The Allais Paradox

The Allais Paradox
The Allais Paradox

The so-called rational choice models assume that in order to maximize utility people have consistent preferences and make decisions that express those preferences.

 Rational choice models, undeniably effective

By the mid-20th century, rational choice models dominated economics not only because those models could be built up from basic axioms and mathematical operations, but also because rational choice models were undeniably effective.

Economists and other social scientists used them to explain market behavior: how companies develop incentives for their workers, how consumers respond to changes in prices and even question seemingly outside economics like how people vote or why countries go to war.

But, in some ways the very power of rational choice models had a blinding effect on the social sciences. When people’s real-world decisions and deviated from what was predicted by those models then the behavior was questioned not the models.

The Allais paradox

Deviations from the models were often seen as unimportant anomalies, oddities of human behavior that were explained away or simply dismissed, but there have been clear examples that question the core assumptions of rational choice models
let me give you two: one is historical and one is modern. One of the first and clearest challenges to rational choice models particular to the idea of expected utility came from the economist Maurice Allais in 1953.

Allais was an economist’s economist, not some interloper from another field, he would later win a Nobel Prize for his work on how markets can be structured to be maximally efficient, including work on monetary supply and demand, but Allais was also interested in rationality and in particular how psychological factors might influence people’s choices. He proposed a simple experiment that has come to be known as the Allais paradox.

To make this paradox tangible let’s suppose that you are a contestant on a game show, you walk onto the stage and in front you are too large covered urns, each filled with 100 balls. On each ball is written a dollar amount, the host blindfold you while explaining that you’ll get to reach into one urn and pull out one ball to determine your prize.

The host goes on to explain the prizes that you might win in the urn to your left there are 33 balls that are worth $2500, 66 balls there were $2400 in one ball that is worth nothing. So you have a 99 and 100 chance of winning something in that urn. In the urn to your right all of the balls are worth $2,400 Which urn you choose?

Most people choose the earn on the right in scenarios like this first even though this the expected value of the earth on the left is high because of all those balls worth $2500. They’re afraid of that 1 in 100 chance of getting nothing. But let’s suppose you walk onto the stage and the host describes a different scenario: now the left turn has 33 balls that are worth $2500 and 67 that are worth nothing. The right urn has 34 balls that are worth $2400 and 66 that are worth nothing.

Most people choosing her on the left in scenarios like the second one, the difference between 34 balls and 33 balls doesn’t seem like a big deal so they go for the urn with the larger potential reward. So in the Allais paradox people choose the right arm in the first scenario, but the left turn in the second scenario. These two scenarios might have sounded different but the actually involved exactly the same trade-off.

The left turn has 33 balls that are worth $100 more than their counterparts in the right, but that also has one extra ball that’s worth nothing. Everything else is common across the two urns and rational choice models assume that you should make your decision based on the differences between your options, but the difference in small probabilities 0% versus 1% matter a lot more to us than differences in intermediate probabilities say 33% versus 34%.

This phenomenon is called probability waiting and it pervades behavior and many sorts of risky decisions from the willingness to purchase lottery tickets and infinitesimal odds to the bias toward cures and away from prevention and medical decision-making.

By successdotinc

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