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The effect of anxiety and defensiveness on testing expectation theories of decision making Wilson, William Taylor

Abstract

The general purpose of this study was to examine one approach to the study of the relationship of personality variables to expectation theories of gambling. The Coombs and Bezembinder (1964) method of testing expectation theories of gambling behaviour was used to determine how many, among a group of 77 subjects, obeyed each of four expectation theories. These four expectation theories were: EV theory, assuming the maximization of the product of objective prize values and actual probabilities of winning; EU theory, assuming maximization of the product of subjective prize values and actual probabilities of winning; SEV theory, assuming the maximization of the product of objective prize values and subjective probabilities of winning; and SEU theory, assuming the maximization of the product of subjective value of the prize and the subjective probability of winning. The Coombs and Bezembinder method consists of comparing an estimate of an individual's consistency of choices independent of expectation theory assumptions with estimates of consistency under assumptions basic to each of the four expectation theories. A lower value of the consistency estimate under assumptions of a given expectation theory than the value calculated independently of any expectation theory assumptions leads to rejection of that particular theory as a model for the subject's behavior. The Coombs and Bezembinder technique for determining whether an individual obeys the four expectation theories leads to the prediction of an ordering of the expectation theories with respect to the number of subjects who do not satisfy them. The procedure in the present study involved the presentation of 96 pairs of one-outcome gambles to 77 subjects in an introductory psychology class. A subject was required on each pair to choose between a gamble combining high risk with a large prize and a gamble combining a low risk with a small prize. It was found that EV theory was rejected for 57 subjects, EU theory for 31 subjects, SEV theory for 26 subjects and SEU theory for 14 subjects. The hypothesis of monotonicity in the number of rejections for the two sequences SEU-SEV-EV and SEU-EU-EV was accepted. A second hypothesis, that a higher proportion of females will obey the expectation theories than will males, was rejected. The subjects were subdivided into high and low anxious and high and low defensive groups groups on the basis of scores obtained on the Alpert and Haber Test Anxiety Scale and the Crowne and Marlowe Defensiveness Scale. An examination of the data was sufficient to reject the hypothesis that more low anxious-low defensive and high anxious-high defensive subjects would obey the four expectation theories than would subjects who were either low anxious-high defensive or high anxious-low defensive. There were, however, some statistically significant results obtained on the basis of several ad hoc analyses. Fewer high defensive males than low defensive males appeared to obey SEV theory. Furthermore, fewer males who were either high anxious-high defensive or low anxious-low defensive obeyed SEU and SEV theory than did males who were either low anxious-high defensive or high anxious-low defensive. On the basis of these results, it was recommended that further research be conducted on the relationships of personality variables to expectation theories of gambling. It was noted that the use of the Tversky method of testing expectation theories would permit the simultaneous examination of two approaches to the relationship of personality variables to decision making (personality variables versus propensity for risk and personality variables versus rationality of decision). Finally, with respect to technique, it was recommended that better ways of assessing personality variables be found and the subjects be fully trained and run individually through the experiment.

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