User:Yungam99/Lottery (probability)

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The paradox argued by Allais complicates expected utility in the lottery. In contrast to the former example, let there be outcomes consisting of only losing money. The situation 1 is that option 1-a has a certain loss of $500, and option 1-b has the same probability of losing $1000 or $ 0. The other situation 2 is that option 2-a has 0.1 chance of  losing $500 and 0.9 chance of losing $0, and option 2-b has 0.05 chance of losing $ 1000 and 0.95 chance of losing $0. This circumstance can be described as expected utility equations below.

• Situation 1

a. U(-$500)

b. 0.5 U(-$1000) + 0.5 U($0)

• Situation 2

a. 0.1 U(-$500) + 0.9 U($0)

b. 0.05 U(-$1000) + 0.95 U($0)

Many people tend to make different decisions between situations. People prefer option 1-a to 1-b in situation 1, and 2-b to 2-a in situation 2. However two situations have the same structure, which causes paradox.

• Situation 1. U(-$500) > 0.5 U(-$1000) + 0.5 U($0)

• Situation 2.

0.1 U(-$500) + 0.9 U($0) < 0.05 U(-$1000) + 0.95 U($0)

0.1 U(-$500) < 0.05 U(-$1000) + 0.05 U($0)

U(-$500) < 0.5 U(-$1000) + 0.5 U($0)

The possible explanations for the above is that it has a ‘certainty effect’, that the outcomes without probabilities (determined in advance) will make a larger effect on the utility functions and final decisions. In many cases, this focusing on the certainty may cause inconsistent decisions and preferences. Plus, people tend to find some clues from the format or context of the lotteries.

It was additionally argued that how much people got trained about statistics could impact the decision making in the lottery. Throughout a series of experiments, he concluded that a person statistically trained will be more likely to have consistent and confident outcomes which could be a generalized form.