Allais Paradox

The Allais paradox is an interesting phenomenon which proves that people fail to make decisions in a way that would maximize their ulitity/pay off/benefit.
Consider the following two problems:

Problem 1
Which of the following situations would you prefer:

Situation A

$100.00 for certain

Situation B

A 10% chance of winning $500.00
An 89% chance of winning $100.00
A 1% chance of winning nothing


Problem 2
Which of the following situations would you prefer:

Situation C

An 11% chance of winning $100.00
An 89% chance of winning nothing

Situation D

A 10% chance of winning $500.00
A 90% chance of winning nothing



Many studies presented participants with this problem and obtained identical results. Majority of people prefer A to B in Problem 1, and D to C in Problem 2.
For us to decide whether these choices are appropriate, we are required to calculate the utility of each situation. This is very simple to compute, we just need to multiply a pay off and its probability for each situation.

Problem 1
Which of the following situations would you prefer:

Situation A

Utility= $100.00 * 100% = $100.00

Situation B

Utility= $500.00 * 10% = $50.00
Utility (2)= $100.00 * 89% = $89.00
Utility (3)= 0$ * 1% = $0

Total Utility= $50.00 + $89.00 + $0 = $139.00

Since $100.00 < $139.00, Situation A is worse than B.

Problem 2
Which of the following situations would you prefer:

Situation C

Utility= $100.00 * 11% = $11.00
Utility (2)= $0 * 89% = $0

Situation D

Utility= $500,00 * 10% = $50.00
Utility (2)= $0 * 90% = $0

Since $11,00 < $50.00, Situation C is worse than D

Although people make a right choice in Problem 2, they fail in Problem 1...

Now comes the interesting part. Two utilities to chose from in Problem 1 are: $100.00 and $139.00. Therefore, the latter is better by $39.00 ($139,00-$100.00).
Now consider the second problem, where two of the utilities are: $11.00 and $50.00. The latter is better by $39.00 as well!!!! ($50.00-$11.00)

What happens here is that two problems are in fact identical in terms of utlitity. In both, the second situation is better by $39.00. People however, fail to see it when they make their choice and wrongly chose the worse option in problem 1.

This is known as Allais Paradox and is very interesting for psychologists who study effects of certainty and uncertainty on people's choice behaviour.

Hardman, D. (2009). Judgment and Decision Making: Psychological Perspective.

Oxford: Blackwell