negative slope, except that the signs are reversed. 24 Returning t o our previous example, we have a case where there i s an extremely large party, i n terms of votes, which i s also very diffuse, i n the sense that i t i s a "large" party i n every region. However, using the FPP system, i t r e c e i v e s o n l y o n e - t h i r d of the seats i n the l e g i s l a t u r e . The next step i s t o increase the d i s t r i c t magnitude t o two, and observe whether the largest party and the other three parties gain or lose seats. With a d i s t r i c t magnitude of two, the Droop quota i s 33.4 percent. I n Region One, t h i s r e s u l t s i n the Na t i o n a l i s t Party winning h a l f the seats and the Accamncdation Party winning the other h a l f . In Region Three, the Anti-Establishment Party wins h a l f the seats, and the Accommodation Party the other h a l f , since i t has the largest remainder. In Region Two, the Accranmodation Party's 70 percent of the votes exceeds the t o t a l f o r both quotas, and consequently i t wins a l l the seats. Comparing t h i s r e s u l t t o that using that FPP, we see that the two small r e g i o n a l l y concentrated parties each have t h e i r seat share cut from ore-thi r d t o one-sixth of the t o t a l . Conversely, the large d i f f u s e party's seat share has increased from one-third t o two-thirds. From the r e s u l t s of t h i s example, we can set f o r t h as a working h y p o t h e s i s t h a t f o r s m a l l d i s t r i c t magnitudes, the geographical d i s t r i b u t i o n of partisan support can be a more s i g n i f i c a n t determinant than party s i z e of the bias i n favour of or against a party. In addition, i n the above example when the d i s t r i c t magnitude was increased t o two, the Accommodation Party increased i t s t o t a l number of seats while at the same time increasing i t s multi-regional representation. These c r i t e r i a of 25 course are the c r i t e r i a that the a l t e r n a t i v e e l e c t o r a l system must meet. So even though the p a r t i e s i n our example d i f f e r i n s i z e and geographical d i s t r i b u t i o n from Canada's national p o l i t i c a l p a r ties, and even though Canada has more than three regions, when we look at the 1953 t o 1965 Canadian national e l e c t i o n r e s u l t s , we w i l l be looking f o r at l e a s t one party t o display e l e c t o r a l tendencies s i m i l a r t o those of the hypothetical Accomodation Party. The above examples are meant to i l l u s t r a t e the potential e f f e c t of partisan geographical d i s t r i b u t i o n on the proportionality of e l e c t o r a l outcome; they are not meant t o portray the actual e f f e c t of partisan geographical d i s t r i b u t i o n on e l e c t o r a l outcome i n Canada during the period i n question. A more d i r e c t comparison between the e f f e c t s of d i s t r i c t magnitude and geographical d i s t r i b u t i o n of partisan support on e l e c t o r a l outcomes i n Canada i s possible, by using the Rae-Taylor f r a c t i o n a l i z a t i o n i n d e x 1 4 , the Herfindahl-Hirschman c o n c e n t r a t i o n index, Laakso and Taagepera's d e f i n i t i o n of the " e f f e c t i v e " number of p a r t i e s 1 5 , and Rein Taagepera's mathematical formula f o r the relationship between d i s t r i c t magnitude and number of e f f e c t i v e p a r t i e s 1 6 . Here we want t o compare how much of the f r a c t i o n a l i z a t i o n of the Canadian party system can be accounted f o r by d i s t r i c t magnitude, and how much must be attributed t o other factors, including regional concentration of partisan support. The reader w i l l note that, up u n t i l t h i s point, we have been interested i n p r o p o r t i o n a l i t y , and not f r a c t i o n a l i z a t i o n . However, the FPP e l e c t o r a l system i s synonymous with the two-party system. Thus, because the FPP e l e c t o r a l system i s biased i n favour of the two largest 26 p a r t i e s , the huge disp r o p o r t i o n a l i t y of e l e c t o r a l outcome that would occur i f FPP were used i n a multiparty system i s s t a t i s t i c a l l y absent i n most actual outcomes. Hence, p r i o r t o measuring the proximal e f f e c t s of d i s t r i c t magnitude on the proportionality of e l e c t o r a l outcome i n Canada at the national and regional l e v e l s between 1953 and 1965, we f i r s t want t o measure t h e d i s t a l e f f e c t s o f d i s t r i c t magnitude on t h e f r a c t i o n a l i z a t i o n of the Canadian party system. This should enable us to see t h e l i n k , i n mathematical terms, between d i s t r i c t magnitude, geographical d i s t r i b u t i o n of partisan support, and proportionality, while bypassing • the r e c i p r o c a l relationship between the e l e c t o r a l system and the party system. F i r s t , we have t o determine the Herfir*iaM-Hirschman concentration index (HH), which i s calculated by adding the squares of the vote shares f o r each party; HH = (Party l ' s vote share) 2 + ... + (Party n's vote share)' 6. For example, i f there are four parties, with the vote shares i n proporations of 40%, 30%, 20%, and 10%, then HH = (.4) 2 + (.3) 2 + (.2) 2 + ( . l ) 2 = .3. Next, we calculate the " e f f e c t i v e " number of p a r t i e s , N, using the formula N = 1/HH. In the above example, the e f f e c t i v e number of parties would be 1/.3 = 3.33. Taagepera has also devised a formula f o r c a l c u l a t i n g the relationship between the e f f e c t i v e number of p a r t i e s and d i s t r i c t magnitude (M), where N = 1.25 (2 + log M). The Rae-Taylor f r a c t i o n a l i z a t i o n index, F, can then be calculated using the formula 1-1/N. 27 According t o calculations done by Rae f o r the period 1945-65, Canada's party system had a f r a c t i o n a l i z a t i o n of 0.66 1 7. By comparison, Taagepera's formula predicts that f o r a d i s t r i c t magnitude of one, f r a c t i o n a l i z a t i o n would equal 1-1/2.5 = 0.60; and f o r a d i s t r i c t magnitude of two, f r a c t i o n a l i z a t i o n would equal 1-1/2.9 = 0.655. From t h i s we can i n f e r t h a t d i s t r i c t magnitude alone does not explain Canada's party system. Taagepera's formula f o r the r e l a t i o n s h i p between d i s t r i c t magnitude and number of e f f e c t i v e parties predicted a two party system f o r Canada. Yet, according t o Laakso and Taagepera's d e f i n i t i o n , Canada has 1/.33 = three e f f e c t i v e parties. Taagepera and Bernard Grofman explain t h i s difference by concluding that the number of parties i s a function of d i s t r i c t magnitude and of the number of p o l i t i c a l l y s a l i e n t i s s u e s 1 8 . I t was argued e a r l i e r that Canadian p o l i t i c a l p a r t i e s vary i n the concentration or d i f f u s i o n of t h e i r regional partisan support. I t has also been argued that the FPP system ( d i s t r i c t magnitude of one) magnifies the r e g i o n a l d i f f e r e n c e s i n p a r t i s a n support between p a r t i e s , when t r a n s l a t e d from the l e v e l o f the e l e c t o r a t e t o the l e v e l of the l e g i s l a t u r e ; t h i s i s the ''mechanical'' e f f e c t of FPP. There i s also a "psychological" e f f e c t of FPP. As noted by Johnston and Ballantyne, the denial of a party's proportionate share of seats i n a region can lead t o a ''cumulative and s e l f - r e i n f o r c i n g " c y c l e 1 9 . Maurice Duverger describes 28 this psycholcgical effect of FPP as follows: In cases where there are three parties operating under the [FPP] system, the electors soon realize that their votes are wasted i f they continue to give them to the t h i r d party: whence their natural tendency to transfer their vote to the less e v i l of i t s two adversaries i n order to prevent the success of the greater e v i l . 2 0 This factor i s alternatively referred to as a wasted vote, a s p l i t vote, or strategic voting. In any case, support for the t h i r d party continues to decline with each subsequent election u n t i l eventually the "third" party i s relegated to the status of a "fringe" party. In Canada the mechanical and psychological effects of FPP operate on a regional basis. The two most important issue dimensions i n Canada at the national level, the ecx>nomy and ethnicity, both have regional bases. Thus, unless two national parties both have identical policy platforms, they w i l l have to build their planks i n different regions. Consequently, i f a t h i r d party i s established that appeals to the interests of a particular region, then under an FPP system, one of the two original parties, i e . , the one whose platform represents the opposing interests of another region, w i l l eventually become a marginal party i n that region. In other words, d i s t r i c t magnitude can have a long-term effect an the regional d i s t r i b u t i o n of partisan support, the number of effective parties, and the number of salient issues.. We are now at the point where we can be confident i n making an inventory of relevant variables; however, we must s t i l l use caution regarding the correlation and causation amongst these variables. 29 F i r s t , we are on s o l i d ground when we deal with the t r a n s l a t i o n of votes i n t o seats: there i s a s t r i c t l y mechanical e f f e c t between the t r a n s l a t i o n of votes i n t o seats, with p a r t i e s ' seat shares being a function of t h e i r vote shares. However, t h i s i s not a simple b i v a r i a t e r e l a t i o n s h i p ; the propor t i o n a l i t y of votes t o seats i s a function of d i s t r i c t magnitude, the geographical d i s t r i b u t i o n of partisan support 2 1, and the number of p a r t i e s . The aforementioned series of examples i l l u s t r a t e s how d i s t r i c t magnitude, party d i s t r i b u t i o n of votes, and number of p a r t i e s a f f e c t the proportionality of e l e c t o r a l outcomes. By i n c r e a s i n g the number and broadening the range o f e m p i r i c a l and hypothetical examples, we could express t h i s multivariate r e l a t i o n s h i p i n the form of a three-predictor l i n e a r equation. At t h i s point, then, we have a f o u r - v a r i a b l e c a u s a l model; where the dependent variable, proportionality, changes acxxjrding t o changes i n the values of the three independent variables. We thus have a triple-cause caused model. But we also have a t r i p l e - e f f e c t causal model; i n addition t o proportionality, d i s t r i c t magnitude also a f f e c t s how many e f f e c t i v e parties there w i l l be, and how concentrated regional partisan support w i l l be. The number of e f f e c t i v e parties i s a function of d i s t r i c t magnitude and the number of issue dimensions. The geographical d i s t r i b u t i o n of partisan support i s a function of d i s t r i c t magnitude and other p o l i t i c a l variables, such as federalism, and sccic>-econamic variables, such as e t h n i c i t y and economic geography. 