The Allais Paradox

One of the first observed and best known errors people make when told probabilities is the Allais paradox.  People put too much weight on rare extreme outcomes.  This means that choices people make different choices when asked to choose between two  lotteries with the same probabilities of the same outcomes depending on how they are described.

Why do people perceive such a big difference between 99% and 100%, One explanation is that we are used to being offered chances to gamble by crooks. More generally, when we are told something, we consider the possibility that the person telling us is lying. If so it can matter whether we can prove beyond reasonable doubt that they lied. If they say something will happen with 100% probability and something else happens, we can be sure that they told us something false and can prove, it.  If they say it will happen with 99% probability and it doesn’t we can’t know for sure or prove.  So in the case of possible litigation or criminal accusation, 99% is very different from 100 %.  I think subjects don’t have to consciously think about this for the habit of avoiding cases in which we are promised something are favored over cases where we are told something which is not a promise.

This is a possible explanation of uncertainty aversion too.  I won’t explain the Ellsberg paradox.  The point is that people like the case in which they are told something that can be tested by breaking open an urn and checking that it does indeed contain 50 red balls and 50 green balls. They have no intention of breaking laboratory equipment, but still, from habit, prefer a situation in which the other person’s assertions can be tested and proven false if they are false.

The mistakes are still mistakes, but they are comprehensible mistakes.