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What do we learn from whom? an ingroup learning bias for the subjective and its implications for culture Muthukrishna, Michael 2012

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What do we learn from whom? An ingroup learning bias for the subjective and its implications for culture by Michael Muthukrishna B.A., B.Eng (Hon I), University of Queensland, 2010 A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF ARTS in The Faculty of Graduate Studies (Psychology)  THE UNIVERSITY OF BRITISH COLUMBIA (Vancouver) August 2012 © Michael Muthukrishna, 2012  Abstract Some types of cultural content flow between cultures, while others do not. Here I provide an answer to the question “what do we learn from whom?” and in doing so, identify a mechanism that may help explain this puzzle. Two experiments provide evidence for a proclivity to learn subjective content (e.g. opinions and beliefs) from ingroup members. No such learning bias was identified for objective content (e.g. facts), which were instead learnt from the larger population. In the second half of this thesis, I contrast the results of Dynamic Social Impact Theory models with results from more realistic social network models. The results indicate that features of more realistic human social networks affect the transmission of content in ways not captured by traditional Dynamic Social Impact Theory models. Instead, these latter models are at best a crude approximation of cultural transmission in physical space. I build on these models and explore the population level implications of the ingroup learning bias for subjective content identified in the two experiments. These models predict that the correlation between group membership and cultural content increases with greater levels of bias. Based on these results, we expect that subjective cultural content correlates more strongly with cultural identification than does objective cultural content.  ii  Preface This project was a collaborative effort between Dr Joseph Henrich, Dr Mark Schaller, and me. I developed the concept and design of the research project with guidance from Dr Henrich and Dr Schaller. I was in charge of developing the experiment and experimental software, collecting data, developing the model, and analyzing all data. Comments and feedback were provided whenever necessary by Dr Henrich and Dr Schaller. The manuscript was written entirely by me with comments from Dr Schaller, Dr Henrich, and Daniel Randles. This project was conducted under the approval of the UBC Behavioural Research Ethics Board, Certificate Number H11-00432.  iii  Table of Contents Abstract ................................................................................................................................................. ii Preface .................................................................................................................................................. iii Table of Contents ............................................................................................................................... iv List of Tables ..................................................................................................................................... viii List of Figures...................................................................................................................................... ix Acknowledgements............................................................................................................................. xi Chapter 1 : Thesis Overview .............................................................................................................. 1 1.1  Introduction .............................................................................................................. 1  1.2  Theoretical Motivation............................................................................................. 2  1.3  Thesis Outline ........................................................................................................... 3  Chapter 2 : Psychological Experiments ............................................................................................ 5 2.1  Introduction .............................................................................................................. 5 2.1.1  Group identification ................................................................................... 5  2.1.2  Social learning and conformity.................................................................. 6  2.1.3  Interaction between group identity and social learning ......................... 7  2.2  Studies ........................................................................................................................ 9  2.3  Study 1 ...................................................................................................................... 10 2.3.1  Method ....................................................................................................... 10 iv  2.4  2.5  2.3.2  Results ......................................................................................................... 11  2.3.3  Discussion .................................................................................................. 14  Study 2 ...................................................................................................................... 14 2.4.1  Method ....................................................................................................... 15  2.4.2  Results ......................................................................................................... 15  2.4.3  Discussion .................................................................................................. 17  General Discussion................................................................................................. 18  Chapter 3 : Computational Models ................................................................................................. 19 3.1  3.2  3.3  Background.............................................................................................................. 19 3.1.1  Dynamic Social Impact Theory .............................................................. 20  3.1.2  Human social networks ............................................................................ 23  3.1.3  Model overview ......................................................................................... 28  Dynamic Social Impact Theory and Social Networks ...................................... 28 3.2.1  Introduction ............................................................................................... 28  3.2.2  Methods ...................................................................................................... 29  3.2.3  Results ......................................................................................................... 32  3.2.4  Discussion .................................................................................................. 39  Ingroup Learning Bias Implications .................................................................... 40 3.3.1  Introduction ............................................................................................... 40  3.3.2  Methods ...................................................................................................... 40  3.3.3  Results ......................................................................................................... 41 v  3.3.4 3.4  Discussion .................................................................................................. 43  General Discussion................................................................................................. 44  Chapter 4 : Conclusion...................................................................................................................... 46 References ........................................................................................................................................... 49 Appendix A  : Extra Figures ......................................................................................................... 56  Appendix B : Primer on Social Network Construction ............................................................... 57 Watts-Strogatz and Newman-Watts-Strogatz Networks ................................................ 57 Input Parameters .................................................................................................... 57 Non-technical Description of Algorithm ............................................................ 57 Visualization of Algorithm .................................................................................... 58 Barabási-Albert Network .................................................................................................... 58 Input Parameters .................................................................................................... 58 Non-technical Description of Algorithm ............................................................ 59 Visualization of Algorithm .................................................................................... 59 Appendix C : Homophily Algorithms ............................................................................................ 61 Dynamic Social Impact Theory Grid Network ............................................................... 61 Non-technical Description of Algorithm ............................................................ 61 Barabási-Albert Network .................................................................................................... 61 Input Parameters .................................................................................................... 61 Non-technical Description of Algorithm ............................................................ 61 Appendix D : Experimental Software............................................................................................. 63 vi  Screenshots of experiment .................................................................................................. 63 Appendix E : Experimental Details ................................................................................................ 67 Pre-testing Results ................................................................................................................ 67 Experimental Questions ...................................................................................................... 74 Study 2 74 Appendix F : Experiment Complete Raw Results ........................................................................ 76 Study 1 76 Participants .............................................................................................................. 76 Dummy Coding Guide .......................................................................................... 77 All Participants ........................................................................................................ 77 Suspicious about other player removed .............................................................. 82 Suspicious about other players and guessed social learning removed ............ 86 Study 2 90 Participants .............................................................................................................. 90 Condition Coding Guide ....................................................................................... 90 All data91 Results with global vs ingroup majority .............................................................. 95  vii  List of Tables Table 1. Dummy coding guide ......................................................................................................... 12 Table 2. Study 1 overall model fit .................................................................................................... 12 Table 3. Study 1 raw frequencies ..................................................................................................... 13 Table 4. Study 1 results ..................................................................................................................... 13 Table 5. Study 2 regression predictors ............................................................................................ 16 Table 6. Study 2 overall model fit .................................................................................................... 16 Table 7. Study 2 results ..................................................................................................................... 17 Table 8. Mean similar neighbors ...................................................................................................... 35 Table 9. Mean number of clumps ................................................................................................... 37 Table 10. Mean clump size ............................................................................................................... 37 Table 11. Ingroup learning bias value-group correlation for 400 nodes ................................... 41 Table 12. Study 1 participant demographics .................................................................................. 76 Table 13. Study 2 participant demographics .................................................................................. 90  viii  List of Figures Figure 1. Dynamic Social Impact Theory cellular automata grid simulation. Initial state (left) and end state (right) [Source: (Latané, 1996)]............................................................ 22 Figure 2. Generic names for soft drinks by county [Source: (McConchie, 2003)] ................... 22 Figure 3. DSIT change in mean similar neighbors........................................................................ 32 Figure 4. DSIT change in mean clump size and number of clumps .......................................... 33 Figure 5. The distribution of cultural values in a DSIT grid with 400 nodes ........................... 34 Figure 6. Mean similar neighbors using social network geometry with 400 nodes .................. 36 Figure 7. Mean clump size using social network geometry with 400 nodes ............................. 38 Figure 8. Number of clumps using social network geometry with 400 nodes ......................... 38 Figure 9. Ingroup learning bias value-group correlation for 400 nodes .................................... 42 Figure 10. Ingroup learning bias of 1.0 (i.e. no bias) .................................................................... 42 Figure 11. Ingroup learning bias of 1.1........................................................................................... 43 Figure 12. Ingroup learning bias of 3.8........................................................................................... 43 Figure 13. Social Learning Strategies [Source: (Rendell et al., 2011)] ......................................... 56 Figure 14. Watts-Strogatz algorithm with k=4 and increasing p [Source: (Watts & Strogatz, 1998)] ............................................................................................................................... 58 Figure 15. (a) Ring toplogy with no rewiring; (b) Watts-Strogatz algorithm; (c) NewmanWatts-Strogatz algorithm [Source: (Newman, 2003)] .............................................. 