3 0 However, the e f f e c t s of d i s t r i c t magnitude on the number of p a r t i e s and on r e g i o n a l cxxicentration of partisan support are more psychological than mechanical. Consequently, these e f f e c t s of d i s t r i c t magnitude would have t o be measured using a time-series study, with d i f f e r e n t assumptions and interpretations from those used i n t h i s study. In other words, i n the analysis of our data we w i l l only be measuring the short-term and not the long-term effects of d i s t r i c t magnitude on the Canadian p o l i t i c a l system. More s p e c i f i c a l l y , we w i l l be measuring the short-term e f f e c t of d i s t r i c t magnitude on the bias i n favour of a large, d i f f u s e party. This bias depends on hew much a loss of seats by a party i n a region where i t i s overrepresented i s compensated f o r by a gain of seats i n another region where i t i s underrepresented, when d i s t r i c t magnitude i s increased. At the same time, no a p r i o r i assumptions w i l l be made r e g a r d i n g t h e l o n g - t e r m e f f e c t s o f d i s t r i c t magnitude on p r o p o r t i o n a l i t y through the intervening variables of number of parties and d i s t r i b u t i o n of support. The Ctoiectives of t h i s Study Our objectives i n constructing an alternative e l e c t o r a l system are as follows: F i r s t , we want to increase d i s t r i c t magnitude, while at the same time maintaining or increasing the bias i n favour of a large party. We know a p r i o r i that large parties generally have a larger swing r a t i o than small p a r t i e s , and that the more d i f f u s e support i s f o r a large p a r t y , the larger the swing r a t i o . We also know that as d i s t r i c t magnitude increases, the swing r a t i o f o r large parties tends t o decrease. 31 In order f o r the bias i n favour of a large party not t o decrease, therefore, the degree of d i f f u s i o n of i t s support must have a stronger e f f e c t than i t s s i z e ; that i s , i f d i f f u s i o n of party support causes the bias i n favour of a large d i f f u s e party t o increase, while i t s s i z e w i l l tend t o make the bias decrease, when d i s t r i c t magnitude i s increased, which change i s more important? Since the importance of d i s t r i b u t i o n of partisan support decreases as d i s t r i c t magnitude increases, t h i s question i s only relevant f o r small d i s t r i c t magnitudes. Second, we want t o increase the multiregional representation of a large party. Since the geographical d i s t r i b u t i o n of partisan support i s p a r a l l e l t o the regional d i s t r i b u t i o n of partisan support, i t i s obvious that i t i s impossible t o f u l f i l l the f i r s t of our objectives without simultaneously f u l f i l l i n g our second objective. Thus, we w i l l be looking t o increase the bias i n favour of, and the multiregional representation of a large d i f f u s e Canadian p o l i t i c a l party by increasing the d i s t r i c t magnitude from one to two or from one to three. I f the r e s u l t s are p o s i t i v e , we w i l l proceed to argue that the respective e l e c t o r a l system i s preferable t o a l l others, including FPP, w i t h i n the s i t u a t i o n a l context of Canadian p o l i t i c s . 32 CHAPTER 3 METHODOIDGY Collection of Data Canadian federal election results for the period 1953 to 1965 were obtained from a computer tape compiled by Donald E. Blake 2 2. Each case contained the constituency number, the province of the constituency, voter turnout i n the constituency, the votes obtained by each candidate, the election year, and the total v a l i d votes cast. These data are also published by Howard A. Scarrow, Canada Votes (New Orleans: 1963) 2 3, for the 1953 to 1962 elections, and by the Report of the Chief Electoral  Officer for the 1963 and 1965 el e c t i o n s 2 4 . In order t o create hypothetical multiple-seat constituencies, contiguous constituencies have to be added together. Since the data are originally i n alphabetical order, new multiple-seat constituencies cannot be created simply by adding adjacent cases i n the original data set. Consequently, the original data set has been re-ordered such that the cases are i n sets of six, where within each set adjacent cases represent constituencies contiguous with one another. Unless the data set i s again re-ordered into smaller or larger sets, we are l e f t with the options of d i v i d i n g the sets i n t o subsets of one, two, three, or six-seat constituencies. We can also divide the data set on a province-by-province 33 basis. In order t o re-arrange the data set i n t o subsets of contiguous c o n s t i t u e n c i e s , reference was made t o Federal E l e c t o r a l D i s t r i c t Maps 2 5. The d e c i s i o n as t o which constituencies should be added together was based on several geographical c r i t e r i a . Foremost was adherence t o within-province subsets. Whenever subsets had t o cross p r o v i n c i a l boundaries, the northernmost c o n s t i t u e n c i e s were used. Otherwise, s t a r t i n g from one corner of each province, constituencies were added t o w i t h i n - p r o v i n c e constituencies adjacent t o them. In New Brunswick, subsets were created along l i n g u i s t i c l i n e s . In a l l other cases, the next c r i t e r i a f o r adding constituencies were physiographic and rural-urban d i v i s i o n s . Metropolitan areas and r u r a l areas were arranged i n t o separate subsets wherever possible. Where r u r a l areas had to be joined separately, c l i m a t i c differences, and physical b a r r i e r s , such as mountains and bodies of water, were used as d i v i d i n g l i n e s . As was mentioned e a r l i e r , the 1958 e l e c t i o n data are not included. There are several related reasons f o r deciding that the 1958 e l e c t i o n should be treated as an anomaly. F i r s t , the Conservative party d i d not need the FPP system to help i t form a majority government by t r a n s l a t i n g a minority of votes into an a r t i f i c i a l majority of seats; the Conservatives won a majority of the votes. Second, the 1958 e l e c t i o n d i d not r e s u l t i n a s i t u a t i o n where the government party was s i g n i f i c a n t l y underrepresented i n one or more regions; the Conservatives were the largest party i n every region. 34 Also, we expect the mean of our sample set f o r Conservative vote shares t o deviate from the population mean (the population equals a l l national elections from approximately 1935 t o the present). However, the r e s u l t s of the 1958 elect i o n would skew the d i s t r i b u t i o n of in d i v i d u a l r e s u l t s w i t h i n the small sample set s i g n i f i c a n t l y more than they would the d i s t r i b u t i o n of the population. I f we include the r e s u l t s of the 1958 ele c t i o n , the population mean equals 34.27. I f we exclude 1958, i t equals 32.86. In contrast, i f we include 1958 i n our sample, the sample mean equals 37.67, while i f we exclude 1958, i t equals 34.4. For the province of Quebec, the skewing of the population mean versus the skewing of the sample mean by the 1958 elect i o n r e s u l t s i s even more s i g n i f i c a n t than that on a national scale. By emitting the 1958 ele c t i o n , therefore, we s i g n i f i c a n t l y decrease the standard error of the mean of our sample set. C l a s s i f i c a t i o n of Data We are now i n a posi t i o n t o begin creating hypothetical outcomes f o r the 1953, 1957, 1962, 1963 and 1965 national elections. F i r s t , i n order t o create ocjnstituencies with a d i s t r i c t magnitude of two, the t o t a l v a l i d votes cast are added together i n sets of two adjacent cases. Then we calc u l a t e what f r a c t i o n of the new t o t a l i s contained i n each case. For example, i f there were 40,000 t o t a l v a l i d votes cast i n one case, and 60,000 i n the adjacent case, then one case would contain 40,000/(40,000 + 60,000) = .4 of the t o t a l v a l i d votes cast i n the constituency of d i s t r i c t magnitude two. Next, the percent of t o t a l votes each party obtained i n each case are calculated by d i v i d i n g the votes obtained by each party by 35 the t o t a l v a l i d votes cast. Then each party's share of the to t a l vote for the new constituency of d i s t r i c t roagrdtude two can be calculated, by multiplying the percent of total votes each party obtained i n each case by each case's fraction of the new total of v a l i d votes cast, and adding the two. For example, i f the Liberal party received 50 percent of the vote i n one case and 30 percent i n the adjacent case, and fractions of v a l i d votes were the same as i n the above example, then the Liberal party would obtain (.4 X 50%) + (.6 X 30%) = (.2 + .18) = 38 percent of the vote. We then calculate the hypothetical outcome using the Droop quota, which for d i s t r i c t magnitude of two i s 33.4 percent. In the above example, for instance, the Liberal party would be rewarded one of the two seats. A problem occurs i n our calculations when we add -two contiguous constituencies where a party runs a candidate i n one of the two cases but not i n the other case. This situation occurred most often i n Quebec, where the Conservatives and NDP f a i l e d to run a candidate on several occasions. Where a party received less than 5 percent of the votes i n the constituency where i t did run, i t was assumed that had that party run a candidate i n the constituency adjacent to i t , i t would have received a similarly low vote share, and thus would not have affected the allocation of seats. Where a party received more than 5 percent of the votes i n the constituency where i t did run, i t becomes less certain what would have happened, had i t run a candidate i n the adjacent constituency. Under such circumstances, there i s l i t t l e choice but to treat these cases as single-seat constituencies, omit them from the results, and to assume that this inconsistency does not significantly skew our results. 