Question

5. In 1953, a French economist named Maurice Allais conducted a survey of how people assess risk. He gave each surveyed person two scenarios, and they had to choose one option in each.  

Scenario 1: You have a choice of (A) a 100% chance of gaining $1 million, or (B) a 10% chance of gaining $2.5 million, a 89% chance of gaining $1 million and a 1% chance of gaining nothing.

Scenario 2: You have a choice of (A) an 11% chance of gaining $1 million and a 89% chance of gaining nothing, or (B) a 10% chance of gaining $2.5 million and a 90% chance of gaining nothing.

Allais discovered that for Scenario 1, most people choose A, while for Scenario 2, most people choose B.

For each decision, find the expected value of each scenario. Are the responses given by the survey participants consistent with the expected values? Explain.

Answer 1

Scenario 1

Expected value= probability*amount gained

A ---> 100% chance of gaining $ 1 million

E(A)=1*1= $1 million

B --> 10% chance of gaining$2.5 million ,89% chance of gaining $1 million and 1% chance of gaining nothing

E(B)= 0.1(2.5)+0.89(1)+0.01(0)= 0.25+0.89=1.14

E(B) = $1.14 million

E(B) is more than E(A)

Most people choose B

Scenario 2

A --> 11% chance of gaining$1 and 89% chance of gaining nothing

E(A)= 0.11(1)+0.89(0)= 0.11

B --> 10% chance of gaining$2.5 million and 90% chance of gaining nothing

E(B)= 0.10(2.5)+0.90(0)= 0.25

E(B) is more than E(A)

Most people choose B

According to Allais for scenario 1 most people choose A but we found that B has more expected value than A.

For scenario 2 most people choose B. We also found that same as B has more expected value than A.