58  ix  Figure 16. Iterations of Barabási-Albert algorithm with m = 2 [Source: (Árpád, 2009)]......... 60 Figure 17. Avatar selection ............................................................................................................... 63 Figure 18. Waiting screen.................................................................................................................. 64 Figure 19. Participant number assignment ..................................................................................... 64 Figure 20. Selection from ingroup ................................................................................................... 65 Figure 21. Position assignment ........................................................................................................ 65 Figure 22. Example question screen with other responses.......................................................... 66  x  Acknowledgements I once heard academia described as entering a room where several people are keenly engaged in a conversation that you know very little about. You listen for a while and try to work out what is being discussed. When you think you are ready, you try to enter the conversation and see if anyone pays attention. After some time, you too are fully engaged in the discussion. As the evening wears on, some people leave and newcomers arrive. Finally, when it has grown late, you too leave, but the conversation goes on. My two supervisors, Joe Henrich and Mark Schaller, are major contributors to several conversations, which is why I am incredibly grateful that they take time out to introduce this newcomer to the discussion. Joe and Mark have given me the space to find my own voice, but have guided me in better expressing myself. Thanks to both of them, I have learnt an incredible amount, including how much more there is to learn. This thesis represents some of my first utterances in this conversation. I would also like to thank several of the other people who have assisted me, in particular Ara Norenzayan and Steve Heine, both of whom have been sources of guidance over the last two years. Thanks also to my peers, in particular, Daniel Randles, who read an early draft of this manuscript. I am grateful to my undergraduate supervisor, mentor, and friend, Penny Sanderson for introducing me to the world of academia and helping me get to this point. Thank you to my mother, Shanthi, for her love and support over the years. Finally, I wish to thank my wife, Steph, for her guidance, love, and support, for assisting me in her roles as editor, sounding board, and secretary, and for ensuring I was clothed, hydrated, and fed during the course of this thesis.  xi  Chapter 1: Thesis Overview 1.1 Introduction In 1769, Lieutenant James Cook arrived on the shores of New Zealand, home of the Maori people. His arrival was not the first encounter between Europeans and Maori1, but it marked the beginning of the relationship between the two cultures. By the mid-1800s, the Maori had acquired European technologies (such as clinker-built boats, tools, and firearms), domestic animals and plants (in particular potatoes), and even some of their spiritual beliefs. At the same time, their values and traditions remained largely unchanged. Michael King (2003) explains that the Maori gained access to “those aspects of European technology and culture that it suited them to have – and, on the whole, they did so without compromising their Maori cultural identity” (p.123; italics added for emphasis). Some types of cultural content flow between cultures, while others do not, as the interactions between the Maori and Europeans, along with many other intercultural encounters from the historical and anthropological record illustrate2. What factors determine what content gets transmitted and what does not? The aim of this thesis was to answer a more modest question, that may provide some insight into this larger puzzle: “what do we learn from whom?”. I used two experiments to help answer this question and then used computational models to explore their population-level implications. Based on evolutionary theories of norm and ethnic psychology, I predict that we have a learning bias toward our ingroup for some kinds of content, but not for others. In the next section, I outline why we should expect to see such a bias in our species.  1  In 1642, over a century prior, Abel Tasman of the Dutch East India Company briefly encountered the  Maori, but did not set foot in New Zealand (King, 2003). 2  For instance, Amazonians acquired steel tools from Europeans, but continued their traditional methods of  farming (Werner, Flowers, Ritter, & Gross, 1979). Several technologies, including paper, stirrups, and gunpowder flowed out of China, but Confucian values did not (Ebrey, 1996).  1  1.2 Theoretical Motivation McElreath, Boyd, and Richerson (2003) model how coordination can lead to the evolution of ethnic markers (e.g. clothing, dialect) and a preference for interacting with and learning from those who share these markers (i.e. ingroup members). Efferson, Lalive, and Fehr (2008) conducted an experiment showing how freely and flexibly chosen markers can become accurate predictors of behavior, which results in a bias toward interacting with others with the same marker. Interactions between individuals who share the same normative beliefs yield higher payoffs than interactions between people with discordant beliefs. The utility of markers and resulting bias toward the ingroup is based on their strength as predictors of normative behavior. From a different angle, Chudek and Henrich (2011) present an argument for the evolution of a norm psychology that enables humans to recognize, represent, recall, and adopt social norms as well as noticing, condemning, and punishing violations. This norm psychology eventually leads to ingroup biases, including a proclivity to learn from the ingroup. However, the ingroup learning bias shown in the McElreath, et al. (2003) model and Efferson, et al. (2008) experiments do not apply to all cultural content and although individually maladaptive norms can be enforced by a norm psychology, it can be argued that not all cultural content is normative. Instead, I argue that these models indicate that we should expect to find an ingroup learning bias for only some types of cultural content, but not others. As part of their argument, Chudek and Henrich (2011) explain that “the evolutionary emergence of a capacity for cumulative culture involves (and then amplifies) two types of selection pressures: those associated with the acquisition of adaptive non-social information by learning from others (e.g., which plants are toxic) and social behaviors or strategies that permit coordinating with conspecifics (e.g. seasonally aggregating at the same locations or using the same gesture when a viper is spotted)” (p. 218). Since adaptive non-social information is by definition adaptive, regardless of who it is learnt from, we should expect to see biases for accuracy, but not necessarily toward learning from ingroup members. Indeed, not having access to such objectively adaptive information that others, including outgroups possess, reduces both yours and your group’s payoffs. For example, if the outgroup possesses superior weapons in a conflict, then your group is at a disadvantage. Similarly, if your neighbor knows about safe, higher calorie foods, she has an advantage over you. The competing pressures for learning normative behaviors from your ingroup, but not having objectively adaptive information, should lead to a psychology that can discern between types of 2  cultural content and then selectively learn them from ingroups or from the most accurate source, irrespective of group membership. Based on this distinction, I separate cultural content into objective and subjective content. I define objective content as content that is perceived to be concerned with evidence about the real world and especially content that is perceived to be verifiable in the real world (i.e. a “fact”) and I define subjective content as the converse; content that is perceived to not be verifiable in the real world (i.e. an “opinion”). Since people do not have access to a “metaphysical realism,” it does not matter if cultural content is objectively objective or subjective, but rather, how it is perceived. I distinguish the objective/subjective dichotomy from the normative/non-normative dichotomy in the following way. Norms may be perceived as either subjective or objective, but while both non-normative and normative objective content may be copied based on its objective value, only normative subjective content will be copied. Returning to the Maori example at the beginning of this chapter, all but spiritual beliefs are clearly objective. However, since it is perceived objectivity that matters, norms such as spiritual beliefs, democracy, or human rights may be objective for some and subjective for others and this perception will affect its transmission (that is non-normative subjective content will not be copied). Of course, cultural content does not exist in isolation, and all cultural content interacts with existing cultural content. For instance, there may be taboos against some objectively richer foods for other reasons. But, in general, there is little fitness benefit in learning outgroup subjective cultural content, but there may be huge fitness benefits in learning outgroup objective cultural content. This argument leads to the prediction that people will show an ingroup learning bias for subjective content, but not for objective content, ceteris paribus with respect to other factors that are known to influence learning (e.g. prestige, expertise, majority views, etc.). I test for this bias using two psychological experiments, exploiting the majority bias, and explore the population-level implications for cultural transmission using computational models.  1.3 Thesis Outline This thesis is composed of two parts. Chapter 2, consists of two psychological experiments that provide preliminary evidence that there exists an ingroup learning bias for subjective content, but not for objective content. Chapter 3, consists of computational models that explore the impact of this learning bias on the clustering of cultural content. 3  More specifically, in Chapter 2, I review the relevant literature on group identification and social learning, as well as research that has explored the interaction between these two processes. I then present the results of the two studies that test for an ingroup learning bias for subjective content. In Chapter 3, I review an area of psychology known as Dynamic Social Impact Theory (Latané, 1996) that has explored the population-level implications of social influence. I also review relevant literature in the area of social networks and social network modeling. I discuss the strengths and limitations of these approaches and then present the results of some preliminary models of an ingroup learning bias for subjective content. In Chapter 4, I discuss the contributions and limitations of the thesis and suggest directions for future research.  4  Chapter 2: Psychological Experiments 2.1 Introduction I tested for the presence of an ingroup learning bias for subjective information using two minimal group paradigm studies. In this section, I review the relevant literature on group identification, social learning, and the interaction between these two processes.  2.1.1 Group identification Individuals randomly assigned into two arbitrary groups will identify with their ingroup, and exhibit ingroup favoritism and outgroup discrimination, despite the arbitrariness of the group and allocation (Tajfel & Turner, 1979). This minimal group paradigm is a useful way to test “pure” group processes without worrying about the confounding variables (such as power differences and stereotypes) associated with real social group dynamics. Therefore, discovering an effect using the minimal group paradigm increases the generalizability of the findings by avoiding alternative explanations. On the other hand, there are several caveats in the use of minimal groups in experimentation. For one, minimal group studies lack the ecological validity that comes from studying real groups. Further, several studies have indicated that ingroup favoritism relies on some important assumptions (e.g. positive stimulus valence (Mummendey et al., 1992); interdependence of interests or expected reciprocity among ingroup (Karp, Jin, Yamagishi, & Shinotsuka, 1993; Yamagishi & Kiyonari, 2000). In everyday life, individuals identify with and belong to overlapping, hierarchical groups and different groups are salient in different contexts. The social identity approach, encompassing social identity theory and self-categorization theory (e.g. Hogg & Reid, 2006; Hornsey, 2008; Hornsey & Hogg, 2000) predicts that the salient ingroup will depend on accessibility and fit in identifying the salient outgroup. That is, individuals will identify categories based on their accessibility and then search for the category that minimizes intragroup differences and maximizes intergroup differences (Hornsey, 2008). For example, the theory predicts that an Asian-Canadian will be more likely to identify with other Asian-Canadians when surrounded by European-Canadians in Canada, but more likely to identify as a Canadian more 5  generally while on holiday in the United States. However, not all categorical aggregations are meaningful as groups (e.g. cyclists, contact lens wearers, laptop users), so what determines what categories are used? Based on McElreath et al. (2003) and  Efferson et al. (2008), discussed  previously, in the present study I have people select colored avatars. These avatars serve as ethnic cues, which in turn should activate an ethnic psychology. Despite the multiple ingroups and outgroups people navigate in everyday life, very little research has attempted to use the minimal group paradigm with more than two groups. One exception is a study by Hartstone and Augoustinos (1995) who failed to find ingroup effects with two outgroups. Few researchers have replicated or pursued these findings. In the present studies, there were three groups. The two outgroups had six and eight avatars respectively. The ingroup had nine, including the participant. Thus, the ingroup was a plurality, but together, the two outgroups formed a majority. I designed the study in this way to avoid minority influence effects and to create a global majority without the use of ingroup members.  