36 To create hypothetical constituencies and hypothetical outcomes f o r d i s t r i c t magnitudes of three, we follow b a s i c a l l y the same method of calculations as we d i d f o r d i s t r i c t magnitudes of two. F i r s t , the v a l i d votes of each case are divided by the sum of the v a l i d votes f o r a l l three cases. Then we multiply these three values by the percent of votes each party obtained i n each respective case, and add the three. For example, i f the number of v a l i d votes i n three adjacent cases were indentical, a l l three fractions would be .33. So i f the L i b e r a l party received 50% of the vote i n one case, 40% i n another, and 30% i n the t h i r d case, then the L i b e r a l party would obtain (.33 X 50%) + (.33 X 40%) + (.33 X 30%) = 40 percent of the vote i n the constituency of d i s t r i c t magnitude three. The Droop quota f o r d i s t r i c t magnitude of three i s (l/# seats + 1) *100 = 25 percent. In the above example, t h i s would r e s u l t i n the Li b e r a l party being awarded one of the three available seats on the basis of a quota, and being l e f t with a remainder of 15 percent. The same method of calculations i s used to determine each party's share of the vote i n hypothetical constituencies of d i s t r i c t magnitude s i x as was used f o r that of d i s t r i c t magnitude two and d i s t r i c t magnitude three. Each party's seat share f o r d i s t r i c t magnitude of s i x i s allocated using a Droop quota of (1/7) *100 = 14.3. The same method of calculations can also be used to determine each party's vote share and seat share i n regional constituencies, f o r example, province-wide constituencies. 37 In order t o calculate what the e l e c t i o n outcomes would have been i f d i s t r i c t magnitudes of two, three, s i x or province-wide had been used i n the 1953, 1957, 1962, 1963 or 1965 elections, c e t e r i s paribus, the seats won by each party using the above method were counted. Appendix A shows the percentage of the vote won by each party i n each e l e c t i o n , and the percentage of seats won by each party using d i s t r i c t magnitudes of one (FPP), two, three, s i x and province-wide. 38 0 CHAPTER 4 ANALYSIS OF NATIONAL DATA Results o f the 1953 E l e c t i o n Looking f i r s t at r e s u l t s an a nation-wide scale, and beginning with the 1953 e l e c t i o n , we see from Table 4.2 that the Lib e r a l s won a majority of the seats with only a minority of the votes. Meanwhile, the Conservatives received a f a r smaller percentage of seats than of votes. At the r i s k of side-tracking from the main issue at hand, i t i s worth n o t i n g t h a t C a i r n s " a r b i t r a r i l y " d e f i n e s an "e f f e c t i v e opposition" necessary t o a working parliamentary system as at le a s t one-third of the seats i n the l e g i s l a t u r e 2 6 . In the 1953 el e c t i o n , a l l the opposition parties combined received j u s t over a t h i r d of the seats. Or, t o look at the outcome another way, the Conservatives received l e s s than orie—quarter of the L i b e r a l and Conservative seats combined. Thus, when changes i n the p a r t i e s ' seat shares are observed f o r increased d i s t r i c t magnitudes applied t o the 1953 e l e c t i o n , we should look f o r d i s t r i c t magnitudes that preserve the L i b e r a l party's seats majority, but that also produces a more ef f e c t i v e opposition. We see from Table 4.1 that f o r a d i s t r i c t magnitude of two, the Lib e r a l s gain a majority of seats. Although not as sizeable a majority of seats as they received when FPP was used, i t i s s u f f i c i e n t l y large that a handful of defections or resignations would not r e s u l t i n the L i b e r a l 39 gcjvernment losing a vote of non-oonfidence. In addition, not only do the Liberals continue to win a majority of seats with a minority of votes when district magnitude is increased from one to two, but the Conservatives are no longer relegated to the status of a small party. TABLE 4.1: Liberal Vote Snares and Seat Shares EMI = Actual Liberal seats DM2 = Liberal seats using district magnitude of 2 DM3 = Liberal " " ••' " •• of 3 DM6 = Liberal " " " " " of 6 DM-province = Liberal " " province-wide constituencies Votes = Liberal votes Year DM1 DM2 DM3 DM6 DM-Province Votes 1953 64.5 56.4 54.2 49.6 50.0 49.0 1957 39.6 48.9 42.8 42.6 42.9 41.0 1962 37.7 43.6 37.5 37.3 36.7 37.0 1963 48.7 49.6 45.5 43.2 41.8 42.0 1965 49.4 46.2 44.7 39.8 40.6 40.0 When district magnitude is increased to three, the results are basically the same as those for district magnitude of two. However, when district magnitude is increased to six, the Liberals no longer win a majority of seats. Also worth noting is that the Conservatives pass the threshold from receiving a smaller share to a larger share of seats than 40 the share of votes they received; however, t h i s outcome i s made le s s s i g n i f i c a n t by the fa c t that the CCF and Social Credit p a r t i e s also passed the threshold. The 1957 Election When we look at the re s u l t s of the 1957 el e c t i o n , we see that the L i b e r a l s r e c e i v e d a l a r g e r share o f the popular v o t e than the Conservatives, but that the FPP system awarded the Conservatives more seats. As a r e s u l t , the Conservatives, the second-largest party i n terms of voter support, were able t o form a minority government. When the d i s t r i c t magnitude i s increased t o two, the e l e c t i o n outcome i s much d i f f e r e n t . Not only do the Liberals gain more seats than votes, and not only do they gain more seats than the Conservatives, but with a vote share of 41 percent they come within one percent of receiving a majority of the seats. From the point of view of obtaining our objective of awarding the largest party at le a s t as many seats as i t received under FPP, t h i s r e s u l t i s spectacular; but i s i t anomalous wit h i n our data set? Before going on t o compare t h i s r e s u l t t o that of l a t e r e lections, l e t us f i r s t continue t o look at the 1957 el e c t i o n outcomes. When d i s t r i c t magnitude i s increased t o three, the relationship between votes and seats approaches complete proportionality. Hence, at d i s t r i c t magnitude of three or higher, there i s l i t t l e l i k e l i h o o d that a large 41 party w i l l have a subst a n t i a l l y larger seat share than vote share; that i s , a d i s t r i c t magnitude of three, i f used i n the 1957 el e c t i o n , would not have s i g n i f i c a n t l y favoured e i t h e r large party. When d i s t r i c t magnitude i s increased from three t o s i x , and from s i x t o province-wide, there i s only a 0.3 percent v a r i a t i o n i n L i b e r a l seat share. This r e s u l t indicates that an increase i n d i s t r i c t magnitude beyond three does not r e s u l t i n an increase i n proportionality. Based on the hypothetical outcomes f o r the 1957 e l e c t i o n , then, we w i l l be looking f o r the following patterns i n the next e l e c t i o n we look at, 1962. When d i s t r i c t magnitude i s increased from one t o two, the L i b e r a l s ' s e a t share increases while the Conservatives' seat share decreases; when d i s t r i c t magnitude i s increased from two t o three, the el e c t o r a l system i s not biased i n favour of the two large p a r t i e s ; an increase i n d i s t r i c t magnitude beyond three does not r e s u l t i n any change i n L i b e r a l seat share. The 1962 E l e c t i o n In the 1962 ele c t i o n , both the Liberals and the Conservatives received 37 percent of the votes. Yet the FPP system awarded the Conservatives s i x percent more seats; consequently, the Conservatives, as i n 1957, formed a minority government. When d i s t r i c t magnitude i s increased from one t o two, however, the roles are reversed, and the Lib e r a l s are awarded three percent more seats. What the r e s u l t s of the 42 1957 and 1962 elections seem t o suggest, then, i s that when the two large p a r t i e s are of equal s i z e , FPP i s biased i n favour of the party with more regi o n a l l y cxancentrated support, while a d i s t r i c t magnitude of two would be biased i n favour of the party with more d i f f u s e support. When the d i s t r i c t magnitude i s increased from two t o three, the L i b e r a l seat share drops down t o what i t was under FPP, which i s approximately an equal proportion of votes t o seats. The Conservative seat share, on the other hand, goes back up again. This i s the only e l e c t i o n i n the sample set i n which the L i b e r a l vote share was not greater than the Conservative vote share, so i t i s d i f f i c u l t t o base any conclusions on t h i s outcome; but i t does appear as though increasing the d i s t r i c t magnitude from two to three may increase the bias i n favour of a large concentrated party. F i n a l l y , as was the case f o r the 1957 ele c t i o n , when d i s t r i c t magnitude i s increased beyond three, the L i b e r a l seat share remains unchanged. The 1963 Election The r e s u l t s of the 1963 e l e c t i o n are notably d i f f e r e n t from those of 1953 and also from those of 1957 and 1962. 