# What does Paradox 2

## Allais paradox

M. Allais demonstrated violation of decision-makers against the axiom of independence and thus against the Bernoulli principle (expected utility theory).

To clarify, two electoral situations are considered: In electoral situation A, the decision maker has between the sure win 3000 (A_{1}) and a lottery (A_{2}), where there is a probability of 80% that he will win 4000 (with an opposite probability of 20% he will win nothing). In election situation B, the decision maker has to choose between a lottery (A_{3}), in which there is a 25% probability of winning 3000 (with the opposite probability of 75% he will not win anything), and a lottery (A._{4}), where there is a 20% probability of winning 4000 (with an opposite probability of 80% he will not win anything).

If the decision maker is rational in the sense of the Bernoulli Principle, he will either be A._{1} and A_{3} or A_{2} and A_{4} prefer but not A_{1} and A_{4} or A_{2} and A_{3}. Real decision-makers, however, often draw A._{1} and A_{4} in front. This means a violation of the axiom of independence.

The Allais paradox was explained by the security effect (D. Kahneman and A. Tversky, Prospect Theory - An Analysis of Decision under Risk, Econometrica 47 (1979), pp. 263-292). According to this effect, certain results are overweighted compared to probable results, i.e. the evaluation of a certain result exceeds the evaluation of an equally high, non-certain result more than the difference in the probability of occurrence implies. In the example, the profit of 3000 on the transition from A_{3} on A_{1} Sure, the profit of 4000 remains with the transition from A_{4} on A_{2} unsure what A_{1} relative to A_{2} more attractive, although the probability of winning quadruples each time (from 25% to 100% when moving from A_{3} on A_{1} and from 20% to 80% when transitioning from A_{4} on A_{2}).

See also prospect theory.

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