2.1.2 Social learning and conformity The psychological research in social learning and conformity stretches back to Sherif’s (1935) autokinetic studies and Asch’s (1956) line judgment studies in the early to mid-twentieth century. Since then, there have been several advancements in the area and several ontologies proposed. In the present research, although I recognize that these ontologies exist, I find the notion of perceived objectivity or subjectivity to be more general and useful. In this section, I discuss how these ontologies relate to my distinction between objective and subjective cultural content. In 1955, Deutsch & Gerard (1955) proposed the distinction between normative and informational conformity. Normative conformity was defined as “an influence to conform with the positive expectations of another” (p. 629) and informational conformity was defined as “an influence to accept information obtained from another as evidence of reality” (p. 629). Deutsch and Gerard found that participants in an Asch line judgment study were more likely to conform to others when in a group condition compared to an individual condition, separated by barriers, but with others’ answers visible. The distinction between normative and informational conformity map on to subjective and objective content and refers to proximate motivations for conformity. Zaki, Schirmer, and Mitchell (2011) provide neurological evidence for the private acceptance of normative 6  ratings of attractiveness. The ratings are normative, but is this acceptance based on “conforming to positive expectations” or “evidence of reality”? Such examples blur the normative-informational distinction. Cialdini and Goldstein (2004) delve deeper into these proximate motivations separating conformity into the goals of accuracy, affiliation, and maintaining a positive self-concept. Similarly, Kelman (1958) classifies the processes of attitude change into compliance, identification, and internalization. Compliance occurs when an individual accepts influence to gain a favorable outcome or to avoid an unfavorable outcome, identification occurs when an individual accepts influence in order to identify with another individual or group, and internalization occurs when an individual accepts influence because the content of influence is useful or correct. Normative conformity is generally associated with compliance or identification and driven by the goal of affiliation. Similarly, informational conformity is associated with internalization and driven by the goal of accuracy. In the present research, I use perceived subjectivity and objectivity to focus on the perception of the content rather than proximate motivation, which is a slightly different question. The ultimate explanation for such a distinction was discussed in section 1.2. In the present research, I am interested in the interaction between social learning biases and group identification. Rendell et al. (2011) review several social learning strategies for which there is significant theoretical or empirical support (see Appendix A, Figure 13 for tree of strategies). For the studies described in this thesis, we focus on the bias toward copying the majority. In psychology, there has been a lot of work on how people develop perceptions of majority behavior and attitudes. Cialdini and colleagues (Cialdini, 2003; Cialdini, Reno, & Kallgren, 1990) distinguish between descriptive (actual behavior) and injunctive (approved or disapproved behavior), and show how these perceptions can independently influence people. In the present research, participants only have access to actual behavior.  2.1.3 Interaction between group identity and social learning Cialdini (2001) identified “social proof”, the tendency to look to others when uncertain, as one of the six principles of social influence. Contrary to our hypothesis, Abrams, et al. (1990) argued that under conditions of uncertainty, people have an ingroup learning bias for both normative and informational conformity. To show an ingroup learning bias for informational conformity, Abrams, 7  et al. (1990) had an equal sized ingroup and outgroup in an autokinetic study. The authors manipulated strength of ingroup identity and found that as identification with the ingroup increased, so did conformity to ingroup information. Although this autokinetic study represented informational conformity, since both the ingroup and outgroup were of the same size, no learning bias (such as a majority or prestige bias) predicted conformity to either group. In the absence of such biases, participants had no reason to believe that either group was more likely to be correct and it is therefore unsurprising that increased ingroup identification pushed participants over the 50-50 edge toward their ingroup. The Abrams et al. (1990) studies notwithstanding, there has been very little work directly examining the interaction between group identity and types of information. One exception is a minimal groups study by Crano and Hannula-Bral (1994). Crano and Hannula-Bral divided participants into a minority or majority group and found that influence was greater for objective questions than subjective questions. More pertinent to the hypothesis at hand, for subjective questions, the ingroup was more influential for minority participants, but not for majority participants. In contrast, for objective questions, the minority (outgroup) was more influential for the majority participants, but there was no differential influence for the minority. These results contradict our hypothesis, but may have other explanations. The authors found weaker ingroup identification amongst those in the majority group, which may explain why majority participants ignored ingroup answers. Minority participants having a greater influence on the ingroup for objective question results are more challenging. One explanation is that the minority were perceived as having special knowledge or skills by the majority. Participants were assigned to minimal groups based on people supposedly processing information differently, which may have caused the majority to assume the minority had a rare and perhaps better ability to answer objective questions (i.e. they were perceived as smarter). Knowing their own ability, the minority may not have had this selfperception. Based on the reported data, there is no way to know if this is true. Although they did not evoke any of the standard channels of minority influence (e.g. consistency, flexibility, and appeals to identification), Crano and Hannula-Bral’s (1994) research falls into a larger body of work in this area (e.g. Moscovici & Nemeth, 1974; Wood, Lundgren, Ouellette, Busceme, & Blackstone, 1994). Some minority influence researchers (e.g. Wood, 2000; Wood et al., 1994) have argued that similar others are more influential for subjective attitudes, because they are likely to have similar reactions to stimuli as oneself, but that “for objective judgments of fact, dissimilar-form-self, 8  minority sources should provide especially useful information about objective reality and should be more influential than similar-to-self, majority sources” (Wood et al., 1994, p. 327). The explanation for these findings stand in contrast to the evolutionary norm psychology account presented in this thesis. Instead, the theory presented in this thesis would predict that minorities will be influential for objective information insofar as they are perceived to have access to more accurate information. In most cases, however, we would predict that people use more general learning biases (e.g. learn from the majority, learn from experts; see Figure 13). Several studies from other areas of research have shown an ingroup learning bias for subjective content. For example, children preferentially accept toys from people who share their language or accent (Kinzler, Dupoux, & Spelke, 2007), and undergraduate students are more persuaded by ingroup opinions than outgroup opinions (Mackie, Worth, & Asuncion, 1990) and are more certain of existing attitudes if they are shared by ingroup members than outgroup members (Holtz & Miller, 1985). In the present study, I use a minimal group paradigm with freely chosen colored avatar groups to represent ethnic markers. I also control for minority group effects and other potential confounds, such as prestige (e.g. Tafarodi, Kang, & Milne, 2002).  2.2 Studies I ran two experiments to test for any group bias in acquiring subjective and objective information using an Asch-style (1956) questionnaire presented in a format similar to many online games. Participants were allocated into groups using a minimal group paradigm design inspired by Shteynberg’s (2010) social tuning studies. They then answered a series of subjective or objective questions with previous answers purportedly provided by other players. Screenshots showing what the participants saw, can be found in Appendix D. One important point to note is that there were three groups in total, of which one was the ingroup. The experimental questions were pre-tested (see Appendix E) by asking participants to classify questions as either a fact or opinion and ensuring that more than 90% of people perceived the question as either one or the other. For subjective questions, obscure multiple-choice responses were offered and for objective questions, very similar plausible answers were offered. I also asked 9  pre-testers “if presented with multiple choice answers, what percentage of people do you think would have an answer to the following questions, without having to guess: i.e. hold an opinion (if opinion) or know the answer without looking it up (if fact)” to ensure that a non-random distribution of participant responses was plausible. My goal was to create questions that had relatively unknown answers, but that were clearly objective or subjective.  2.3 Study 1 2.3.1 Method 2.3.1.1 Participants Participants were 186 (103 female; mean age of 33.19) United States residents recruited using Amazon’s Mechanical Turk (3 participants were removed for not completing the background survey questions). Participants were told that they were playing an online quiz game with people from around the world, although in reality, all participants were recruited from the United States. They were paid 50c for their time, plus 5c for every question for which they provided an answer. The bonus payment discouraged participants from skipping questions. Twenty-nine participants in the experimental conditions indicated that they did not believe there were other human players. I ran analyses with and without these participants. A further 32 participants in the experimental conditions guessed that the study had something to do with social influence. I ran a further analysis without these participants as well. These questions were not of interest in the control condition, since I simply wanted to know how people would respond when no previous responses were provided, regardless of whether they thought there were other players or not. Participants were of mostly European descent (76%). Educational levels were mixed – 23% had completed high school, 29% post-secondary, 34% Bachelors, and 19% Masters and above. Further details can be found in Appendix F.  2.3.1.2 Procedure After reading and agreeing to the consent form, participants selected one of three colored avatars. They were then given instructions to “please wait while we setup the round” and shown a screen 10  with a progress bar typical of many online games. Participants were assigned a participant number and told that they would be playing with 23 other people. On the next screen, participants reselected their participant number from among all the participants of their avatar color in order to reinforce their group membership. The software ostensibly at random assigned participants to position 24 and gave them instructions that they would have 30 seconds to answer each question. Participants entered an online game environment with 23 other ostensible players, of which some were part of their ingroup and others were part of two different colored outgroups. In reality, the computer generated all non-participant players and their answers. Participants were asked 10 objective or subjective questions and asked to respond with one of four multiple-choice answers. For each question, participants waited for all other participants to answer, after which they were shown the question, multiple-choice responses, and in the experimental condition, previous participant responses. In the control condition, previous participant responses were blank. Multiple choice response order was randomized, but questions and other participant responses were not. Question 10, the main experimental question had a unanimous ingroup against a unanimous outgroup (ingroup vs. outgroup). In the subjective condition, participants were asked the question “Who of the following is your favorite basketball player?” with Rajon Rondo, Chris Paul, Deron Williams, and Kevin Durant as choices. In the objective condition, participants were asked the question, “What is the highest grossing film of all time?” with Titanic, The Dark Knight, Lord of the Rings III, and Avatar as choices. Choice order was randomized. Outgroup members gave the answer B and ingroup members gave the answer C. Participant answered demographic and suspicion questions after completing the quiz. Education was measured by asking participants for their highest level of education (high school, post-secondary, bachelors, masters and above). Education was treated as a rank order.  2.3.2 Results I analyzed the data using a multinomial logistic regression (Hosmer & Lemeshow, 2000) comparing the responses when participants could see previous responses (experimental) to when they could not (control) for objective and subjective questions. A multinomial logistic regression tests how different predictors affect the likelihood of different discrete dependent variable outcomes. In this study, the 11  dependent variable was participant response, coded as “2” for copying the ingroup, “1” for copying the outgroup (global majority) and “0” for not matching either (base condition). For each predictor, a Relative Risk Ratio (RRR) is reported. Relative Risk Ratios indicate the increased or decreased probability of a particular outcome (e.g. matching ingroup) compared to the base condition (matching neither outgroup nor ingroup) for every unit change in the predictor. To test each experimental condition against the relevant control condition, I dummy coded the conditions as v1, v2, v3, and v4, setting each version to be “1” for a participant in that version and 0 otherwise, as shown in Table 1 below. By setting the base condition to each of the controls (v3 or v4), I could compare the control to its corresponding experimental condition. Table 1. Dummy coding guide Dummy Variables Condition V1 V2 V3 Subjective Experimental 1 0 0 Objective Experimental 0 1 0 Subjective Control 0 0 1 Objective Control 0 0 0  V4 0 0 0 1  I also controlled for age and education by entering these two variables as predictors. Gender was found to be a very weak predictor and was highly non-significant (p > .9) and was not included. I ran separate analyses with all participants, people who guessed they were playing with a computer removed, and people who guessed the study had to do with social influence removed. A multinomial logistic regression was run with all participants (All), without participants who guessed they were the only real player (Sus1) and without participants who guessed they were the only real player and that the study was about social learning (Sus2). In each case, the overall model indicated a significant relationship between the predictors and the dependent variable. Table 2. Study 1 overall model fit Analysis Observations χ2(10) All 184 30.89 Sus1 155 30.76 Sus2 123 35.58  12  p .0006 .0006 .0001  Analysis All  Sus1  Sus2  Analysis All  Sus1  Sus2  Table 3. Study 1 raw frequencies Response Condition A B (global) C (ingroup) Control 14 (31%) 7 (16%) 8 (18%) Subjective Experimental 7 (14%) 17 (35%) 15 (31%) Control 11 (25%) 4 (9%) 20 (45%) Objective Experimental 7 (15%) 19 (41%) 9 (20%) Control 14 (31%) 7 (16%) 8 (18%) Subjective Experimental 3 (10%) 11 (37%) 9 (30%) Control 11 (25%) 4 (9%) 20 (45%) Objective Experimental 3 (8%) 17 (47%) 6 (17%) Control 14 (31%) 7 (16%) 8 (18%) Subjective Experimental 1 (6%) 8 (47%) 5 (29%) Control 11 (25%) 4 (9%) 20 (45%) Objective Experimental 2 (12%) 9 (53%) 3 (18%)  Predictor Age Education Objective Subjective Age Education Objective Subjective Age Education Objective Subjective  Table 4. Study 1 results Copy Global RRR p 95% CI 1.04 .024 (1.00, 1.07) 0.60 .019 (0.39, 0.92) 5.19 .011 (1.43, 18.79) 4.29 .009 (1.42, 12.63) 1.06 .008 (1.01, 1.10) 0.75 .247 (0.46, 1.22) 5.92 .008 (1.58, 22.21) 4.45 .017 (1.30, 15.25) 1.03 .040 (1.00, 1.07) 0.64 .154 (0.35, 1.18) 8.53 .008 (1.75, 41.53) 7.16 .012 (1.54, 33.31)  RRR 1.02 0.75 0.49 3.32 1.03 0.73 0.43 3.06 1.05 0.73 0.56 4.16  D 16 (36%) 10 (20%) 9 (20%) 11 (24%) 16 (36%) 7 (23%) 9 (20%) 10 (28%) 16 (36%) 3 (18%) 9 (20%) 3 (18%)  Copy Ingroup p 95% CI .166 (0.99, 1.06) .113 (0.53, 1.07) .175 (0.17, 1.38) .026 (1.16, 9.57) .173 (0.99, 1.06) .118 (0.49, 1.08) .156 (0.13, 1.38) .070 (0.91, 10.22) .023 (1.01, 1.09) .183 (0.47, 1.16) .453 (0.12, 2.54) .081 (0.84, 20.67)  The results in Table 4 above indicate that the effect of age is small, but older participants are slightly more likely to copy. More educated participants are less likely to copy either the ingroup or the outgroup. For both the objective and subjective question, participants are much more likely to copy the global majority. However, compared to the control condition, participants in the experimental condition are approximately 2 times less likely to copy the ingroup majority for objective questions, but up to 4.16 times more likely to copy the ingroup majority for subjective questions.  