1953 was the l a s t e l e c t i o n i n which the L i b e r a l party received more than 45 percent of the vote. In the other four elections i n the sample set, the Liberals averaged 40 percent of the vote. P r i o r t o 1957, and between 1963 and 1984, the 43 Conservatives received vote shares i n the lower 30 percent range. Thus, i n the 1963 el e c t i o n , the Conservatives returned t o a vote share i n the lower 30's and the Liberals s h i f t e d t o a new vote range i n the lower 40's. With the Lib e r a l s only receiving 42 percent of the vote i n the 1963 elec t i o n , i t would have been d i f f i c u l t f o r the FPP e l e c t o r a l system to manufacture an a r t i f i c i a l majority of seats. However, because the Conservatives 1 voter support dropped t o 33 percent, the cxancentration of Conservative party voter support was unable t o compensate f o r i t s lack of si z e . Consequently, whereas the Li b e r a l s received 41 percent of the vote i n 1957, but received fewer seats than votes, i n 1963 they received 42 percent of the vote and came with i n 1.3 percent of a majority of the seats. When the d i s t r i c t magnitude i s increased from one t o two, the bias i n favour of the Liberals i s increased, so that they are within 0.4 percent of a majority of the seats. Of the four elections we have looked at t o t h i s point, the L i b e r a l seat share increased, when the d i s t r i c t magnitude was increased t o two, i n three of the four cases. The only exception was 1953, when i n c r e a s i n g the d i s t r i c t magnitude t o two transformed an undesirable landslide L i b e r a l v i c t o r y i n t o a comfortable majority. I t thus appears from these r e s u l t s that the swing r a t i o f o r the Li b e r a l party i s much larger f o r FPP than f o r a d i s t r i c t magnitude of two, and that the d i s t r i c t magnitude of two i s biased i n favour of the L i b e r a l party at a lower vote percentage than FPP i s . This means that a d i s t r i c t magnitude of two tends to award the L i b e r a l party a majority of seats at a 44 lower vote snare than does FPP, while FPP begins awarding exorbitantly more seats t o the Liberals than does d i s t r i c t magnitude of two only when such seats are superfluous and an impediment t o a working parliamentary system. Also, under FPP the threshold i s 40 percent of the vote share; anywhere below t h i s and the chances of the Libe r a l s forming even a minority government appear remote. On the other hand, when d i s t r i c t magnitude of two i s used, the threshold f o r the L i b e r a l party i s probably below 30 percent, and the L i b e r a l s are l i k e l y t o form a minority government with as l i t t l e as 35 percent of the vote. When the d i s t r i c t magnitude i s increased from two t o three f o r the 1963 e l e c t i o n , f o r the fourth consecutive case L i b e r a l seats decrease while Conservative seats increase. F i n a l l y , when d i s t r i c t magnitude i s increased from three t o s i x , and from s i x t o province-wide, both L i b e r a l and Conservative seat shares decrease as d i s t r i c t magnitude increases, u n t i l t h e i r seat shares are proportional t o t h e i r vote shares. The pattern so f a r , then, i s f o r FPP t o be biased i n favour of the Conservatives moreso than the Li b e r a l s , while d i s t r i c t magnitude of two s h i f t s the lar g e r bias t o the L i b e r a l party. When d i s t r i c t magnitude i s increased from two t o three, however, the larger bias s h i f t s back to the Conservative party; but both large p a r t i e s ' biases become smaller, as the increased d i s t r i c t magnitude i s less biased against small part i e s . Also, the r a t i o of seat shares t o vote shares approaches proportionality at d i s t r i c t magnitude of s i x . 45 The 1965 E l e c t i o n In the l a s t e l e c t i o n i n the sample set, 1965, the Li b e r a l s , with 40 percent of the vote, came with i n 0.6 percent of a majority of the seats; thus, the FPP e l e c t o r a l system was almost able t o manufacture an a r t i f i c i a l majority of seats out of a minority of votes. However, the L i b e r a l s had t o s e t t l e f o r another minority government. When d i s t r i c t magnitude i s increased from one t o two, the L i b e r a l party's seat share decreases from 49.4 t o 46.2 percent. Based on our c r i t e r i a that an a l t e r n a t i v e e l e c t o r a l system should award the largest party a t l e a s t as many seats as does FPP (at least u n t i l i t has a majority of the seats), t h i s i s the only case i n our set where d i s t r i c t magnitude of two has f a i l e d . However, under a d i s t r i c t magnitude of two, the Li b e r a l s s t i l l won more seats than the second and t h i r d largest p a r ties combined, even though these two parties together received a majority of the v o t e s . Thus, the Liberals would s t i l l have formed a minority government. When d i s t r i c t magnitude i s increased from two t o three, both large p a r t i e s ' seat shares decreased. This i s because the t h i r d largest party, the New Democratic Party (NDP), had continued to grow i n voter support, u n t i l by 1965 i t received 18 percent of the vote share. As a r e s u l t , the number of e f f e c t i v e p a r t i e s began t o be a more s i g n i f i c a n t variable a f f e c t i n g the p r o p o r t i o n a l i t y of e l e c t o r a l cuteame; which means the geographical d i s t r i b u t i o n of partisan support would have l e s s of an e f f e c t , a t l e a s t f o r larger d i s t r i c t magnitudes. 46 Effects of D i s t r i c t Maojrirude can T . i i w a l Seat Shares Figure 4.1 shows the r e l a t i o n between L i b e r a l votes and seats f o r the 1953, 1957, 1962, 1963 and 1965 elections f o r d i s t r i c t nagnitudes of one (FPP), two, three, s i x and province-^wide. As the figure i l l u s t r a t e s , the slope (regression coefficient) f o r the l i n e a r equation r e l a t i n g L i b e r a l votes t o L i b e r a l seats i s steeper f o r FPP than f o r d i s t r i c t magnitude of two. Meanwhile, the intercept (regression constant) of FPP i s much smaller. However, when d i s t r i c t magnitude i s increased from two to three, the slope increases again and the intercept decreases again. This would seem to indicate that the geographical d i s t r i b u t i o n of voter support f o r the L i b e r a l party s t i l l has a s i g n i f i c a n t e f f e c t on the t r a n s l a t i o n of votes i n t o seats at a d i s t r i c t magnitude of three. The l i n e passing a t a 45 degree angle through the o r i g i n i n Figure 4.1 re p r e s e n t s an equality between votes and seats. I t s slope i s therefore 1.0 and i t s intercept i s zero. I f we translate t h i s into the terminology we have been using so f a r , a party with a r e l a t i o n of votes t o seats the same as t h i s l i n e would have a swing r a t i o of 1.0 and a zero bias f o r a l l values of votes: This i s almost the s i t u a t i o n f o r the L i b e r a l p a r t y when d i s t r i c t magnitude i s increased t o s i x or province-^wide. Figure 4.2 shows the r e l a t i o n between L i b e r a l votes and seats f o r the 1953, 1957, 1962, 1963 and 1965 elections f o r a d i s t r i c t magnitude of two, and between 1935 and 1980 f o r FPP. (Note: the data f o r t h i s figure 47 are revealed below i n Table 4.2) There are three horizontal l i n e s on the graph. The l i n e a t seats = 41% represents the smallest seat share any party has ever received and s t i l l managed t o form a minority government. The l i n e at seats = 50% represents the miriimum number of seats necessary t o form a majority government. The l i n e at seats = 66% represents the maximum number of seats held by a government party before problems such as the lack of an e f f e c t i v e opposition and the overabundance of unruly government backbenchers begin t o h i n d e r the w o r k a b i l i t y o f the parliamentary system. Table 4.2: LIBERAL VOTES AND SEATS FOR DM2 and FPP Year L i b e r a l Seats (%) Li b e r a l Votes (%) Li b e r a l Seats 1935 71 45 -1940 74 51 -1945 51 41 -1949 74 49 -1953 65 49 56 1957 40 41 49 1958 18 34 -1962 38 37 44 1963 49 42 50 1965 49 40 46 1968 59 45 -1972 41 38 -1974 53 43 -1979 40 40 -1980 52 44 49 FIGURE 4.x L I B E R A L S E A T S H A R E S U S I N Q F P P A N D D M 2 1 o __ H 1 1 1 1 1 1 1 0 2 0 3 0 4 0 5 0 6 0 7 0 V O T E S ( % ) Recalling that our primary objective i s t o increase the multiregional representation of a large d i f f u s e party without decreasing i t s t o t a l number of seats, Figure 4.2 has several implications, a l l of which can be interpreted as p o s i t i v e . F i r s t , regarding FPP's tendency to manufacture a majority of seats out of a minority of votes, we see that both FPP and a d i s t r i c t magnitude of two (DM2) produce a majority of seats with between 42 and 43 percent of votes. IjDok±ng next at minority governments, the reader w i l l r e c a l l that i n two of the elections i n our sample set the Conservatives formed minority governments, even though the Liberals received more votes. In contrast, i f we compare FPP to DM2 we see that whereas the L i b e r a l s need on average 40 percent of votes i f they wish t o form a minority government under FPP, they would need only 34 percent under DM2. In other words, i f a large d i f f u s e party f a l l s short of forming a majority government, i t stands a f a r better chance of at l e a s t forming a minority government i f DM2 i s used, then i f FPP i s used. In our sample set, f o r example, the L i b e r a l s would have formed minority governments i n the 1957 and 1962 elections i f DM2 had been used. We see from Figure 4.2 that once the Liberals get over 50 percent of the seats, they begin receiving more seats per vote under FPP than under DM2. However, t h i s does not mean that a large d i f f u s e party with more than approximately 42 percent of votes would necessarily prefer FPP t o DM2. Certainly a government would not want t o be i n the precarious p o s i t i o n of having t h e i r majority l o s t i f one or two of t h e i r seats i n the 51 l e g i s l a t u r e were somehow l o s t . Both FPP and DM2 produce a comfortable margin of extra seats a t 44 percent of votes; hence, i t i s only at between 42 percent and 44 percent of votes that the Liberals would encounter an uncomfortably s l i m majority of seats under DM2. Cn the other hand, once the Lib e r a l s gain more than approximately 47 percent of the votes, under