The following example is taken from an experiment in Bar-Hillel (1973, p. 397):

Subjects were given the opportunity to bet on one of two events. Three types of events were used: (i) simple events, such as drawing a red marble from a bag containing 50 percent red marbles and 50 percent white marbles; (ii) conjunctive events, such as drawing a red marble seven times in succession, with replacement, from a bag containing 90 percent red marbles and 10 percent white marbles; and (iii) disjunctive events, such as drawing a red marble at least once in seven successive tries, with replacement, from a bag containing 10 percent red marbles and 90 percent white marbles. In this problem, a significant majority of subjects preferred to bet on the conjunctive event rather than on the simple event. Subject also preferred to bet on the simple event rather than on the disjunctive event.

Required: Show (using mathematics) that the result conflicts with the expected utility theory. What is this phenomenon called? What mechanisms and explanations have been proposed for it in the literature? How does it affect decision making under uncertainty? What aspects of individual behaviour, other than decision making under uncertainty, does this phenomenon affect? Have there been any suggestions in the literature to ameliorate or eliminate it? Discuss.

The journal article marked with * below is the main reading material. The remaining articles may be used to answer the questions completely. You may include other journal articles to improve your discussion. Note that unpublished online sources (i.e., webpages) are not acceptable.     

Reading List

Bar-Hillel, M. (1973). On the subjective probability of compound events. Organizational behavior and human performance, 9(3), 396-406.

Bergman, O., Ellingsen, T., Johannesson, M., & Svensson, C. (2010). Anchoring and cognitive ability. Economics Letters, 107(1), 66-68.
McElroy, T., & Dowd, K. (2007). Susceptibility to anchoring effects: How openness-to-experience influences responses to anchoring cues. Judgment and Decision making, 2(1), 48.
Oechssler, J., Roider, A., & Schmitz, P. W. (2009). Cognitive abilities and behavioral biases. Journal of Economic Behavior & Organization, 72(1), 147-152.
Strack, F., & Mussweiler, T. (1997). Explaining the enigmatic anchoring effect: Mechanisms of selective accessibility. Journal of personality and social psychology, 73(3), 437.
*Tversky, A., & Kahneman, D. (1974). Judgment under uncertainty: Heuristics and biases. science, 185(4157), 1124-1131.
Tversky, A., & Kahneman, D. (1992). Advances in prospect theory: Cumulative representation of uncertainty. Journal of Risk and uncertainty, 5(4), 297-323.