13  2.3.3 Discussion Overall, these results support my hypothesis. Controlling for age and education, with or without suspicious individuals, participants are always more likely to match the global majority. Compared to the controls, participants are 5.19 times as likely to copy the global majority for objective questions and 4.29 times as likely to copy the global majority for subjective questions than to copy neither the ingroup nor the outgroup. This probability increases with suspicious individuals removed. However, participants are only more likely to match the ingroup for subjective questions. Compared to the control, participants are 3.32 times as likely to copy the ingroup for subjective questions and 2.04 times less likely (reciprocal of RRR) to copy the ingroup for objective questions than to copy neither the ingroup nor the outgroup. Nevertheless, before I could establish the existence of an ingroup learning bias for subjective information, there were experimental design concerns that needed to be addressed. These include the single questions used and the non-randomizing of computer players responses, response order, and question order. The non-random distribution of control responses may also be a problem. All of these factors may have contributed to our findings. We addressed these concerns in Study 2 using a slightly different experimental design.  2.4 Study 2 In Study 2, I sought to address several limitations of Study 1. First, I wanted to reduce the amount of suspicion. Based on incredulous debriefing responses, I removed the unanimous condition and instead focused on how increasing ingroup and outgroup majorities affected conformity. I was also concerned that my suspicion probe was itself creating suspicion. To allay this concern I included a funnel debriefing. Finally, I wanted to ensure that the results were not based on the particular question I used or the order in which the questions were given, the particular letter responses the other players gave or the order in which those responses appeared. To control for these factors, I used a variety of questions, randomized the order in which the questions were asked, and randomized the multiple choice responses (as in Study 1), and randomized the other participant response order and actual letter response.  14  2.4.1 Method 2.4.1.1 Participants Participants were 378 United States residents (212 female; mean age 31.91) recruited using Amazon’s Mechanical Turk, in the same manner as Study 1 with the same compensation (35 participants were removed for not completing the background survey questions). Thirty-seven participants in the experimental conditions indicated that they did not believe there were other human players. I ran analyses with and without these participants. A further 122 participants in the experimental conditions guessed that the study had something to do with social influence. I ran a further analysis without these participants as well. Participants were of mostly European descent (56%). Educational levels were mixed – 26% had completed high school, 29% post-secondary, 31% Bachelors, and 26% Masters and above. Further details can be found in Appendix F.  2.4.1.2 Procedure The method was largely the same as Study 1. The only difference was the other player responses seen by the participants and the debriefing. Participants were asked either 10 objective or subjective questions. The first was an easy question, which was the same for all participants. Six of the remaining 9 questions were randomly chosen to be our experimental questions. Experimental questions had between 9 and 13 (64-93%) of the 14 outgroup members give the same answer. For these questions, no ingroup member gave the outgroup majority answer. This outgroup majority always represented the global plurality. Similarly, between 6 and 8 (67-89%) of 9 ingroup members gave the same response. For these questions, no outgroup member gave this ingroup majority answer. These percentages were varied independently. Finally, I used a funnel debriefing to ensure that the suspicion check itself was not generating suspicion.  2.4.2 Results As in Study 1, I analyzed the data using a multinomial logistic regression (Hosmer & Lemeshow, 2000), but this time with outgroup majority, ingroup majority, condition (subjective vs. objective), and condition-outgroup and condition-ingroup interactions as predictors. I standardized percentage 15  majorities because they had different ranges and I was interested in how their increase and decrease affect conformity. Since participants answered multiple questions, I used clustered robust standard errors (Hosmer & Lemeshow, 2000) clustering at the individual participant level to control for intraperson correlations on responses. All other aspects of the analysis were identical to Study 1. Table 5 below describes each of the predictors in detail.  Predictor Age Education Objective Condition Global-Objective Global-Subjective Ingroup-Objective Ingroup-Subjective  Table 5. Study 2 regression predictors Description Age of participants in years Rank order of highest level of education completed Increased probability of copying for objective question responses compared to subjective question responses Increased probability of copying objective question responses for every standard deviation increase in global majority percentage Increased probability of copying subjective question responses for every standard deviation increase in global majority percentage Increased probability of copying objective question responses for every standard deviation increase in ingroup majority percentage Increased probability of copying subjective question responses for every standard deviation increase in ingroup majority percentage  A multinomial logistic regression was run with all participants (All), without participants who guessed they were the only real player (Sus1) and without participants who guessed they were the only real player and that the study was about social learning (Sus2). Standard errors were adjusted for clusters on participant ID. In each case, the overall model indicated a significant relationship between the predictors and the dependent variable.  Analysis All Sus1 Sus2  Table 6. Study 2 overall model fit Observations Clusters χ2(14) 1473 377 26.96 1330 340 32.34 852 219 32.42  16  p .0195 .0036 .0035  Analysis  All  Sus1  Sus2  Predictor (Z) Age Education Objective Condition Global-Objective Global-Subjective Ingroup-Objective Ingroup-Subjective Age Education Objective Condition Global-Objective Global-Subjective Ingroup-Objective Ingroup-Subjective Age Education Objective Condition Global-Objective Global-Subjective Ingroup-Objective Ingroup-Subjective  Table 7. Study 2 results Copy Global Majority RRR p 95% CI 0.99 .905 (0.87, 1.14) 0.97 .631 (0.85, 1.10) 1.43 .006 (1.11, 1.84) 1.16 .080 (0.98, 1.37) 0.99 .912 (0.83, 1.18) 1.02 .807 (0.86, 1.22) 1.17 .058 (.99, 1.38) 1.01 .930 (0.87, 1.16) 0.94 .395 (0.83, 1.08) 1.51 .002 (1.16, 1.96) 1.20 .044 (1.01, 1.43) 0.95 .593 (0.79, 1.14) 1.01 .926 (0.84, 1.21) 1.17 .071 (.99, 1.39) 1.00 .979 (0.83, 1.20) 0.94 .493 (0.80, 1.12) 1.61 .004 (1.16, 2.22) 1.34 .006 (1.09, 1.65) 0.91 .435 (0.72, 1.15) 0.90 .370 (0.71, 1.14) 1.16 .171 (.94, 1.42)  Copy Ingroup Majority RRR p 95% CI 0.97 .583 (0.86, 1.09) 0.87 .025 (0.77, 0.98) 1.15 .289 (0.89, 1.49) 0.95 .556 (0.80, 1.12) 0.82 .035 (0.69, 0.99) 1.09 .353 (0.91, 1.32) 1.14 .197 (0.94, 1.38) 0.96 .487 (0.84, 1.08) 0.86 .019 (0.76, 0.98) 1.27 .082 (0.97, 1.66) 0.98 .850 (0.82, 1.18) 0.79 .014 (0.65, 0.95) 1.11 .314 (0.91, 1.34) 1.14 .207 (0.93, 1.40) 0.92 .338 (0.77, 1.10) 0.84 .046 (0.72, 1.00) 1.30 .144 (0.92, 1.84) 1.04 .736 (0.83, 1.37) 0.74 .012 (0.59, 0.94) 1.07 .620 (0.83, 1.37) 1.19 .208 (0.91, 1.55)  The results of Table 7 above indicate that more educated participants are less likely to copy in general, but particularly the ingroup majority. Participants are up to 1.61 times more likely to copy the global majority than an ingroup majority for objective questions and up to 1.34 times as likely with every standard deviation increase in the global majority. For subjective questions, participants are up to 1.35 times as likely to copy the ingroup majority with every standard deviation decrease in the global majority. Ingroup majority changes did not significantly affect copying.  2.4.3 Discussion Overall, these results provide some support for the hypothesis. Controlling for age and education, even with suspicious individuals removed, participants are more likely to copy the global majority for objective questions compared to subjective questions. The analysis with all participants indicates that participants are 1.43 times as likely to copy the global majority for objective questions than subjective questions (compared to copying neither the global nor ingroup majority). Moreover, this 17  analysis reveals that participants are 1.16 times more likely to copy the global majority for every standard deviation increase in the majority. Participants are not significantly more likely to copy the ingroup majority as the ingroup majority increases. They are, however, more likely to copy the ingroup majority with a decreasing global majority, but only for subjective questions. The analysis with all participants indicates that for every standard deviation decrease in the global majority percentage, participants are 1.22 (reciprocal of 0.82) times as likely to copy the ingroup majority. This probability increases with the removal of suspicious participants. This finding somewhat supports the hypothesis, since participants are still more likely to copy the ingroup majority rather than copy neither the global nor ingroup majority. The failure to find increasing levels of ingroup conformity as the ingroup majority increases may be a result of the small range of ingroup majorities (3 people). As per social impact theory (Latane, 1981), the study may have faced diminishing returns with a majority increase. In future studies, I could address this concern by using larger groups or perhaps by increasing the number of multiple choice responses (Nakahashi, Wakano, & Henrich, forthcoming).  2.5 General Discussion I tested the hypothesis that there exists an ingroup learning bias for subjective content, but not objective content in two experiments. Study 1 provided evidence for the existence of an ingroup learning bias for subjective content, but there were a number of limitations in the study design. Study 2 addressed these limitations, but offered inconclusive evidence for the existence of this bias. In support of the theory, however, neither experiment indicated any evidence of an ingroup learning bias for objective content. In the next study, I hope to use a more sensitive measure to test for a content-based ingroup learning bias. I plan to strengthen group identification, perhaps by using real groups rather than minimal groups. I will also test individual perceptions of cultural content to directly test how perceived objectivity or subjectivity influences group conformity. Based on Nakahashi, et al. (forthcoming) model, I will also introduce more multiple-choice options, which should increase the pressure to conform. Finally, further studies should examine other learning strategies, such as prestige biases, as well as other types of objective and subjective cultural content. In the next section, I look at the implications of an ingroup learning bias for the transmission of cultural content.  