FPP they receive so many seats that t h e i r lopsided v i c t o r y begins t o act t o the detriment of themselves and the parliamentary system. Regarding the problems incurred by a government with an extraordinary majority, the prime minister i s unable t o reward everyone i n the government caucus with positions of r e s p o n s i b i l i t y . The i d l e baddoenchers then become re s t l e s s backbenchers. Also, the larger the caucus, the more increased i s the l i k e l i h o o d of disagreement of opinion. The most l i k e l y outcome i s f o r the cabinet t o f i n d the most formidable opposition t o same of i t s p o l i c i e s coming from a group of disaffected backbenchers w i t h i n i t s own caucus. At the same time, the a b i l i t y of the opposition party or pa r t i e s t o e f f e c t i v e l y f u l f i l l t h e i r function of constructively c r i t i c i z i n g government p o l i c i e s i s seriously hindered by a shortage of personnel. F i n a l l y , when we look at Figure 4.2, we see that there are several occasions when the number of seats won by the Liberals under FPP was much greater or le s s than that predicted by the l i n e a r equation. Hence, i f the Libe r a l s were deciding whether or not t o c a l l an election based on t h e i r popularity amongst decided voters, they would have t o be highly uncertain about how many seats those votes would translate into, i f FPP were used. For example, there i s one occasion where the Liberals, with 41 percent of 52 the vote, were unable t o win enough seats t o form a itiinority government; meanwhile, on another occasion 41 percent of the vote was enough f o r the Li b e r a l s t o win a majority of the seats. In contrast, f o r the f i v e elections i n the sample set, there i s less than one percent variance between actual outcomes, i n terms of the Li b e r a l seats, and the outcomes predicted by the l i n e a r equation f o r DM2. Effects of D i s t r i c t Magnitudes on Conservative Seat Shares Before looking at the regional breakdown of L i b e r a l support, we should f i r s t observe the ef f e c t s of increased d i s t r i c t magnitude on the Conservative party's t o t a l seat share. Figure 4.3 shows the r e l a t i o n between Conservative votes and seats f o r the 1953, 1957, 1962, 1963 and 1965 elections f o r d i s t r i c t magnitudes of one (FPP), two (DM2), three, s i x and province-wide. Conservative seat shares f o r 1935 t o 1980 are also shown and are represented by the scatterplot diagram i n Figure 3.1. (The data f o r Figure 4.3 are l i s t e d i n Table 4.3) The pattern f o r the t r a n s l a t i o n of votes i n t o seats f o r the Conservative party when d i s t r i c t magnitude i s increased from one t o two and from two t o three i s b a s i c a l l y the same as f o r the L i b e r a l party. The slope f o r FPP i s steeper than f o r DM2, while the intercept f o r FPP i s smaller than f o r DM2. When d i s t r i c t magnitude i s increased from two t o three, the slope increases again and the intercept decreases again, j u s t as i t does f o r the Lib e r a l s . However, while the slopes f o r the Liberals and Conservatives f o r DM2 are nearly i d e n t i c a l , the L i b e r a l party's intercept f o r DM2 i s approximately 6 53 seat-share percentages higher. This 6 percent bias in favour of the Liberals results in same fundamental differences in electoral outcomes for the two parties. Table 4.3: CONSERVATIVE VOTES AND SEATS FOR FPP, DM2 and DM3 Year Cons. Seats Cons. Votes DM2 Seats DM3 Seats 1935 16 30 _ — 1940 16 31 - -1945 27 27 - -1949 16 30 - -1953 19 31 28 28 1957 42 39 36 41 1958 78 54 - -1962 44 37 41 41 1963 36 33 33 37 1965 37 32 34 34 1968 27 31 - -1972 41 35 - -1974 36 35 - -1979 48 36 - -1980 37 33 — — 54 FIGURE 4 .3 S E A T S (%) 8 0 C O N S E R V A T I V E S E A T S H A R E S U S I N G F P P , D M 2 A N D D M 9 ( F P P result* I n c l u d * • t a c t i o n f r o m 1 S 3 S - S O ) 7 0 6 0 5 0 4 0 3 0 2 0 1 0 F P P E F F E C T I V E O P P O S I T I O N M A J O R I T Y G O V E R N M E N T M I N O R I T Y G O V E R N M E N T L E G E N D • F P P 1 0 2 0 3 0 4-0 5 0 6 0 7 0 V O T E S ( % ) The horizontal l i n e i n Figure 4.3 at seats = 41% represents the minimum seat share necessary t o form a minority government. The l i n e at 50% represents the minimum seat share necessary t o form a majority government. We see from Figure 4.3 that under FPP the Conservatives need approximately 37 percent of the vote share t o form a minority government. With a d i s t r i c t magnitude of three, they heed 39 percent, and with DM2, 41 percent. To form a m a j o r i t y government, the Conservatives need approximately 41 percent of the vote share under FPP, while a d i s t r i c t magnitude of three would require 45 percent, and with DM2 they would need 49 percent. Hence, what the Conservatives need t o form a minority government using DM2 (41 percent of the vote share) would be enough t o catapult them t o a majority government under FPP. The l i n e s of the equations f o r the r e l a t i o n between votes and seats f o r the Conservative party when FPP, DM2 and d i s t r i c t magnitude of three are used a l l cross the threshold at about 34 percent. Above the threshold, the l i n e f o r d i s t r i c t magnitude of three l i e s approximately equidistant between FPP and DM2. Thus, the decrease i n the bias i n favour of the Conservatives i s only h a l f as great when d i s t r i c t magnitude i s increased from one t o three, as when i t i s increased from one t o two. Thus, while DM2 would be the most preferred e l e c t o r a l system f o r the L i b e r a l party, the Conservatives benefit more under FPP. In terms of a l t e r i n g the outcome of an e l e c t i o n , the most important advantage t o one p a r t y over the other occurs w i t h r e s p e c t t o forming a m i n o r i t y 56 government. Under FPP, the Conservatives need approximately 37 percent of the vote share t o form a minority government, while the Lib e r a l s need approximately 39 percent. In contrast, when DM2 i s used the Lib e r a l s need approximately 34 percent of the votes to form a minority government, while the Conservatives need approximately 41 percent. 57 CHAPTER 5 ANALYSIS OF REGIONAL DATA Looking now at the regional breakdown of partisan support and e l e c t o r a l outcome, the two regions where t r a n s l a t i o n of voter support i n t o representation i n the l e g i s l a t u r e i s most skewed are Quebec and the four western-most provinces. I t i s therefore i n these two "regions" that increases i n d i s t r i c t magnitude w i l l r e s u l t i n substantial changes i n party seat shares. With respect t o the L i b e r a l party, we w i l l be looking f o r a decrease i n i t s overrepresentation i n Quebec, and an increase i n i t s representation i n the West. Hopefully, the gain of seats f o r the Lib e r a l s i n the West w i l l at least compensate f o r t h e i r l o s s of seats i n Quebec, when d i s t r i c t magnitude i s increased. The T.iherals i n the West Appendix B shews the breakdown of support f o r the L i b e r a l s i n Quebec and i n the West, and f o r the Conservatives i n Quebec. Looking f i r s t a t the Liberals i n the West, we see that i n 1953 the L i b e r a l party received a seat share equal to i t s vote share. Assuming that the FPP system has the same tendencies, with respect t o the t r a n s l a t i o n of votes i n t o seats, on a regional scale as i t does on a national scale, i t appears that the threshold i s approximately 35 percent of the votes. Just above t h i s threshold, a party begins winning 3 seat shares f o r every one percent 58 increase i n vote shares. Just below t h i s threshold, a party begins l o s i n g equally dramatic seat shares f o r every one percent decrease i n i t s vote share. In B r i t i s h Columbia, the impact of Diefenbaker on L i b e r a l voter support was short-lived. From 1962 u n t i l 1972 L i b e r a l vote shares i n B.C. rebounded t o pre-1957 l e v e l s . However, while L i b e r a l support i n the P r a i r i e provinces also rebounded i n 1962, i t never reached pre-1957 l e v e l s again. Because of the d i s t o r t i o n of votes i n t o seats by FPP, a decrease of 12 percent i n L i b e r a l voter support i n the West would be enough t o deny the Li b e r a l s any seat representation i n the national l e g i s l a t u r e . The post-1962 l e v e l of L i b e r a l voter support i n the West i s approximately 6 t o 7 percent lower than the pre-1957 l e v e l . As a r e s u l t , the Liberals were not completely wiped out i n the West, but t h e i r seat share dropped approximately 20 percent. From 1963 t o 1972, the Liberals were s t i l l a "large" party i n the West, i n terms of vote shares (approximately 30 percent). However, with only 11 percent of the seats i n the West, the Lib e r a l s were a Western "fri n g e " party, i n terms of representation i n the l e g i s l a t u r e . I f B.C., where L i b e r a l support returned t o pre-1957 l e v e l s , i s taken out of the Western equation, the h i s t o r i c l o s s of L i b e r a l voter support i n the West i s even greater. In f a c t , i t i s almost exactly the 12 percent l o s s that we predicted would completely wipe out the L i b e r a l s ; with approximately one-quarter of the vote share, they received cn average 4 percent of the seats i n the P r a i r i e s i n the 1962, 1963, and 1965 elections. 