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COPYRIGHT NOTICE: Edited by Richard H. Thaler: Advances in Behavioral Finance, Volume II - page 19 / 23





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Kahneman and Tversky (1979) also offer the following violation of EU as evidence that people focus on gains and losses. Subjects are asked:12

In addition to whatever you own, you have been given 1000. Now choose between

A (1000, 0.5) B (500, 1).

B was the more popular choice. The same subjects were then asked:

In addition to whatever you own, you have been given 2000. Now choose between

C (1000, 0.5) D (500, 1).

This time, C was more popular.

Note that the two problems are identical in terms of their final wealth positions and yet people choose differently. The subjects are apparently fo- cusing only on gains and losses. Indeed, when they are not given any infor- mation about prior winnings, they choose B over A and C over D.

The second important feature is the shape of the value function υ, namely its concavity in the domain of gains and convexity in the domain of losses. Put simply, people are risk averse over gains, and risk-seeking over losses. Simple evidence for this comes from the fact just mentioned, namely that in the absence of any information about prior winnings13

Β f Α, C f D.

The υ function also has a kink at the origin, indicating a greater sensitivity to losses than to gains, a feature known as loss aversion. Loss aversion is introduced to capture aversion to bets of the form:

E (110,

1 2


  • 100,

1 2


It may seem surprising that we need to depart from the expected utility framework in order to understand attitudes to gambles as simple as E, but it is nonetheless true. In a remarkable paper, Rabin (2000) shows that if an expected utility maximizer rejects gamble E at all wealth levels, then he will also reject


1 2


  • 1000,

1 2


an utterly implausible prediction. The intuition is simple: if a smooth, in- creasing, and concave utility function defined over final wealth has sufficient

All the experiments in Kahneman and Tversky (1979) are conducted in terms of Israeli currency. The authors note that at the time of their research, the median monthly family in- come was about 3,000 Israeli lira. 12

In this section G1 f G2 should be read as “a statistically significant fraction of Kahneman and Tversky’s subjects preferred G1 to G2.” 13

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