“history of one’s wealth” : Other factors contributed to the longevity of
Bernoulli’s theory. One is that it is natural to formulate choices between
gambles in terms of gains, or mixed gains and losses. Not many people
thought about choices in which all options are bad, although we were by no
means the first to observe risk seeking. Another fact that favors Bernoulli’s
theory is that thinking in terms of final states of wealth and ignoring the past
is often a very reasonable thing to do. Economists were traditionally
concerned with rational choices, and Bernoulli’s model suited their goal.

26: Prospect Theory

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subjective value of wealth : Stanley S. Stevens, “To Honor Fechner and
Repeal His Law,” Science 133 (1961): 80–86. Stevens, Psychophysics.
The three principles : Writing this sentence reminded me that the graph of
the value function has already been used as an emblem. Every Nobel
laureate receives an individual certificate with a personalized drawing,
which is presumably chosen by the committee. My illustration was a
stylized rendition of figure 10.
“loss aversion ratio” : The loss aversion ratio is often found to be in the
range of 1. 5 and 2.5: Nathan Novemsky and Daniel Kahneman, “The
Boundaries of Loss Aversion,” Journal of Marketing Research 42 (2005):
119–28.
emotional reaction to losses : Peter Sokol-Hessner et al., “Thinking Like a
Trader Selectively Reduces Individuals’ Loss Aversion,” PNAS 106
(2009): 5035–40.
Rabin’s theorem : For several consecutive years, I gave a guest lecture in
the introductory finance class of my colleague Burton Malkiel. I discussed
the implausibility of Bernoulli’s theory each year. I noticed a distinct change
in my colleague’s attitude when I first mentioned Rabin’s proof. He was
now prepared to take the conclusion much more seriously than in the past.
Mathematical arguments have a definitive quality that is more compelling
than appeals to common sense. Economists are particularly sensitive to
this advantage.
rejects that gamble : The intuition of the proof can be illustrated by an
example. Suppose an individual’s wealth is W, and she rejects a gamble
with equal probabilities to win $11 or lose $10. If the utility function for
wealth is concave (bent down), the preference implies that the value of $1
has decreased by over 9% over an interval of $21! This is an
extraordinarily steep decline and the effect increases steadily as the
gambles become more extreme.
“Even a lousy lawyer” : Matthew Rabin, “Risk Aversion and Expected-Utility
Theory: A Calibration Theorem,” Econometrica 68 (2000): 1281–92.