59 The biggest losers when L i b e r a l fortunes i n the P r a i r i e s declined were not the Li b e r a l s - they s t i l l formed the government. The biggest losers were the people of the P r a i r i e provinces, who were deprived of representation i n the government caucus and i n the cabinet. One of the two main objectives of t h i s study i s of course t o a l l e v i a t e t h i s problem of regional imbalance i n the national p o l i t i c a l p a r t i e s . The means of ac h i e v i n g t h i s o b j e c t i v e i s by increasing d i s t r i c t magnitude u n t i l p r o p o r t i o n a l i t y i s achieved. When proportionality i s achieved, L i b e r a l seat shares w i l l equal vote shares i n the four Western provinces, which averaged 27 percent f o r the 1957, 1962, 1963 and 1965 elections. As can be seen from Table B - l , when d i s t r i c t magnitude i s increased from one t o two, L i b e r a l seat shares increase t o 29.5 percent, a c t u a l l y exceeding t h e i r vote share. In a two-party system, t h i s would be an unexpected r e s u l t , since the quota f o r a DM2 system i s 33 .4 percent. In a two-party system, a party with 27 percent of the vote would not begin receiving seats u n t i l d i s t r i c t magnitude was increased t o three, f o r which the quota i s 25 percent. However, i n Western Canada during t h i s period there was a three-party system, and i n B.C. and Alberta there were four e f f e c t i v e p a r t i e s . As a r e s u l t , most of the seats are awarded using the largest remainder instead of the quota. When d i s t r i c t magnitude i s increased from two t o three, instead of the seats being allocated using the quota of 25 percent, with the Lib e r a l s therefore being awarded one-third of the seats, the Lib e r a l party's seat share decreases t o 26 percent. When d i s t r i c t magnitude i s 60 increased from three to s i x , the L i b e r a l seat share i s 28 percent. Hence, the L i b e r a l vote-to-seat r a t i o reaches propo r t i o n a l i t y a t d i s t r i c t magnitude of three, while t h e i r seat share a c t u a l l y exceeds t h e i r vote share under DM2. The number of seats i n Quebec and the West are unequal. Thus, i n order t o compare the gain of L i b e r a l seats i n the West t o the loss of L i b e r a l seats i n Quebec, the average number of seats gained or l o s t , and not the average percent, must be used. Under FPP, the Lib e r a l s averaged 11.4 seats i n the West. Using DM2, the Lib e r a l s average 23.6 seats. There i s therefore an average gain of 12.2 seats i n the West f o r the Libe r a l s when DM2 i s used. The L i b e r a l loss of seats i n Quebec under DM2 w i l l be calculated and compared to the gain i n the West shortly. But f i r s t we want t o go through the same sort of analysis f o r the Li b e r a l party i n Quebec as we have gone through f o r the Liberals i n the West. The Li b e r a l s i n Quebec As shewn by Table B-2, the FPP system has the same tendencies i n Quebec as i t does i n the West and on a national scale. However, the L i b e r a l party's vote share i s above 35 percent i n Quebec. So instead of the Tliberal party l o s i n g three seat shares f o r every loss of one percent i n vote shares, as i t does i n the West, i t gains three seat shares f o r every increase of one percent i n vote shares. The reader w i l l note that t h i s equation no longer applies when L i b e r a l vote shares are above 50 percent. This i s because the r e l a t i o n between votes and seats i s ac t u a l l y 61 an S-shaped curve. For the national r e s u l t s and r e s u l t s i n the West, L i b e r a l vote percentages have a l l been i n the range where the S-shaped curve can be approximated by a simple l i n e a r equation. In Quebec, however, L i b e r a l vote shares often exceed 50 percent, above which the vote-to-seat r a t i o r a p i d l y decreases; thus, a 57 percent vote share does not r e s u l t i n a 100 percent seat share. I f the tendencies of FPP and DM2 are the same i n Quebec as on a national scale, then above 42 percent of the votes the L i b e r a l s w i l l get more seats when FPP i s used, while below 42 percent they w i l l get more seats when DM2 i s used. Also, above 50 percent of the votes the swing r a t i o f o r DM2 i s again larger than that of FPP. From Table B-2 we see that i n only one of the f i v e elections d i d the Tliberals receive l e s s than 42 percent of the votes. We thus expect FPP t o reward more seats t o the Liberals i n Quebec than would DM2, i n four of the f i v e elections. In order t o consider our r e s u l t s p o s i t i v e , therefore, the Li b e r a l s must continue t o receive more seats than votes i n Quebec when DM2 i s used, and the Liberals must on average gain more seats i n the West than they lose i n Quebec when FPP i s replaced by DM2. Comparing the r e s u l t s i n Quebec using FPP and DM2, we see that i n the one e l e c t i o n where the Liberals received less than 42 percent of the vote share, they were awarded more seats by DM2 than by FPP. Also, while the L i b e r a l s received w e l l over 50 percent of the votes i n two of the elections, FPP only rewarded them with a few more seats than i t would have had they they only received 50 percent of the votes. As a r e s u l t of these 62 outcomes and the outcomes of the other two elections, the L i b e r a l s gained 1.4 seat shares f o r every vote share under FPP, and 1.2 using DM2. So the r e s u l t s are p o s i t i v e with respect t o the L i b e r a l s continuing t o receive more seats than votes i n Quebec when DM2 i s used. The Results Far the T.iherals i n Quebec and i n the West Compared In order t o compare the loss of seats by the L i b e r a l s i n Quebec when FPP i s replaced with DM2 with t h e i r gain of seats i n the West, the average number o f i n d i v i d u a l seats l o s t i n Quebec must f i r s t be calculated. Under FPP, the Liberals averaged 53.2 seats i n Quebec. Using DM2, they average 43.6. There i s therefore an average loss of 9.6 seats i n Quebec f o r the Liberals when DM2 i s used. By comparison, i t was calculated that the Liberals on average gained 12.2 seats i n the West when DM2 i s used. There i s therefore a net gain of 2.6 seats f o r the L i b e r a l s . In other words, the loss of L i b e r a l seats i n Quebec when d i s t r i c t magnitude i s increased from one t o two i s more than compensated f o r by t h e i r gain of seats i n the West. However, our objective i s not t o increase the number of seats of the more d i f f u s e l a r g e p a r t y . Our o b j e c t i v e i s to increase the multiregional representation of a large party without at the same time decreasing i t s seat t o t a l . Having attained t h i s objective by using DM2, we should turn our attention t o the other large party/ the Conservatives. 63 The Conservatives i n Quebec The geographical d i s t r i b u t i o n of support f o r the Conservatives i s a l s o q u i t e d i f f u s e . We would therefore expect that increasing the d i s t r i c t magnitude would also increase the multiregional representation of the Conservative party/ but at the expense of i t s seat t o t a l . Table B-3 shows the breakdown of support f o r the Conservatives i n Quebec i n the 1953, 1957, 1962, 1963 and 1965 elections. In the f i r s t two of these elections, 1953 and 1957, the Conservatives averaged 30 percent of the votes, but received only 8.5 percent of the seats. Thus, the p o s i t i o n of the Conservative party i n Quebec was s i m i l a r t o that of the L i b e r a l party i n the West: they were a large party i n terms of voter support, but a marginal p a r t y i n terms of representation i n the l e g i s l a t u r e . The s i t u a t i o n i n Quebec i n 1963 was d i f f e r e n t from previous elections. The S o c i a l Credit party equalled the Conservative party i n vote shares, and exceeded the Conservatives i n seats from Quebec. This three-party system altered the tendencies of the FPP e l e c t o r a l system. Where three parties competed i n a constituency, the winner no longer needed over h a l f the votes. Also, the Conservatives and S o c i a l Credit could agree not to s p l i t the ''anti-Liberal'' vote, and thus follow an e l e c t i o n s t r a t e g y whereby the t h i r d - p l a c e p a r t y i n an i n d i v i d u a l constituency would not run a candidate. As a r e s u l t , a party might run candidates i n only h a l f the r i d i n g s and receive an average of 50 percent 64 of the votes where they d i d run; however, i n the f i n a l e l e c t i o n r e s u l t s i t would appear that t h i s party only won 25 percent of the votes. This i s b a s i c a l l y the same s i t u a t i o n as the one i n our examples i l l u s t r a t i n g the e f f e c t of geographical d i s t r i b u t i o n of partisan support cn e l e c t o r a l outcomes. Aware, then, that the Conservatives may not have run candidates i n every r i d i n g , and that they may have faced one other party i n some ridings and two i n others, we can proceed with caution t o look at the outcomes i n Quebec of the 1962, 1963 and 1965 elections. In these three elections, the Conservatives averaged 23.3 of the votes, and received 13.7 percent of the seats. They thus received 7 percent fewer votes but 5 percent more seats i n t h i s period than i n 1953 and 1957. When d i s t r i c t magnitude i s increased from one t o two, therefore, the changes i n Conservative seat share are not expected t o be the same f o r the two periods. When d i s t r i c t magnitude i s increased from one t o two f o r 1953 and 1957, Conservative seat shares increase from 8.5 percent t o 23.5 percent. Over the 1962 t o 1965 period, Conservative seat shares increase from 13.7 percent t o 20 percent. The effects of FPP and the ef f e c t s of increasing d i s t r i c t magnitude are thus d i f f e r e n t f o r two-party and three-party systems. However, the tendencies are the same; increasing the d i s t r i c t magnitude r e s u l t s i n a s i g n i f i c a n t increase i n Conservative seat shares i n Quebec. Over the course of the f i v e elections i n the sample, increasing the d i s t r i c t magnitude t o two re s u l t s i n the Conservative party receiving 65 an average of 21 . 