18  Chapter 3: Computational Models 3.1 Background Culture refers to two related concepts. The first concept is captured by Richerson and Boyd (2004): culture is information stored in individual minds capable of affecting individuals’ behavior that they acquire from other members of their species through teaching, imitation, and other forms of social transmission. The second concept refers to the distribution of this cultural content, and more specifically, differences in distributions. When people discuss Asian culture versus Canadian culture, or Vancouver culture versus Toronto culture, they are discussing perceived distributions of the first definition of culture – the behaviors, beliefs, norms, and other cultural content that are present at different hierarchical and overlapping distributions. In section 2.1.1, I discussed some of the processes that underlie the identification of these cultures. In the present chapter, I am more concerned with the second definition of culture and will therefore refer to the first as cultural content from herein. These two definitions of culture are linked, because rather than existing in the ether, culture exists as cultural content in the brains of human beings who have evolved to begin the process of enculturation at birth (or possible before (Vouloumanos, Hauser, Werker, & Martin, 2010)). Humans transmit social information, which is sometimes externalized in the form of “material culture” (e.g. art, buildings, tools, etc.) and has more recently been transmitted through this material culture (e.g. writing, television, Internet, etc.). Sometimes these cultures are formalized as organized institutions, such as schools, corporations, and nation-states, with codified beliefs, norms, behaviors, traditions, and so on. In addition, through time, culture and cultural content exerts a selection pressure on genes, which in turn shape and enable more cultural content in a process referred to as gene-culture coevolution (Richerson & Boyd, 2004). The point to these distinctions is that the study of culture requires a different approach than is typically used in psychology. Psychologists typically focus on linear explanations for proximate phenomena, rather than exploring their population level implications or ultimate explanations. I argue that such an approach cannot possibly capture the dynamic processes of culture. Both cultural evolution and the nonrandom distribution of cultural content is an emergent property of a complex system of individual interactions, and the study of culture is both complex in the sense of complicated, and in the sense 19  of the non-linear dynamics that need exploration. One exception to the typical psychological approach is an area of research known as Dynamic Social Impact Theory (DSIT; Latané, 1996), which attempts to model the population level implications of social influence. Since psychologists are already familiar with the DSIT approach and continue to use it to explore the population level implications of proximate psychology (Kenrick, Li, & Butner, 2003), in the next section I introduce DSIT and review its strengths and limitations. I then review the latest advancements in human social network modeling. The remainder of this chapter is composed of two preliminary models. In the first section, I use social network models to show how features of human social networks affect some of the results found in previous DSIT models. In the second section, I apply a homophily algorithm to a DSIT model and a social network model and explore what predictions each model makes for the presence of an ingroup learning bias. Both models represent very preliminary work and in the final section, I discuss improvements, as well as other approaches that allow us to explore the population level implications of an ingroup learning bias.  3.1.1 Dynamic Social Impact Theory Many social psychological theories implicitly assume linear causality, at best seeking out mediating or moderating variables. However, even in a simple dyadic social interaction, rarely is communication one-way. Rather, individual A influences individual B and individual B influences individual A. Even in this simple dyadic example, the assumption of linear causality is no longer valid due to the resulting feedback loop. Most interactions are of course more complicated than this example, and so too are the non-linear dynamics. The first attempt in psychology to capture these dynamics came from Latané in the form of Dynamic Social Impact Theory (DSIT; Latané, 1996). Dynamic Social Impact Theory was an extension to Social Impact Theory (Latane, 1981), which predicted that social influence was proportional to a multiplicative function of strength, immediacy, and number of sources of influence. Latané presented five propositions, which he explored using a cellular automata (e.g. Wolfram, 1983) model consisting of individuals on a grid mutually influencing each other. The left image in Figure 1 illustrates the initial distribution of individuals in physical space with black and white denoting their preference for eating bagels. At each time step of the simulation, individuals change their preference based on the preference of their neighbors. Latané’s (1996) propositions were: (1) individuals differ (in strength of influence); (2) individuals have relatively stable locations in space; (3) social influence is proportional to a multiplicative function of the 20  strength, immediacy, and number of sources; (4) the iterative, recursive outcome of individual influence processes will lead to the global self-organization of socially influenceable attributes and the emergence of group-level phenomena; and (5) social influence will be incremental for unimportant issues and catastrophic for important ones. Latané’s DSIT models had four main findings (Harton & Bullock, 2007). First and second, cultural values initially randomly distributed, cluster3 and correlate over time. The distribution of influential individuals drives the correlation. These effects have been explored in detail (Nowak & Vallacher, 1998). Third and fourth, cultural values consolidate, but continue in diversity. That is, majorities grow, but minorities persist. Initial conditions have a large influence on these latter two effects and the presence of minorities are strengthened by more influential individuals with minority values. The general results of DSIT are supported by experimental evidence (e.g. behavior in electronic and face communication games) and real-world measurements (e.g. sorority girls’ attitudes over time, the geographic distribution of religious attitudes, food, music, and television preferences, slang, accents, life satisfaction, punctuality, etc.) (see Harton & Bullock, 2007). Bourgeois and Bowen’s (2001) finding that not just dormitory building, but dormitory floor predicted alcohol related attitudes, is particularly compelling and illustrates the effect of physical proximity on the distribution of cultural values. On a larger scale, Figure 2 maps the distribution of generic names for soft drinks by county in the United States, showing not just clumping and consolidation, but also the persistence of minorities.  3  Latané and others use the word “clustering” to refer to the increasing likelihood of having neighbors in the  grid with the same cultural content as you. In social network research, “clustering” has a precise meaning, which I discuss later. To avoid confusion between these two concepts, I refer to the clustering of cultural content as “clumping”.  21  Figure 1. Dynamic Social Impact Theory cellular automata grid simulation. Initial state (left) and end state (right) [Source: (Latané, 1996)]  Figure 2. Generic names for soft drinks by county [Source: (McConchie, 2003)]  Although there is evidence for the predictions of DSIT, in part, this is because these predictions are very general. Despite some more specific predictions (such as important values will be more likely to be polarized than unimportant values), at its most superficial level, DSIT predicts 22  that social influence will lead to the clumping of values. There is some disagreement, however, as to what the nodes and grid structure of DSIT actually represent. Some authors (e.g. Latané & L'Herrou, 1996; Nowak & Vallacher, 1998) have interpreted DSIT geometries as representing both physical space and social space, presumably on the assumption that social relationships can be simplified to physical geographic proximity, such that those who are physically distant are also socially distant and do not have a direct influence on one another. There is some evidence that influence decreases with distance despite interactions with distant others (Latané, Liu, Nowak, Bonevento, & Zheng, 1995), but recent advances in our understanding of the structure of human social networks challenge some of the assumptions of DSIT if interpreted as a social geometry. For instance, DSIT assumes that all individuals have the same number of partners, but social network research indicates that a power law (e.g. Zheng, Salganik, & Gelman, 2006) best describes this distribution (the “degree distribution” in social network parlance). Given these unrealistic assumptions, at best, DSIT models are interpretable as a crude approximation of physical geometry, from which we can generate only very general predictions. Past research has attempted to incorporate social geometries into DSIT (e.g. Latané & Bourgeois, 1996), but with new advances in the mathematics of social networks (e.g. Barabási & Albert, 1999; Watts & Strogatz, 1998), we can now do a lot better. One approach to capture both physical and social geometry would be to examine the relationship between social connections and physical proximity and develop models that contain both these pieces of information. Alternatively, simulations can be run on representations of networks of real people where both relationships and physical location are known for each individual. Nevertheless, as an approximation of physical geometry, DSIT models have the advantage that they are easier to analyze and interpret than more complicated social geometries. In the next section, I review social network research and what is currently known about the features of human social networks. We then use this information to generate social networks and compare how they behave with DSIT networks in terms of the transmission of cultural traits.  3.1.2 Human social networks Social network research has exploded over the last decade (Borgatti, Mehra, Brass, & Labianca, 2009), including in the field of psychology. Two catalysts for this flurry of activity were seminal 23  papers published by Duncan Watts and Steven Strogatz in 1998 and Albert-László Barabási and Réka Albert in 1999. These papers provided algorithms for generating networks that have properties commonly found in human social networks. In the remainder of this section, I focus on three defining properties of a class of social networks referred to as “small world” networks: low average shortest path length, high clustering, and skewed degree distribution. The Watts-Strogatz algorithm generates networks with the high clustering property and the Barabási-Albert algorithm generates networks with a skewed degree distribution. In the last part of this section, I briefly review other properties associated with human social networks, including homophily, which I build into my simulations of an ingroup learning bias.  3.1.2.1 Average shortest path length Watts and Strogatz (1998) solved the decades long “small world” problem, captured by Stanley Milgram’s (1967) letter chain experiment. Milgram’s experiment showed that despite a large population size, the average social distance between two people was quite small – the so called “six degrees of separation”. This mystery was solved in Watts and Strogatz’s discovery that average shortest path length (geodesic) significantly decreases when you introduce just a little bit of randomness into an ordered network. One way to visualize this is to consider a city laid out in a grid pattern. Two friends living on opposite ends of the city would ordinarily have a long way to drive to visit each other. If, however, a few shortcut highways connected different parts of the city, the friends could then use these highways and significantly decrease their travel time. Only a few shortcuts would be necessary to make all parts of the city accessible. Mathematically, the geodesic (L) is proportional to the absolute number of shortcuts (Nkp in a Watts-Strogatz network, where N is the number of nodes, k is the number of connections between two nodes, and p is proportion of connections that are randomly rewired – see Appendix B for more details) (Newman, Moore, & Watts, 2000; Watts, 2004). An implication of this relationship is that the addition of only five random shortcuts will halve the geodesic of a network, regardless of the number of nodes (Newman et al., 2000). These results have also been shown to generalize to any large sparse network; that is, any large sparse network with a small amount of randomness will have a small geodesic (Watts, 2004). These discoveries demonstrate that the seemingly surprising low geodesic commonly associated with human networks, is actually very common.  24  3.1.2.2 Clustering Clustering can be thought of as two friends of yours being more likely to also be friends than two randomly chosen people. The major benefit of the Watts-Strogatz algorithm is that it possesses both a low geodesic and significant clustering, unlike random networks, such as the Erdıs–Rényi random network model, which only has the low geodesic property. Mathematically, clustering in a network is a function of the fraction of random shortcuts (p), decreasing as p increases (Barrat & Weigt, 2000; Watts, 2004). The network clustering coefficient is defined as the number of connected triads (all three nodes are mutual friends) as a proportion of number of potential triads (triples that are not fully connected).  3.1.2.3 Degree distribution Degree distribution refers to the distribution of number of connections (edges) to each node. In human social networks, some people are highly connected, while others only have a few connections. The distribution is skewed because there are far fewer people with many connections compared to those with only a handful. Mathematically, the degree distributions of many human social networks follow a power law (Newman, 2003). The main weakness of the Watts-Strogatz algorithm is that it fails to show this skewed degree distribution. In contrast, Barabási and Albert’s (1999) algorithm solves this problem by generating a small-world network using a growth algorithm rather than a rewiring algorithm4. The Barabási-Albert (1999) algorithm uses two mechanisms based on what is commonly referred to as the Matthew effect (Merton, 1968), named after the passage in the Gospel of Matthew5. In the Barabási-Albert algorithm, new nodes are added to the network and preferentially connect to nodes with a large number of existing connections. The resulting network  4  The rewiring process of the Watts-Strogatz (1998) algorithm can sometimes cause the network to separate  into two disconnected networks, which is why I use the modified Newman-Watts-Strogatz (1999) algorithm in this thesis. I refer to these class of networks as Watts-Strogatz networks unless the point being made specifically refers to the Newman-Watts modification. 5  For unto every one that hath shall be given, and he shall have abundance: but from him that hath not shall  be taken even that which he hath. (Matthew 25:29, King James Version)  25  has a power law degree distribution and a short average path length, but does not have the high level of clustering present in Watts-Strogatz networks. Thus, human networks are sometimes seen as lying between these two networks (e.g. Yeaman, Schick, & Lehmann, 2011). But since these two properties are not necessarily directly related (e.g. Ravasz & Barabási, 2003), I think it is more useful to think of these networks as possessing different properties that are common to human social networks. We can then use these models to look at how these properties affect the behavior of these networks in terms of cultural transmission. In the present thesis, I compare cultural transmission in a Barabási-Albert network, Watts-Strogatz network, and DSIT network. Apart from low geodesic, high clustering, and skewed degree distribution, there are several other properties commonly associated with human social networks. It is important to realize, however, that the rapid space of research in this area is continually revealing more about what human social networks look like and how they behave, spurred on by access to new techniques and datasets (e.g. small-scale societies (Apicella, Marlowe, Fowler, & Christakis, 2012) and online social networks (Ahn, Han, Kwak, Moon, & Jeong, 2007; Sala, Zheng, Zhao, Gaito, & Rossi, 2010). Recent research has even challenged long established properties, such as the power-law degree distribution (Ahn et al., 2007; Clauset, Shalizi, & Newman, 2007). Many common aspects of human social networks have been identified, but the extent of variation in human social networks is currently unknown. With this in mind, in the next section I discuss other measures and properties that are associated with human social networks, including homophily, which is necessary for my simulations.  