In 1953, a French economist named Maurice Allais conducted a survey of how people assess risk. Here are two scenarios that he used, each of which required people to choose between two options.
Decision 1:
Option A: 100% chance of gaining $1,000,000
Option B: 10% chance of gaining $2,500,000; 89% chance of gaining $1,000,000; and 1% chance of gaining nothing
Decision 2:
Option A: 11% chance of gaining $1,000,000 and 89% chance of gaining nothing Option B: 10% chance of gaining $2,500,000 and 90% chance of gaining nothing
Allais discovered that for decision 1, most people chose option A, while for decision 2, most people chose option B.
a. For each decision, find the expected value of each option.
b. Are the responses given in the survey consistent with the expected values?
c. Give a possible explanation for the responses in Allais's survey.