4 percent of the seats, as compared t o the 11.6 percent they received under FPP, and the 25.8 percent of the Quebec vote they r e c e i v e d . This r e s u l t i s only s l i g h t l y l e s s s i g n i f i c a n t than that regarding the Liberals i n the West. 66 CHAPTER 6 OONCLDSICNS Summary of Firriinqs In conclusion, replacing the sirgle-member constituency e l e c t o r a l system presently used i n Canada with d i s t r i c t magnitudes of two would increase the multi-regional representation of Canada's national p o l i t i c a l p a r t i e s . At the same time, DM2 would have no immediate e f f e c t on the t r a d i t i o n of single-party government. DM2 thus s a t i s f i e s both of the c r i t e r i a n e c e s s a r y f o r an e l e c t o r a l system t o complement a parliamentary-federal hybrid system of government. In addition, DM2 has other tendencies which make i t superior t o First-Past-the-Post, and to other e l e c t o r a l systems that have previously been offered as alternatives t o FPP. Regarding the f i r s t c r i t e r i o n , manufacturing a majority government f o r a party with a minority of seats, FPP and DM2 both award the L i b e r a l Party during the period of the sample with 50 percent of the seats when i t receives 42 percent of the votes. However, whereas FPP rewarded the Conservative party more seats than the Liberals i n the 1957 and 1962 elections, even though the Liberals received more votes, DM2 allocates more seats t o the Li b e r a l s . Thus, under DM2, the Libe r a l s , with more votes than the Conservatives, would have formed minority governments i n 1957 and 1962. Also, whereas the FPP el e c t o r a l system rewards a party 67 winning a majority of the votes with an extraordinary majority of the seats, DM2 tends t o award i t with a smaller, but s t i l l comfortable, majority. DM2 thus prevents parliaments lacking i n e f f e c t i v e opposition and governments burdened with unruly backbenchers. F i n a l l y , the outcomes of elections using FPP are highly uncertain, even i f the vote shares are known ahead of time. In contrast, the outcomes of elections using DM2 are more predictable. Regarding the second c r i t e r i o n , multiregional representation of national p o l i t i c a l p a r t i e s , under FPP a large d i f f u s e party which i s "large" i n terms of voter support i n a region, i s a fringe party i n terms of seats i n that region. By comparison, under DM2 a party which i s large i n terms of votes i n a region i s also large i n terms of seats. Hence, i f DM2 had been used during the period of the sample set, the L i b e r a l party would have been a large party i n Western Canada, and the Conservative party would have been a large .party i n Quebec. Psvcfxjlocrlcal E f f e c t s However, while DM2 does not have an immediate e f f e c t on the t r a d i t i o n of single-party government, i t may i n the long-term a f f e c t the number of p a r t i e s and the geographical d i s t r i b u t i o n of partisan support. According t o Taagepera' s formula, there i s a relationship between the number of e f f e c t i v e parties and d i s t r i c t magnitude, with the number of pa r t i e s increasing when d i s t r i c t magnitude increases. But there i s also a re l a t i o n s h i p between the number of parties and the number of p o l i t i c a l l y 68 s a l i e n t i s s u e s . At the same time, changes i n the geographical d i s t r i b u t i o n of partisan support may a l t e r the national p o l i t i c a l p a r t i e s ' platforms, which may i n turn a l t e r the number and types of issues that are most s a l i e n t . H i s t o r i c a l l y , and at present, the two most s a l i e n t p o l i t i c a l issue-dimensions i n Canadian p o l i t i c s are both regionally defined. Probably not coincidentally, a l l of Canada's "national" p o l i t i c a l p a r t i e s have h i s t o r i c a l l y had r e g i o n a l l y - c o n c e n t r a t e d support bases and regionally-biased p o l i c y platforms. However, even i n regions where the two largest p a r t i e s are r e l a t i v e l y weak, they are s t i l l "large" p a r t i e s i n terms of vote shares. Consequently, i f DM2 were used instead of FPP, the two largest p a r t i e s would f i n d that instead of being marginal p a r t i e s i n one or two regions, they would be large parties i n those regions. Also, i n terms of the p o l i t i c a l pay-off, instead of a party being a d i s t a n t second or t h i r d i n i n d i v i d u a l ridings when FPP i s used, under DM2 i t would f i n d i t s e l f e i t h e r winning the second seat or coming within a few vote percentages o f doing so. As a r e s u l t , instead of w r i t i n g o f f a constituency, or even an entire region, a party may a l t e r i t s campaign strategy and formulate p o l i c i e s that appeal, more t o that constituency or r e g i o n . I f vote shares and seat shares subsequently increased, cross-regional p o l i t i c a l platforms could become i n s t i t u t i o n a l i z e d . At the same time, increasing d i s t r i c t magnitude makes i t easier f o r smaller p a r t i e s t o gain a seat share proportionate t o t h e i r share of the vote. This increase i n seat a c c e s s i b i l i t y may lead t o an increase i n the number of e f f e c t i v e parties from the present number of three. In a 69 scenario where there are four or more e f f e c t i v e p a r t i e s and none has a majority of the seats, the prospect of a c o a l i t i o n cpvernment would increase. So increasing the d i s t r i c t magnitude may increase the number of p a r t i e s . But i t w i l l more l i k e l y lead t o a s i t u a t i o n where the issue dimensions that divide the two largest p a r t i e s are ones that cross-cut regional differences. Hence, the other factor that a f f e c t s the number of p a r t i e s , the number of issue dimensions, may decrease when d i s t r i c t magnitude increases. I f t h i s were t o occur, then when d i s t r i c t magnitude i s increased from one t o two, the number of e f f e c t i v e p a r t i e s may decrease from three t o two. I t i s therefore impossible t o predict what the long-term e f f e c t s of using DM2 would be. I t may lead t o a multiparty system. Or i t may lead t o a two-party system. Or the number of e f f e c t i v e p a r t i e s may remain unchanged. Al t e r n a t i v e Proposals Since Cairns* f i r s t a r t i c l e , several a l t e r n a t i v e e l e c t o r a l systems have been proposed 2 7. A l l of these proposals have included a two-tier system, under which some members of the l e g i s l a t u r e would continue t o be elected from single-member constituencies, while others would be chosen from prcr/ince-wide or nation-wide pools. Numerous objections have been made t o the two-tier system, including i t s creation of two classes of l e g i s l a t o r s . However, where i t f a i l s most i n comparison with DM2 i s i n terms of p o l i t i c a l payoff. 70 Under DM2, there i s an incentive f o r parties t o increase t h e i r appeal t o a region where t h e i r vote-share borders between that of a small and a large party; a s l i g h t increase i n voter support may r e s u l t i n a large increase i n seats. With the two-tier system, however, p a r t i e s are assured of s i g n i f i c a n t numbers of seats, even i f there i s v i r t u a l l y no e f f o r t on t h e i r part t o increase t h e i r appeal, with respect t o p o l i c i e s of concern t o a respective region. In other words, the two-tier system gives regional representation to parties that do not deserve i t , and provides no incentive f o r them t o broaden t h e i r appeal. C l a r i f i c a t i o n DM2 should not be confused with "double r i d i n g s " . Both e l e c t two representatives from one constituency; however, under DM2 each ele c t o r gets one vote, while i n double-ridings each elector gets two votes. G i v i n g e l e c t o r s more than one vote v i o l a t e s at l e a s t one important democratic p r i n c i p l e , and leads t o e n t i r e l y d i f f e r e n t r e s u l t s from those of DM2. Those who argue that electors generally vote f o r the party, and not f o r the i n d i v i d u a l candidate, usually use the e l e c t i o n r e s u l t s from double-ridings as t h e i r primary evidence. The cases abound where parties competing i n double-ridings have run one candidate whose experience and respect w i t h i n the community i s unquestioned, and another candidate whose 71 backgrcund i s more dubious. Where the margin of v i c t o r y between the second and t h i r d f i n i s h e r s i s quite large, the two winners are invariably from the same party, and only a handful of votes separate the more i l l u s t r i o u s winner from h i s l e s s distinguished running-mate. I t i s pr e c i s e l y because electors vote f o r pa r t i e s , and not f o r ind i v i d u a l s , that double-ridings represent same of the worst cases of gerry mandering. For example, take the case where Party A has a margin of v i c t o r y of 20 percent i n one r i d i n g , and loses by a margin of 10 percent i n the r i d i n g adjacent t o i t . I f these two rid i n g s are merged in t o a dajble - r i d i n g i n the next el e c t i o n , and party support remains unchanged from the l a s t e l e c t i o n , then instead of Party A winning only one of the two seats, i t w i l l win both seats, with a margin of v i c t o r y of (20-10)/2 = 5 percent. Thus, by creating double-ridings, a government party could increase i t s number of seats, even i f i t s voter support d i d not increase. I n c o n t r a s t , the opportunity f o r a government to manipulate constituency boundaries t o i t s advantage i s diitunished i f FPP i s replaced by DM2. This i s because the a b i l i t y t o manipulate boundaries i s a function of the wasted vote; with the a b i l i t y t o manipulate decreasing as the wasted vote decreases. As we have seen, the amount of wasted votes decreases as d i s t r i c t magnitude increases. Thus, when d i s t r i c t magnitude i s i n c r e a s e d from one t o two, the a b i l i t y t o manipulate boundaries decreases. 