3.1.2.4 Homophily The concept of homophily refers to the tendency for people who are physically or socially close to share common traits and is captured by the idiom “birds of a feather, flock together”. Homophily can be achieved in different ways. For example, through assortativity, whereby people who are similar become physically or socially closer; through social influence, whereby people who are physically or socially closer become more similar through mutual or common sources of influence (as in DSIT models); or through selection attrition, whereby people with certain traits leave or die. Homophily is present in human social networks and there is evidence for all three of these processes (see Kandel, 1978; McPherson, Smith-Lovin, & Cook, 2001). In the present thesis, I am interested in the transmission of cultural traits rather than changes in group membership. In the first models 26  presented in this thesis, I therefore focus on a physical or social world where group-based homophily already exists and where group membership does not change. I then explore how random cultural traits flow between and within these groups. It is easy to show how homophily leads to segregation in a physical geometry by modeling migration from one cell to another (Schelling, 1971). Schelling’s (1971) famous model showed this using pennies and dimes on graph paper and this general relationship has been confirmed empirically (Clark, 1991). Homophily is also present in social networks (McPherson et al., 2001), but is more difficult to simulate, since to use the same approach, we would have to formally define the social analog to physical migration. Another option is to build homophily into the model. Watts, Dodds, and Newman (2002) offer some insight into the problem in their use of a separate hierarchical network tracking levels of culture as measured on a particular trait. In the present thesis, I use a novel approach, modifying the Barabási-Albert (Barabási & Albert, 1999) algorithm to build in homophily (see Appendix C for details). Future approaches could modify the Watts-Strogatz algorithm inspired by the Watts, Dodds, and Newman (2002) approach to look at multiple hierarchical cultures defined by different dimensions.  3.1.2.5 Other properties Other properties associated with human social networks include sparseness (e.g. Watts & Strogatz, 1998) and searchability (e.g. Watts et al., 2002). Searchability is not of great interest to the topic of this thesis, but I will briefly explain the sparseness property. Sparseness refers to a low connection to node ratio and is found in large social networks, such as the global community. Within these networks there are several dense (highly connected) communities, like those found in a small scale society, but overall the connection to node ratio is low. Community detection, methods of identifying these highly connected nodes, is an active area of research (e.g. McDaid & Hurley, 2010; Reichardt & Bornholdt, 2006). Furthermore, although sparseness is typical of large social networks, this may not be the case for small or ego-networks (centered on a single person). In summary, human social networks have (1) short geodesics, (2) significant clustering, (3) skewed degree distributions, (4) homophily, (5) searchability, and (6) sparseness. One aspect of social network research that we have not discussed is measures of networks and nodes within networks. Such metrics include measures for the properties previously discussed, 27  other graph level properties, such as community (denser subgraphs) and clique (complete subgraphs) detection, distance measures (e.g. diameter, radius, eccentricity, etc.) and node-level measures, such as centrality (betweeness, closeness, degree, eigenvector, etc.). These are active areas of research, but are beyond the scope of my thesis.  3.1.3 Model overview My thesis makes two contributions using computational models. The first is that it compares the behavior of Dynamic Social Impact Theory (DSIT; (Harton & Bullock, 2007; Latané, 1996)) models to Watts-Strogatz (Watts & Strogatz, 1998) and Barabási-Albert (Barabási & Albert, 1999) smallworld social network models. The second is that it explores the implications of an ingroup learning bias on the correlation between group membership and cultural value. In doing so, I compare the behavior of a DSIT model to a Barabási-Albert model, both with group-based homophily applied. A primer on the construction of Watts-Strogatz and Barabási-Albert small-world social networks can be found in Appendix B.  3.2 Dynamic Social Impact Theory and Social Networks 3.2.1 Introduction Dynamic Social Impact Theory (Harton & Bullock, 2007) makes four predictions about randomly distributed cultural content: (1) content will clump over time, (2) independent content will correlate over time, (3) content will consolidate into majorities, but (4) minorities will persist. Some DSIT models (see Nowak & Vallacher, 1998) incorporate differential influence, without which we would not expect to see correlation between independent cultural content. The models presented here are a first and incomplete attempt to compare DSIT models to social network models. In these first models, I assume that individuals are equally influential. I make this assumption for two reasons: (1) in order for there to be parity between the DSIT and social network models, differential influence would also need to be built into the social network models and I could not justify randomly distributing influence irrespective of node connectivity, and (2) differential influence would make social network models and to a lesser extent DSIT models difficult to generalize and interpret. Nevertheless, it is critical that the next models incorporate differential influence and explore its 28  effects. The implication of my decision is that we would not expect to find the second DSIT finding, correlation between independent cultural content, and as such, correlation is not measured. Further, I expect that the persistence of minorities should be lower than in typical DSIT results (Nowak & Vallacher, 1998). Another attribute sometimes incorporated in DSIT models is random influence (noise). I have left random influence as an avenue for future research. Finally, some DSIT models use a torus geometry (the sides of the grid wrap around so that all nodes have the same number of connections), which would make the model analytically tractable, removing the need to simulate its behavior. Since social networks are not symmetric and cannot be guaranteed to be a torus, the DSIT models here have edges. Finally, DSIT generally uses two possible values (0 or 1) for cultural traits, which I do as well. I used the Watts-Strogatz (Watts & Strogatz, 1998) and Barabási-Albert (Barabási & Albert, 1999) algorithms to generate small-world networks. Both of these algorithms generate undirected networks, such that if individual A influences individual B, individual B also influences individual A. In the real world, especially in the modern world, directed connections exist. For example, actor Tom Cruise may influence your neighbor, but your neighbor is unlikely to influence Tom Cruise. The lack of directed links is a serious limitation of my model and this must be addressed in future research. I chose to use undirected networks for two reasons. First, although there have been some attempts to develop algorithms to generate directed small world networks (e.g. Jiang, Hua, Zhu, Wang, & Zhou, 2008; Ramezanpour & Karimipour, 2002; Sánchez, López, & Rodríguez, 2002), there are no widely accepted algorithms nor have these networks been as widely studied. Second, since DSIT networks are undirected, having undirected social networks ensures a meaningful comparison. A solution to at least the first problem is to use real social network data (see Banerjee, Chandrasekhar, Duflo, & Jackson, 2012; Jackson, 2008) rather than generating simulated networks. These networks are increasingly available and I hope to use them to test my findings. In the next section, I discuss the specifics of the models I used and how I measured the clumping predicted by DSIT.  3.2.2 Methods Clumping is not a common measure in social network research, so there were not many off-theshelf techniques that measure it. I measure clumping in two ways. First, I measure clumping as a 29  mean percentage of neighbors that have the same cultural content as a particular node. Mathematically, this measure can be expressed as: ே  1 ‫ݏ‬௜ ‫ܥ‬1 = ෍ ‫ݏ‬௜ + ݀௜ ܰ ௜  Where C1 is mean similar neighbors, N is the number of individuals, s is the number of neighbors an individual has that have the same cultural value and d is the number of neighbors an individual has that have a different cultural value. Mean similar neighbors is a good measure of the first DSIT finding. I also measure clumping using a novel algorithm that measures the number and size of connected subnetworks with the same value. The algorithm works as follows for a network with binary cultural values: With a copy of the network, remove all nodes of a particular cultural value. Record the number and size of connected subnetworks. Repeat with a new copy of the whole network for the other cultural value. Return the number and mean size of the subnetworks. This second measure maps onto the third and fourth DSIT findings. Watts-Strogatz networks are generated with three parameters – the population size (N), the number of initial connections between individuals (k), and the probability of reassigning a connection (p). I assumed fixed population sizes of 100, 225, and 400 with twice the number of connections (k = 4)6. I also set p = 0.1, after which clustering gets too low (see Watts & Strogatz, 1998). Barabási-Albert networks are generated with two parameters – the population size (N) and the number of connections per new node (m). I again assumed the same fixed population sizes with twice the number of connections (m = 2) to ensure parity between our two social network models. I generated our DSIT grid with the same fixed population sizes and being a grid, there are approximately twice the number of connections (slightly less due to the edges of the grid). Although  6  I use the Newman-Watts-Strogatz algorithm (Newman & Watts, 1999) to prevent the possibility of  disconnected networks. As a result the number of expected edges is ‫ ݌‬more. I set p = 0.1, so I expect there to be 10% more edges than the Watts-Strogatz algorithm (Watts & Strogatz, 1998).  30  I could have explored more of the parameter space in generating social networks, this was not my main interest. Instead, I focused on how the DSIT approach differs when realistic aspects of social geometry are used. The influence algorithm was a simple binary decision rule based on the majority values of an individual’s neighbors. At each time step, a random individual was selected. The individual applied a binary decision rule to decide whether they should change their value or not (keeping in mind that values were binary). The decision (D) can be expressed as a function of the cultural content (v; 1 or 1), group status (g; 1 if same as individual, 0 if different), and influence (p; set to 1 in my model) of an individual’s k neighbors (individuals with which they had a direct connection), a bias toward their self (bs; influencability, set to 0.5 for our models), a learning bias toward their ingroup (f; ingroup favoritism, > 1 for an ingroup learning bias), and noise (e; set to 0 in my model). Mathematically this can be expressed as: ௞  ‫ ݁ = ܦ‬+ ܾ௦ ∙ ‫ݒ‬௦ + ෍ ݂ ௚ೖ ∙ ‫݌‬௞ ∙ ‫ݒ‬௞ ௜  Where the new cultural content is: ܾ < 	0 New	value	=	 ൝ܾ = 	0 ܾ>0  −1 old	value 1  Another way to think about this is that the individual changes his cultural content value to the majority of his neighbors’ cultural content, weighted by an ingroup learning bias, with his own values and any noise tipping the balance. In this first set of models, group status (g) was always zero, hence there was no ingroup learning bias. This decision was applied to random individuals until twice the number of individuals time steps had passed with no change occurring; our terminating condition. I ran 10 iterations for each model. All code was written in Python 2.7 using the Networkx libraries. All results were analyzed using the R package.  31  3.2.3 Results 3.2.3.1 Dynamic Social Impact Theory Figure 3, plots C1 against the number of steps for 100, 225, and 400 nodes:  Figure 3. DSIT change in mean similar neighbors  Clumping (as measured by mean similar neighbors) unsurprisingly increases over time (influence counts). Quantitatively we can extract some measures that focus of the speed of clumping and the deviation in final clumping equilibria between the 10 simulations. Our graphs suggest an exponential recovery function, so we used the drc package (Ritz & Streibig, 2005) in R to fit our data to an asymptotic regression model of the form: ݂ሺ‫ݔ‬ሻ = ܿ + ሺ݀ − ܿሻ൫1 − ݁  ௫ൗ ௚൯  Asymptotic regression models are commonly used in the biological sciences (Ratkowsky, 1983; Ritz & Streibig, 2005). An asymptotic regression model fits data points to an exponential recovery or decay function. We can check the fit with a lack of fit test. The drc package was actually designed for the analysis of dose response curves. The variable c in the function above indicates the y intercept, d is the asymptote, and g is a measure of the “slope” of the function. I performed a lackof-fit test on our models to ensure that they fit well. I also measured the mean and standard deviation of the final equilibria of our 10 simulation iterations to explore how initial conditions affect the final outcome. Figure 4 shows clumps grow in size (mean clump size) and by corollary decrease in number. 32  Figure 4. DSIT change in mean clump size and number of clumps For DSIT geometries, mean clump size appears to follow an exponential decay function. I therefore fit the data to an asymptotic regression model7 and compare the mean and standard  7  Note: We use an exponential decay function rather than exponential recovery function: ݂ሺ‫ݔ‬ሻ = ܿ +  ሺ݀ − ܿሻ ቀ݁  ௫ൗ ௚ቁ  to avoid redefining c and d.  33  deviation of the final equilibria. The behavior of the “number of clumps” graph is less clear. I therefore only compare the mean and standard deviation measure of the final equilibria. Overall, these results indicate that cultural values clump in a social network and visually (see Figure 5 for an example), it is clear that minorities persist. In the next section we use these same measures to determine how the behavior of cultural transmission in a social network differs.  