When respondents are given the following two choices A and B, a majority choose B over A.
Choice A: $5,000,000 with probability .10, $1,000,000 with probability .89; 0 with probability .01.
Choice B: $1,000,000 with probability 1.
When respondents are given the following two choices C and D, a majority choose C over D.
Choice C: $5,000,000 with probability .10 and 0 with probability .90.
Choice D: $1,000,000 with probability .11 and 0 with probability .89.
These choices are a violation of the principles of Expected Utility theory, which suggests that if one chooses B over A, then that person should choose D over C.
A potential explanation for this pattern of behaviour is the following.
A) In A, the 0.89 probability on $1,000,000 is underweighted, making the gamble relatively less appealing than the certain million. However, in C and D, the low probabilities of both gambles are now being over-weighted, making C the relatively more attractive choice.
B) This is an example of the well-known conjunction fallacy, where people evaluate the probability of a subset of an event as being higher than the event itself.
C) In A, the 0.89 probability on $1,000,000 is over-weighted making this gamble less appealing than the certain million. However, in C and D, the low probabilities of both gambles both gambles are now being under-weighted, making C the relatively more attractive choice.
D) People judge choices from some reference point and here the reference point is $1 million.

Question

Quizplus · Accepted Answer

This pattern of behavior is explained by the prospect theory, which suggests that people tend to overvalue certain outcomes over probabilistic ones, even when the expected value is higher. In choice A, the high probability of winning $1,000,000 is underweighted, making the certain $1,000,000 in choice B more appealing. Conversely, in choices C and D, the low probabilities are over-weighted, making the higher potential payout in C more attractive despite its lower probability, illustrating a shift in how probabilities are perceived when comparing high versus low probability events.

When Respondents Are Given the Following Two Choices a and B