72 Present Day Relevance At t h i s point i n time (July, 1988), the nature of Canada's party system i s notably d i f f e r e n t from that of the period of t h i s study. Hence, the e l e c t o r a l outcome, i f DM2 were introduced, would be d i f f e r e n t now than i t would have been then. However, the two most s a l i e n t issues i n Canadian p o l i t i c s are s t i l l economics and e t h n i c i t y . Thus, when a l l three of the largest p a r t i e s t a k e t h e same p o l i c y p o s i t i o n on one o f t h e s e two issue-dimensions, they e f f e c t i v e l y disenfranchise a l l the voters who favour an opposing p o s i t i o n . Meanwhile, using the FPP system means that only one of the pa r t i e s w i l l be rewarded f o r t h e i r p o s i t i o n . Depending on how r e l a t i v e l y s a l i e n t t h i s issue i s i n a p a r t i c u l a r region, and depending on whether or not the p l u r a l i t y of voters i n the respective region favour the opposing p o s i t i o n , the only options open to the other two parties are to e i t h e r lose the e l e c t i o n and f i n d themselves without any regional support-base, or t o appeal t o the in t e r e s t s of the p l u r a l i t y of voters i n the respective region. I f no party appeals t o the interests of the p l u r a l i t y of voters i n the respective region, then the door i s open f o r a new party t o do so. In other words, when FPP i s used i n a country where the most s a l i e n t issues are regionally-defined, regionally cx>ncentrated p o l i t i c a l p a r t i e s are the r u l e , and p a r t i e s w i t h m u l t i r e g i o n a l representation are the exception. Oansecpently, i f Canada continues t o use FPP, then i n the long-term regional c o n f l i c t s w i l l continue t o be a major source of i n s t a b i l i t y . 73 In contrast, i f DM2 i s used, a party does not have t o have p o l i c y positions favoured by the p l u r a l i t y of voters i n a region, i n order t o gain a large seat share i n that region. In other words, i f DM2 were t o be used i n Canada, i t i s p o s s i b l e t h a t p a r t i e s w i t h m u l t i r e g i o n a l representation could become the r u l e . Further Study I t has already been noted that the high values f o r the c o r r e l a t i o n c o e f f i c i e n t s was i n part the r e s u l t of the degrees of freedom of the small sample. This i s probably not the only small-sample phenomenon i n the r e s u l t s ; i t i s probable that the swing r a t i o s are also at l e a s t s l i g h t l y o f f . The only way t o decrease the standard error of the regression c o e f f i c i e n t i s of course t o increase the s i z e of the sample. In order t o increase the sample-size, the same methodology would have t o be applied t o the e l e c t i o n r e s u l t s of another period i n which the e l e c t o r a l boundaries were not changed. In addition, changes i n the t o t a l number of constituencies, and h i s t o r i c a l realignments i n party support and geographical d i s t r i b u t i o n , would have t o be taken i n t o account. So, while more e l e c t i o n s i n the sample would increase cur knowledge of the properties of DM2, the amount of research involved i s beyond the scope of t h i s study. 74 APPENDIX A The Percentage of the Vote Won by Each forty In Each Election, and the Percentage of Seats Won by Each Party Using D i s t r i c t Magnitudes of One, Two, Three, Six, and Provirice--Wide P a r t y Y e a r 0M1 DM2 DM3 DM6 P r o v i n c e - W i d e V o t e s S e a t s ( X ) S e a t s (%) S e a t s ( X ) S e a t s ( X ) S e a t s ( X ) ( X ) L i b e r a l 1 9 5 3 6 4 . 5 5 6 . 4 5 4 . 2 4 9 . 6 5 0 . 0 4 9 . 0 C o n s e r v a t i v e 1 9 5 3 1 9 . 2 2 7 . 7 2 8 . 4 3 1 . 7 2 9 . 6 3 1 . 0 CCF 1 9 5 3 8 . 7 8 . 3 9 . 5 1 1 . 1 1 1 . 2 1 1 . 0 S o c i a l C r e d i t 1 9 5 3 5 . 7 5 . 3 6 . 4 5 . 6 5 . 8 5 . 0 C r e d i t i s t e 1953 n / a n / a n / a n / a n / a n / a I n d e p e n d e n t s 1953 1 . 9 2 . 3 1 . 5 2 . 0 3 . 5 4 . 0 L i b e r a l 1 9 5 7 3 9 . 6 4 8 . 9 4 2 . 8 4 2 . 6 4 2 . 9 4 1 . 0 C o n s e r v a t i v e 1 9 5 7 4 2 . 3 3 6 . 4 4 0 . 5 3 7 . 6 3 9 . 4 3 9 . 0 CCF 1 9 5 7 9 . 4 6 . 4 8 . 3 9 . 7 1 0 . 6 1 1 . 0 S o c i a l C r e d i t 1 9 5 7 7 . 2 6 . 1 6 . 1 7 . 4 6 . 7 7 . 0 C r e d i t i s t e 1 9 5 7 n / a n / a n / a n / a n / a n / a I n d e p e n d e n t s 1 9 5 7 1 . 9 2 . 3 2 . 3 2 . 7 0 . 4 2 . 0 L i b e r a l 1962 3 7 . 7 4 3 . 6 3 7 . 5 3 7 . 3 3 6 . 7 3 7 . 0 C o n s e r v a t i v e 1962 4 3 . 8 4 0 . 5 4 1 . 3 3 8 . 1 3 7 . 8 3 7 . 0 N . D . P . 1962 7 . 2 6 . 4 1 0 . 2 1 3 . 1 1 3 . 1 1 4 . 0 S o c i a l C r e d i t 1962 1 1 . 3 9 . 5 1 1 . 0 1 1 . 5 1 2 . 0 1 2 . 0 C r e d i t i s t e 1962 n / a n / a n / a n / a n / a n / a I n d e p e n d e n t s 1962 n / a n / a n / a n / a n / a n / a L i b e r a l 1 9 6 3 4 8 . 7 4 9 . 6 4 5 . 5 4 3 . 2 4 1 . 8 4 2 . 0 C o n s e r v a t i v e 1963 3 5 . 8 3 3 . 3 3 6 . 7 3 3 . 0 3 3 . 0 3 3 . 0 N . D . P . 1 9 6 3 6 . 4 5 . 7 6 . 4 1 1 . 0 1 2 . 6 1 3 . 0 S o c i a l C r e d i t 1963 9 . 1 1 1 . 4 1 1 . 4 1 2 . 9 1 2 . 6 1 2 . 0 C r e d i t i s t e 1963 n / a n / a n / a n / a n / a n / a I n d e p e n d e n t s 1963 n / a n / a n / a n / a n / a n / a L i b e r a l 1965 4 9 . 4 4 6 . 2 4 4 . 7 3 9 . 8 4 0 . 6 4 0 . 0 C o n s e r v a t i v e 1965 3 6 . 6 3 4 . 1 3 3 . 7 3 2 . 2 3 2 . 2 3 2 . 0 N . D . P . 1965 7 . 9 1 1 . 4 1 4 . 0 1 7 . 8 1 7 . 6 1 8 . 0 S o c i a l C r e d i t 1965 5 . 3 8 . 0 7 . 2 8 . 7 8 . 4 4 . 0 C r e d i t i s t e 1965 3 . 4 6 . 1 4 . 9 0 . 0 0 . 0 5 . 0 I n d e p e n d e n t s 1965 0 . 8 0 . 4 0 . 4 1 . 5 1 .1 1 . 0 75 APPENDIX B The Regional Breakdown of Results f o r the Li b e r a l s i n the West and Quebec, and Far the Conservatives i n Quebec Table B - l : The Liberals i n the West Year DM1 DM2 Seats m Seats (%) 1953 36.0 47.0 1957 11.0 31.0 1962 9.0 29.0 1963 14.0 29.0 1965 11.0 29.0 DM3 DM6 Votes Seats (%) Seats (%) (%) 38.0 33.0 35.0 25.0 28.0 27.0 22.0 26.0 24.0 28.0 31.0 29.0 29.0 26.0 28.0 Table B-2: The Li b e r a l s i n Quebec Year DM1 DM2 Seats (%) Seats (%) 1953 88.0 71.6 1957 82.7 64.9 1962 46.7 47.3 1963 62.7 56.8 1965 74.7 54.1 DM3 DM6 Votes Seats (%) Seats (%) (%) 70.8 62.5 62.7 62.5 59.7 60.3 44.4 40.3 39.2 50.0 45.8 45.3 55.6 44.4 45.3 Table B-3: The CcHTservatives i n Quebec Year DM1 DM2 DM3 DM6 Votes Seats m Seats (%) Seats (%) Seats (%) (%) 1953 5.0 20.0 25.0 31.0 28.0 1957 12.0 27.0 29.0 32.0 31.0 1962 19.0 30.0 29.0 31.0 30.0 1963 11.0 12.0 21.0 19.0 19.0 1965 11.0 18.0 21.0 22.0 21.0 76 P R O P O R T I O N A U T Y 1 0 0 9 9 _ 9 8 _ 9 7 _ 9 6 _ 9 5 _ 9 4 9 3 _ 9 2 _ 91 _ (%) D B 3 - P R O V P r o p o r t i o n a l i t y I n c r e a s e s a t a d e c r e a s i n g r a t * a s d i s t r i c t m a g n i t u d e I n c r e a s e s . P r o p o r t i o n a l i t y a p p r o a c h e s , b u t n e v e r r e a c h e s , 1 0 0 % 5 . 0 1 0 . 0 1 5 . 0 2 0 . 0 DISTRICT MAGNITUDE APPENDIX D Regression Coefficients T liberals DKL Seat Snare = -43.6 +2.2 Vote Share DM2 Seat Share = (.56) T = 3 . 9 4.15 + 1.07 Vote Share DM3 Seat Share = -10.6 (.08) T = 1 2 . 9 + 1.33 Vote Share DM6 Seat Share = -0.47 (.17) T= 7 . 7 + 1.03 Vote Share DM-Prov Seat Share = -2.58 (.09) T = 1 1 . 2 +1.08 Vote Share (.11) T = 9 . 8 Conservatives DM1 Seat Share = -41.2 + 2.23 Vote Share (1.02) T = 2 . 1 8 4 DM2 Seat Share = -2.1 + 1.06 Vote Share (0.49) T = 2 . 1 5 9 DM3 Seat Share = -11.0 + 1.37 Vote Share (0.40) T = 3 . 4 4 4 Note: E n t r i e s i n parentheses are standard errors of b r e j e c t n u l l h y p o t h e s i s i f t 4 > 0 5 > 2 - 1 3 2 78 ENDNOTES 1 Alan C. C a i r n s , "The E l e c t o r a l System and the Party System i n Canada, 1921-1965." Canadian J o u r n a l of P o l i t i c a l  Science, No. 1 (1968). 2 Alan C. C a i r n s , "The Strong Case For Modest E l e c t o r a l Reform i n Canada," A Paper De l i v e r e d to the Harvard U n i v e r s i t y Seminar on Canadian-United States R e l a t i o n s , Sept. 25, 1979. 3 Ca i r n s , "The E l e c t o r a l , " p. 55. 4 Edmond S. Morgan, "Government by F i c t i o n : The Idea of Representation," The Yale Review, 72 (1983), p. 321. .5 Cai r n s , "The E l e c t o r a l , " p. 56. 6 Ca i r n s , "The Strong Case," p. 8. 7 Howard A. Scarrow, Canada Votes, (New Orleans: Hanser Press, 1963). 8 C a i r n s , "The E l e c t o r a l , " pp. 56, 57. 9 Douglas W. Rae, The P o l i t i c a l Consequences of E l e c t o r a l Laws, (New Haven": Yale U n i v e r s i t y Press, (1971), pp. 139, 117-118. 10 Rae, p. 139. ' ' 11 C a i r n s , "The E l e c t o r a l , " p. 60. 12 Richard Johnston and Janet B a l l a n t y n e , "Geography and the E l e c t o r a l System," Canadian J o u r n a l of P o l i t i c a l Science, 10 (1977), p. 861. Edward R. Tufte s t a t e s the same thing i n more general terms when he argues that the more d i f f u s e support i s f o r a la r g e p a r t y , the larger, the swing r a t i o (swing r a t i o r e f e r s to the r a t e of t r a n s l a t i o n of votes i n t o seats) i n "The R e l a t i o n Between Seats and Votes i n Two-Party Systems", i n American Journal of P o l i t i c a l  Science Review, 67 (1973) , pT 547. 13 Johnston and B a l l a n t y n e , I b i d , p. 862, define the term "wasted vote" i n t h i s way. Advocates of E r o p o r t i o n a l Representation a l s o f r e q u e n t l y use t h i s notion of wasted vote. 14 Douglas Rae def i n e s " f r a c t i o n a l i z a t i o n " as "the pr o p o r t i o n of p a i r s of members i n a system which contains persons who ( have voted f o r d i f f e r e n t p a r t i e s i n the l a s t previous e l e c t i o n i n ; "A Note on the F r a c t i o n a l i z a t i o n of Some European Party Systems," Comparative P o l i t i c a l Studies, 1 (1968), p. 414. 79 15 Markku Laasko and Rein Taagepera, " E f f e c t i v e Number of P a r t i e s : A Measure wi t h A p p l i c a t i o n to West Europe," Comparative P o l i t i c a l S tudies, 12 (1979), pp. 3-27. 16 Rein Taagepera, "The E f f e c t of D i s t r i c t Magnitude and P r o p e r t i e s of Two-Seat D i s t r i c t s , " i n Arendt L i j p h a r t and Bernard Grofman, eds., Choosing an E l e c t o r a l System:  Issues and Al t e r n a t i v e s " ! (New York: Praeger, 1984), p. 97. 17 Taagepera, "The E f f e c t o f , " p. 98. 18 Rein Taagepera and Bernard Grofman, "Rethinking Duverger's Law: P r e d i c t i n g the e f f e c t i v e number of p a r t i e s i n p l u r a l i t y and P.R. systems," European J o u r n a l of P o l i t i c a l Research, 13 (1985), pp. 341-352. 19 Johnston and B a l l a n t y n e , p. 858. 20 Maurice Duverger, P o l i t i c a l P a r t i e s , (New York: John Wiley & Sons, 1963), p. 224. 21 Johnston and B a l l a n t y n e , "Geography," measure the geographical d i s t r i b u t i o n of p a r t i s a n support using a c o e f f i c i e n t of v a r i a t i o n of a party's vote across provinces, p. 860. Duff Spafford separates the d i s t r i b u t i o n of votes i n t o urban and r u r a l c a t e g o r i e s i n , "The E l e c t o r a l System of Canada," American P o l i t i c a l Science Review, 64 (1970), p. 168. 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