Figure 5. The distribution of cultural values in a DSIT grid with 400 nodes  34  3.2.3.2 Social network I now apply the same simulation with social network geometries to determine how they behave differently. The results are summarized in Table 8, Table 9, and Table 10. Table 8. Mean similar neighbors Overall model Model N Intercept (c) Asymptote (d) Slope (g) Lack of fit B-A 400 .52 .80 418.24 F(4479, 33741) = 0.459, p = 1.00 B-A 225 .52 .81 295.75 F(2118, 15971) = 1.260, p < .001 DSIT 400 .51 .81 439.24 F(3873, 31102) = 0.523, p = 1.00 DSIT 225 .54 .82 246.63 F(2049, 16113) = 0.491, p = 1.00 DSIT 100 .53 .82 98.49 F(1057, 6611) = 0.332, p = 1.00 W-S 400 .51 .85 439.87 F(3397, 27393) = 0.161, p = 1.00 1 W-S 100 .52 .87 127.57 F(738, 5499) = 0.321, p = 1.00 W-S 225 .51 .85 247.45 F(1693, 13852) = 0.163, p = 1.00 2 B-A 100 .57 .97 257.53 F(879, 6849) = 1.015, p = .383 1 Watts-Strogatz Small-world Social Network 2 Barabási-Albert Small-world Social Network  35  Equilibria Mean Sd .80 .02 .80  .04  .81  .02  .82  .02  .82  .04  .85  .02  .85  .03  .85  .03  .87  .06  Figure 6. Mean similar neighbors using social network geometry with 400 nodes As Table 8 shows, overall our asymptotic regression model fit our data well. Based on the equilibria means, these results seem to indicate that a Watts-Strogatz network structure results in a higher mean proportion of similar neighbors than either the DSIT or in Barabási-Albert structures, although these results were not found for the 100 node graphs. Since these models are a first pass at showing how social networks differ from DSIT, I am cautious about making too many generalizations, but presumably this higher degree of clumping is due to the higher clustering of the Watts-Strogatz geometry.  36  Table 9. Mean number of clumps Overall model Model N Intercept (c) Asymptote (d) Slope (g) Lack of fit B-A 225 37.41 2.81 212.47 F(2118, 15971) = 0.842, p = 1.00 B-A 400 69.46 3.64 327.24 F(4479, 33741) = 0.835, p = 1.00 DSIT 100 18.45 4.22 52.32 F(1057, 6611) = 0.514, p = 1.00 2 B-A 100 18.46 3.09 138.60 F(879, 6849) = 0.256, p = 1.00 W-S1 100 15.00 3.76 123.91 F(738, 5499) = 0.492, p = 1.00 W-S 400 53.61 5.20 404.18 F(3397, 27393) = 0.467, p = 1.00 33.41 6.19 166.02 F(2049, 16113) DSIT 225 = 1.20, p < .001 W-S 225 38.84 7.31 224.53 F(1693, 13852) = 0.219, p = 1.00 63.47 9.42 248.87 F(3873, 31102) DSIT 400 = 2.811, p < .001 1 Watts-Strogatz Small-world Social Network 2 Barabási-Albert Small-world Social Network Table 10. Mean clump size Equilibria Model N Mean Sd W-S1 100 23.83 4.16 DSIT 100 24.83 5.35 B-A2 100 28.08 12.72 W-S 225 31.88 6.71 DSIT 225 37.74 5.90 DSIT 400 45.83 6.48 W-S 400 82.83 26.05 B-A 225 87.00 23.77 B-A 400 152.38 47.09 1 Watts-Strogatz Small-world Social Network 2 Barabási-Albert Small-world Social Network 37  Equilibria Mean sd 2.80 0.92 3.00  1.49  4.20  0.92  4.20  1.75  4.30  0.67  5.30  1.77  6.10  0.99  7.50  2.42  8.90  1.37  Figure 7. Mean clump size using social network geometry with 400 nodes  Figure 8. Number of clumps using social network geometry with 400 nodes  Table 9 and Table 10 indicate that in most cases, our asymptotic regression model fit our data well. These equilibria means seem to indicate that a Barabási-Albert structure results in larger 38  clumps (and therefore less minorities) than either the DSIT or Watts-Strogatz network, although once again, no clear differences were seen with only 100 nodes. The social network graphs also seem far more sensitive to initial conditions, and in several cases, the Barabási-Albert structure resulted in polarization, as evinced in Figure 7 by the simulations with a mean clump size of 200 (half the nodes). This is very difficult to see visually by inspecting the network itself and I have therefore avoided including a figure. Once again, since these models are a first pass at showing how social networks differ from DSIT, I am cautious about making too many generalizations, but presumably a more skewed degree distribution in the Barabási-Albert structure resulted in larger clumps  3.2.4 Discussion The results indicate that clustering results in a greater proportion of mean similar neighbors, but that skewed degree distribution results in larger, sometimes polarized groups. In contrast, minorities persisted more robustly when physically separated. There seemed to be no consistent effect on speed of transmission, as shown by the g value of the asymptotic regression model. I recommend running more simulations with a larger population in order to generalize these results. Further, it would be useful to be able to statistically compare the equilibria means. The effect of initial conditions, particularly in the social network models is interesting and needs further investigation. Another avenue for further investigation might be test how individual node parameters, such as centrality measures affect the transmission and clumping of values. For example, there is some empirical evidence that individuals with higher eigenvector centrality have a greater influence on other nodes (Banerjee et al., 2012). Finally, the results presented in this chapter represent a first effort to compare cultural transmission and clumping in DSIT models to social network models. Before any firm conclusions can be drawn, several limitations in the present models must be addressed. In particular, it is critical that we explore the effect of differential influence and influencability. In the next section, we use these models with group homophily to explore the population level implication of an ingroup learning bias.  39  3.3 Ingroup Learning Bias Implications 3.3.1 Introduction In Chapter 2, I presented some evidence for the existence of an ingroup learning bias for subjective information. These results suggested that an ingroup learning bias may exist for subjective information, but there was no evidence that this bias was exclusive. That is, there was no evidence that people learn subjective information only from the ingroup. In this section, I present the results of models of such an ingroup learning bias. I use a segregated DSIT model and a modified BarabásiAlbert model, where individuals are more likely to have a connection to members of their own group. Appendix C contains a description of the construction of these networks. Although the nonexclusivity of the bias found in my experiment may have been an artifact of weak group identification in a minimal group paradigm, even in the real world, group identification varies. As such, I also varied the ingroup learning bias in my models. In the next section, I provide more details about the model construction and simulations.  3.3.2 Methods Every individual in the network has one of two group memberships. Groups are not randomly distributed in either physical or social space, so I first apply homophily (based on group membership) to the networks. I achieve this in a DSIT model by randomly distributing individuals on a grid and then allowing each individual to swap with any neighbor who has more neighbors of the same group type than they did. To illustrate this, consider Alice, a violinist who has one violinist neighbor and three drummer neighbors. One of her drummer neighbors, Bob, has three violinist neighbors. Since Bob has more violinist neighbors than Alice, Alice and Bob will swap physical locations. Watts-Strogatz networks are made by randomly reconnecting a very small percentage of connections in a ring structure and as such, it was less clear how to apply homophily to the algorithm. Instead, I focused on introducing homophily into the Barabási-Albert growth algorithm. This was achieved by making new nodes not only more likely to attach themselves to nodes with more existing connections, but also likely to attach themselves to nodes in their ingroup. See Appendix C for more details. 40  The influence algorithm was identical to the influence algorithm in section 3.2. The ingroup learning bias was varied between 1.0 and 3.8. One can think of a 3.8 ingroup learning bias as every ingroup member having the influence of 3.8 outgroup members. Thus 1.0 means that there is no bias. In the graphs below, we compare the results of no ingroup learning bias (1.0) with a slight ingroup learning bias (1.1) and a large ingroup learning bias (3.8) in a population size of 400.  3.3.3 Results Table 11. Ingroup learning bias value-group correlation for 400 nodes Equilibria Model Bias Mean Sd DSIT 1.0 .03 .03 DSIT 2.3 .04 .04 .05 .03 DSIT 1.1 DSIT 1.4 .05 .04 .05 .04 DSIT 2 B-A 1.0 .06 .03 .06 .03 B-A 1.1 DSIT 1.7 .06 .05 .06 .03 DSIT 2.6 DSIT 2.9 .06 .05 .06 .04 DSIT 3.2 DSIT 3.5 .06 .05 .07 .06 B-A 2.3 DSIT 3.8 .08 .07 .09 .06 B-A 2 B-A 2.9 .09 .14 .09 .08 B-A 3.2 B-A 1.4 .10 .07 .11 .09 B-A 2.6 B-A 1.7 .12 .09 B-A 3.8 .14 .09 B-A 3.5 .16 .10  41  0.3 B-A  DSIT  Value-Group Correlation  0.25 0.2 0.15 0.1 0.05 0 0  1  2  3  4  5  -0.05 -0.1  Bias  Figure 9. Ingroup learning bias value-group correlation for 400 nodes  Figure 10. Ingroup learning bias of 1.0 (i.e. no bias)  42  Figure 11. Ingroup learning bias of 1.1  Figure 12. Ingroup learning bias of 3.8  Figure 10, Figure 11, and Figure 12 show that initial conditions and randomness has a large impact on the final value-group correlation, but along with Table 11 and Figure 9, show that overall, Barabási-Albert networks result in a larger value-group correlation than do DSIT networks.  3.3.4 Discussion The means of the final equilibria indicate that an ingroup learning bias will result in an increased correlation between group identity and cultural content at the population level. Therefore, an ingroup learning bias for subjective cultural content and not objective cultural content should result 43  in a higher correlation between subjective cultural content and group identity compared to objective cultural content, which more freely flows between groups. Furthermore, these results indicate that features of Barabási-Albert social networks, seem to result in a higher correlation between group and cultural content than the crude physical geometry represented by the DSIT grid. Finally, although most simulations resulted in a higher correlation between group identity and cultural value, not all did. In particular, Barabási-Albert social networks seem to have a larger variability in values. This variability indicates the importance of initial conditions and warrants further investigation. I suspect it is based on the initial distribution of values among more central nodes. There are of course some caveats to these conclusions due to the model limitations, including a lack of directed connections and a lack of differential influence. I discussed these limitations in more detail at the beginning of this chapter.  3.4 General Discussion This chapter presented (1) comparisons between cultural transmission in DSIT models and social network models and (2) the population level implications of an ingroup learning bias. Both these attempts represent initial research and all results should be interpreted in this light. The models used suggested that though cultural values clump in all cases, there are some key differences in the behavior of social network models compared to DSIT models. First, minorities are less likely to persist in a social network geometry. Second, skewed degree distribution, seems to drive groups to become larger and polarized. And third, high clustering results in a greater proportion of neighbors who share your cultural values. The results of the ingroup learning bias models indicate that an ingroup learning bias for subjective information will result in a correlation between group identity and subjective cultural content. Further, an increasing ingroup learning bias will result in a greater correlation between groups and subjective cultural content. In contrast, objective cultural content will flow between groups. The models also indicate that social networks, at least those with skewed degree distribution, seem to facilitate this process. At the same time, despite a large ingroup learning bias, group identity and subjective cultural content do not always become correlated, and this unexpected finding needs to be further investigated. One notable absence in this chapter are models from research on cultural evolution in anthropology and biology (see Boyd and Richerson (1988) for examples). This research tradition has 44  a rich history of more sophisticated models of culture than psychology and its Dynamic Social Impact Theory (DSIT) approach. I began with DSIT rather than these models, because DSIT originated in psychology and psychologists were already familiar with these models and would therefore be more receptive to this approach. Nevertheless, the next step will be to also integrate these earlier approaches with the latest research in human social network modeling. The models presented here represent preliminary work. There are many limitations, which need to be addressed in future research. Future research will need to test a greater range of realistic assumptions, including differential influence and directed connections, run more than 10 simulations, and test a greater range of social network parameters (e.g. p and N in a Watts-Strogatz network). In the present models, we generate social networks and then explore how content flows within them. Of course, in reality, psychological factors, including learning biases, group identity, and differential influence affect the structure of the network itself. For example, Banerjee et al. (2012) do not directly assume or measure differential influence, but measure it as a feature of the network (eigenvector centrality). The effect of network structure on psychology and the effect of psychology on network structure is a further complexity that needs to be considered when using this class of models to explore population level implications of psychology. The greater availability of real social network data (see (Banerjee et al., 2012; Jackson, 2008) for examples) is very useful in tackling these concerns. These real social networks also allow you to analyze the effect of both physical geometry and social geometry directly by gathering this data from individuals when constructing the network. Using this approach, we can dispense with DSIT style models of physical space. A wealth of social network data and tools are becoming increasingly available. Their availability opens up several avenues of research and better ways to answer the questions “what do we learn from whom?” and “what implications does this have for culture?”.  45  Chapter 4: Conclusion My goal in this thesis was two answer two questions: (1) “what do we learn from whom?” and (2) “what implications does this have for culture?”