Thinking, Fast and Slow

Kahneman discovered the flaws in Bernoulli’s theory because he noticed that gambles were often spoken of in terms of a few pennies. He wondered if it was possible to assume that people evaluate gambles by tiny differences in wealth. Likewise, Tversky quickly realized that another economist had proposed that utilities were attached to changes of wealth rather than states of wealth.

In utility theory, there is no way to represent the fact that gains and losses have different utilities. These differences were neither expected nor studied. When Kahneman and Tversky casually shifted from speaking about winning to speaking about losing in different thought experiments, they realized that their preferences shifted as well.

Kahneman asks readers to consider two problems: 1) Get $900 for sure OR 90% chance to get $1,000; 2) Lose $900 for sure OR 90% chance to lose $1,000. Most people choose the sure thing in the first problem and the gamble in the second. In the second problem the sure loss is very aversive, and this drives people to take the risk. People become risk-seeking when all options are bad. Bernoulli’s theory did not have a way to accommodate this difference.

Kahneman gives two more problems: 1) You are given $1,000. You are then asked to choose between a 50% chance to win an additional $1,000 OR get $500 for sure. 2) You are given $2,000. You are then asked to choose between a 50% chance to lose $1,000 OR lose $500 for sure. In both problems, the final states of wealth are identical. According to Bernoulli’s theory, people should have the same preferences in both. In reality, people are risk-averse in the first problem (choosing the sure thing) and risk-seeking in the second (choosing the gamble).

Kahneman and Tversky found three cognitive features at the heart of prospect theory: 1) Evaluation is relative to a neutral reference point—outcomes that are better than the reference points are gains. Below the reference point they are losses. 2) A principle of diminishing sensitivity applies to wealth. The difference between $900 and $1,000 is smaller than the difference between $100 and $200. 3) Losses loom larger than gains.

Many options we face in life are choices between a risk of loss and opportunity for gain. A simple example is this: if a coin shows tails, you lose $100. If a coin shows heads, you win $150. For most people, the fear of losing is more intense than the hope of gaining. To balance the potential loss of $100, most people require the opportunity to win about $200. The greater the potential loss, the more people usually require to offset that loss in a gamble.

Kahneman points out another flaw in Bernoulli’s theory, proved by Matthew Rabin in 2000. He notes that most Humans reject this gamble: 50% chance to lose $100 and 50% to win 200. According to utility theory, that same Human will also turn down this gamble: 50% chance to lose $200 and 50% chance to win $20,000—but of course, no one would turn down this gamble.

Kahneman admits that there are benefits to utility theory, especially in introductory economic texts. The basic concepts of economics are not easy and are also grounded in rationality. Introducing psychology makes those concepts even more complicated.

Prospect theory also has flaws. Consider three gambles: A) One chance in a million to win $1 million. B) 90% chance to win $12 and 10% chance to win nothing. C) 90% chance to win $1 million and 10% chance to win nothing. In each case, winning nothing is possible and prospect theory assigns the same value to each instance of winning nothing—a value of zero. In reality, this is true of the first two options, but in the third option the idea of winning nothing is intensely disappointing. Prospect theory does not change the value of an outcome when it is highly unlikely, or when the alternative is valuable.

Prospect theory and utility theory also fail to allow for regret. Consider problem 6: Choose between 90% chance to win $1 million OR $50 with certainty. Now problem 7: Choose between 90% chance to win $1 million OR $150,000 with certainty. Failing to win is disappointing in both, but problem 7 is made even worse by knowing that if you choose the gamble and lose you will regret the “greedy” decision of not opting for a sure $150,000.