Answer to Question #227547 in Economics for Sachitha

Question

Suppose there is a covered bowl with 3 red balls and 6 other balls, which could be black or yellow. The Decision Maker [DM] doesn’t know how many black or yellow balls there are, other than there are 6 in total. The DM will choose one ball from the bowl; each ball is equally likely to be chosen. The DM is offered a choice between Option A, which pays off LKR1000 if a red ball is drawn (0 otherwise) or Option B, which pays off LKR1000 if a black ball is drawn (0 otherwise). The DM says she prefers A to B. The DM is then offered a choice between Option C, which pays off LKR1000 if a red or yellow ball is drawn (0 otherwise), or option D, which pays off LKR1000 if a black or yellow ball is drawn (0 otherwise). The DM says she prefers D to C. Argue that these preferences are not consistent with the things you learned about decision making under uncertainty and the basics of the theory of expected utility.

Answer 1

A rational player, when choosing a solution, tries to maximize a certain value (good); it seems natural to use the mathematical expectation of the good that appears as a result of the chosen decision as such a quantity. However, experience shows that in real life, many lottery participants choose a solution with a lower mathematical expectation, but also with a lower risk, which is indeed shown in the presented experience.