. To answer this question, I used a two-pronged methodological approach combining two psychological experiments, and several models. Using psychological experiments, I sought to test the hypothesis that there exists an ingroup learning bias for subjective cultural content, but not for objective cultural content. Then, using modeling techniques, I sought to test the population-level implications of such a bias. My experimental results provide some evidence that the answer to the first question, “what do we learn from whom?” is that we learn objective content from everyone, but have a learning bias toward our ingroups for subjective content. My simulation results suggest that the answer to the second question “what implications does this have for culture?” is that subjective content will begin to correlate with group membership, but objective content will flow between groups. My thesis represents some initial answers to these questions, but further research is required before any firm conclusions are drawn. Using two minimal group paradigm studies I found evidence for an ingroup learning bias in my first study. In my second study, I aimed to resolve many of the problems of the first study. The second study found some evidence for an ingroup learning bias, but these results were not sufficiently compelling. In resolving some of the problems of the first study, I may have inadvertently weakened the sensitivity of my measure. I argued that the use of a minimal group paradigm made my results more generalizable, since many confounding variables associated with real groups were removed and I was able to study “pure” group processes. At the same time, I acknowledge that manipulation strength aside, since I am concerned with population level implications, it is important to test my hypothesis amongst real groups. Experimentally, this is my next step. I used computational modeling techniques to explore the population level implications of an ingroup learning bias for subjective information. I first tested for differences in network behavior between Dynamic Social Impact Theory models and social network models. These results indicated that contrary to the predictions of Dynamic Social Impact Theory, social networks predict a smaller number of minority cultural values. Further, a skewed degree distribution arguably predicts larger 46  cultural clumps and even polarization and high clustering predicts a greater proportion of neighbors with similar cultural values. It is difficult to argue that Dynamic Social Impact Theory represents a realistic social network, but it may represent a crude representation of physical proximity. Nevertheless, I argued that using real social network data that contains physical location allows us to test the effect of both physical proximity and social connectivity in a more realistic and justifiable way. This thesis was aimed at psychologists and as such, I began by looking at Dynamic Social Impact Theory, despite the availability of more sophisticated models (e.g. Boyd & Richerson, 1988) that answer similar questions. Since apart from Dynamic Social Impact Theory, psychologists rarely attempt to model population level implications of proximate psychology, I believe this was a useful starting point for psychologists. Nevertheless, the next step will be to also integrate approaches from anthropology and biology with the latest research in human social network modeling with a focus on answering deeper questions about the cultural implications of psychological biases in what we learn from whom. In focusing on answering the research questions themselves, the value of the approach should be judged independent of the domain from which it originated. In testing the population-level implications of an ingroup learning bias for subjective cultural content, I also developed a new algorithm for generating small-world networks with homophily. Supporting my argument, these models indicated that in general, an increased ingroup learning bias would result in an increased correlation between group membership and cultural content. However, these results also indicated that while the correlation increases in general, sometimes the correlation remains low. The reason for these results is unclear and warrants further investigation. In addition, as with all computational models, I had to make decisions about what was important to include and exclude, as well as what parameter space I would explore. Future research needs to check if these results hold up under different assumptions and a greater range of parameters. Researchers should base their choice of assumptions and parameters on real-world data to lend the models greater ecological validity. As mentioned, one immediately available approach will be to use real social network models rather than artificially generated models, and from a modeling perspective, this is my next step. More broadly, my thesis contributes to a number of different areas. First, it contributes to the literature on Dynamic Social Impact Theory, social networks, group processes, social influence, and cultural transmission. Second, it extends previous work by Chudek and Henrich (2011) on a norm psychology account of human evolution. Finally, it contributes to efforts to bridge the 47  proximate study of human behavior with the study of the emergent properties of culture and cultural evolution. These theories and areas in turn offer additional hypotheses and new avenues for future research. For example, we have not considered the effect of status and prestige, important at both the individual and group level, with implications for imitation and social influence (e.g. overimitation). What happens to an ingroup learning bias for subjective cultural content when outgroups have higher status? Schmader et al. (2001) suggest that domains are devalued if status differences are deemed illegitimate. In the context of the theory proposed in this thesis and in line with overimitation research, I would predict that if status differences are seen as legitimate, typically subjective content (e.g. norms) may be perceived as objectively better as it may be difficult to judge what causes the group’s legitimately higher status. Another example is that in our simplification to single group identity, we have not considered the multitude of groups and cultures people belong to and identify with and how conflicting subjective or objective cultural content affects what they learn from whom. I predict that the answer to these questions will be a function of strength of group identity, how much each group values the cultural content, and attributions of domain-expertise. Furthermore, at present, we have only tested the “copy the majority” learning bias. I predict that other learning biases, such as those in Appendix A, Figure 13 will also exhibit a similar ingroup learning bias for subjective content, but not objective content, but this has yet to be tested. These are a few examples of future directions in this area of research. My hope is that my thesis, along with the answers to these and other related questions, will help us develop a richer understanding of this complex phenomenon we call “culture”.  48  References Abrams, D., Wetherell, M., Cochrane, S., Hogg, M. A., & Turner, J. C. (1990). Knowing what to think by knowing who you are: Self‐categorization and the nature of norm formation, conformity and group polarization*. British Journal of Social Psychology, 29(2), 97-119. Ahn, Y.-Y., Han, S., Kwak, H., Moon, S., & Jeong, H. (2007). Analysis of topological characteristics of huge online social networking services. 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Zheng, T., Salganik, M. J., & Gelman, A. (2006). How Many People Do You Know in Prison? Journal of the American Statistical Association, 101(474), 409-423.  55  Appendix A : Extra Figures  r Figure 13. Social Learning Strategies [Source: (Rendell et al., 2011)]  56  Appendix B: Primer on Social Network Construction Watts-Strogatz and Newman-Watts-Strogatz Networks Watts and Strogatz (WS; (Watts & Strogatz, 1998)) developed a rewiring algorithm to generate a small-world network. Newman and Watts (NWS; (Newman & Watts, 1999)) later modified this algorithm to prevent the possibility of the network separting into two or more disconnected networks. To do this, they added new edges (connections) between nodes instead of rewiring, increasing the total number of connections in the network. In this section, I outline the input parameters and algorithm.  Input Parameters Parameter N k p  Description Number of nodes Each node is connected to k nearest neighbors in ring topology Probability of rewiring (WS) or adding a new edge (NWS) for each edge  Non-technical Description of Algorithm 1. Create a ring of n nodes 2. Connect each node with its k nearest neighbors 3. For each edge, replace (WS) or add a new edge (NWS) to a random other node with probability p.  57  Visualization of Algorithm  Figure 14. Watts-Strogatz algorithm with k=4 and increasing p [Source: (Watts & Strogatz, 1998)]  Figure 15. (a) Ring toplogy with no rewiring; (b) Watts-Strogatz algorithm; (c) NewmanWatts-Strogatz algorithm [Source: (Newman, 2003)]  Barabási-Albert Network Barabási and Albert (Barabási & Albert, 1999) developed a growth algorithm to generate a smallworld network. In this section, I outline the input parameters and algorithm.  Input Parameters Parameter N m  Description Number of nodes Number of edges to attach from a new node to an existing node 58  Non-technical Description of Algorithm 1. Start with one node 2. Add a new node and connect to m other nodes. Each node has a probability of being connected to that increases linearly with their existing number of connections 3. Repeat steps 1 and 2 until the network has N nodes  Visualization of Algorithm (1)  (2)  (3)  (4)  (5)  (6)  (7)  (8)  (9)  59  (10)  (11)  (12)  (13)  (14)  (15)  Figure 16. Iterations of Barabási-Albert algorithm with m = 2 [Source: (Árpád, 2009)]  60  Appendix C: Homophily Algorithms Dynamic Social Impact Theory Grid Network Non-technical Description of Algorithm 1. Randomly select node in network 2. Record percentage of neighbors who are in the same group as node 3. For every neighbor of node record percentage of their neighbors who are in the same group as node 4. If a neighbor has a greater percentage of neighbors in the same group as node than node does, swap that neighbor with node 5. Repeat 1 – 4 for steps twice the number of nodes in network with no swaps occurring  Barabási-Albert Network Input Parameters Parameter N m b  Description Number of nodes Number of edges to attach from a new node to an existing node Amount of bias toward ingroup  Non-technical Description of Algorithm 1. Start with one node 2. Add a new node and randomly assign to a group. 3. Connect to m other nodes, where each node has a probability of being connected to that increases linearly with their existing number of connections. If existing nodes are in the same group as the new node, they have b times their chance based on existing number of connections. b=2 by default. 61  4. Repeat steps 1 and 2 until the network has N nodes  62  Appendix D: Experimental Software The experimental software was written in C# and the Microsoft Silverlight 4 application framework and ran over the Internet.  Screenshots of experiment  Figure 17. Avatar selection  63  Figure 18. Waiting screen  Figure 19. Participant number assignment  64  Figure 20. Selection from ingroup  Figure 21. Position assignment  65  Figure 22. Example question screen with other responses  66  Appendix E: Experimental Details Pre-testing Results  67  68  69  70  71  72  73  Experimental Questions Study 2 Subjective Type Subjective  Subjective  Subjective  Subjective  Subjective  Subjective  Subjective  Subjective  Subjective  Question Which of the following words sounds the nicest? Which of the following is your favorite sports brand? Who of the following is your favorite classical composer? Who of the following is your favorite rugby player? Who of the following is your favorite modern painter? Which of the following is your favorite John Irving novel? What is your preferred toilet paper orientation and technique? Who of the following is your favorite mathematician? Who of the following is your favorite basketball player?  Options Efflorescence  Diaphanous  Evanescent  Ineffable  Adidas  Reebok  Puma  Nike  Mahler  Elgar  Schubert  Haydn  Victor Matfield  Shane Williams  Bryan Habana  Mike Blair  Arevalo  Rosenquist  Tollmann  Bernal  A Prayer for Owen Meany  A Widow for One Year  The Hotel New Hampshire  A Son of the Circus  Over, scrunched  Over, folded  Under, scrunched  Under, folded  Lagrange  Hilbert  Riemann  Leibniz  Rajon Rondo  Chris Paul  Deron Williams  Kevin Durant  74  Type Objective  Objective  Objective Objective Objective  Objective  Objective Objective Objective  Question Which country has the tallest building in the world? Which of the following letters is the most common in Shakespeare? What is the smallest country in the world? Which book has sold the most copies? Which of the following seas is the smallest? In which state was the first McDonald's located? Which of the following birds is the smallest? How many piano keys are on a standard piano? What is the highest grossing film of all time?  Options Taiwan  Malaysia  China  United Arab Emirates  H  N  R  S  Nauru  Liechtenstein  Vatican City  Monaco  The Catcher in the Rye  To Kill a Mockingbird  The Da Vinci Code  1984  Balearic Sea  Timor Sea  Yellow Sea  Mawson Sea  California  Illinois  Kentucky  Indiana  Patagona gigas  Serinus canaria  Melopsittacus undulatus  Agapornis  80  86  88  92  Titanic  The Dark Knight  Lord of the Rings III  Avatar  75  Appendix F: Experiment Complete Raw Results Study 1 Participants Table 12. Study 1 participant demographics Participants N Age Female Highest Education All 186 33.19 103 (55%) 42 (23%) (17-62) High School 54 (29%) Post-secondary 63 (34%) Bachelors 27 (15%) Masters and above Guessed 157 33.52 86 (55%) 36 (19%) computer (17-62) High School players 49 (28%) removed Post-secondary 53 (28%) Bachelors 19 (10%) Masters and above Guessed 125 33.94 66 (53%) 25 (13%) computer (17-62) High School players and 39 (21%) guessed Post-secondary social 45 (24%) Bachelors influence 16 (9%) removed Masters and above Note. Age reported as Mean (Range)  76  Ethnicity 141 (76%) European 20 (11%) Other 8 (4%) Mixed 7 (4%) Hispanic 5 (3%) East Asian 4 (2%) African 1 (1%) South Asian 113 (61%) European 19 (10%) Other 8 (4%) Mixed 7 (4%) Hispanic 5 (3%) East Asian 4 (2%) African 1 (1%) South Asian 90 (48%) European 16 (9%) Other 6 (3%) Mixed 4 (2%) Hispanic 5 (3%) East Asian 3 (2%) African 1 (1%) South Asian  Dummy Coding Guide  Condition Subjective Experimental Objective Experimental Subjective Control Objective Control  V1 1 0 0 0  All Participants Question 7: Outgroup support  77  Dummy Variables V2 V3 0 0 1 0 0 1 0 0  V4 0 0 0 1  Question 8: Ingroup betrayal 1  78  Question 9: Ingroup betrayal 2  79  Question 10: Ingroup vs. outgroup  80  81  Suspicious about other player removed Question 7: Outgroup support  82  Question 8: Ingroup betrayal 1  83  Question 9: Ingroup betrayal 2  84  Question 10: Ingroup vs. outgroup  85  Suspicious about other players and guessed social learning removed Question 7: Outgroup support  86  Question 8: Ingroup betrayal 1  87  Question 9: Ingroup betrayal 2  88  Question 10: Ingroup vs. outgroup  89  Study 2 Participants Table 13. Study 2 participant demographics Participants All  N 378  Age 31.91 (15-73)  Female 212 (56%)  Guessed computer players removed  341  31.90 (15-73)  196 (57%)  Guessed 219 31.81 123 (56%) computer (15-73) players and guessed social influence removed Note. Age reported as Mean (Range)  Highest Education 98 (26%) High School 110 (29%) Post-secondary 117 (31%) Bachelors 53 (14%) Masters and above 90 (26%) High School 98 (29%) Post-secondary 105 (31%) Bachelors 48 (14%) Masters and above 64 (29%) High School 65 (30%) Post-secondary 61 (28%) Bachelors 29 (13%) Masters and above  Condition Coding Guide  Variable Cond/C Cond2/C2  Condition Subjective Objective 0 1 1 0  90  Ethnicity 213 (56%) European 85 (22%) Other 22 (6%) Mixed 22 (6%) Hispanic 17 (5%) African 14 (4%) East Asian 5 (1%) South Asian 185 (54%) European 82 (24%) Other 20 (6%) Mixed 20 (6%) Hispanic 15 (4%) African 14 (4%) East Asian 5 (1%) South Asian 99 (45%) European 63 (29%) Other 15 (7%) Mixed 16 (7%) Hispanic 12 (5%) African 9 (4%) East Asian 5 (2%) South Asian  All data All participants  91  Suspicious about other players removed  92  Suspicious about other players and guessed social learning removed  93  94  Results with global vs ingroup majority All participants  95  Suspicious about other players removed  96  Suspicious about other players and guessed social learning removed  97  98  

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