Daniel Kahneman Nobel Lecture

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The reference value to which current stimulation is compared also reflects

the history of adaptation to prior stimulation. A familiar demonstration in-

volves three buckets of water of different temperatures, arranged from cold

on the left to hot on the right, with tepid in the middle. In the adapting

phase, the left and right hands are immersed in cold and hot water, respec-

tively. The initially intense sensations of cold and heat gradually wane. When

both hands are then immersed in the middle bucket, the experience is heat

in the left hand and cold in the right hand.

Reference-dependence in choice

The facts of perceptual adaptation were in our minds when Tversky and I be-

gan our joint research on decision making under risk. Guided by the analogy

of perception, we expected the evaluation of decision outcomes to be refer-

ence-dependent. We noted, however, that reference-dependence is incom-

patible with the standard interpretation of Expected Utility Theory, the pre-

vailing theoretical model in this area. This deficiency can be traced to the

brilliant essay that introduced the first version of expected utility theory

(Bernoulli, 1738). 

One of Bernoulli’s aims was to formalize the intuition that it makes sense

for the poor to buy insurance and for the rich to sell it. He argued that the in-

crement of utility associated with an increment of wealth is inversely propor-

tional to initial wealth, and from this plausible psychological assumption he

derived that the utility function for wealth is logarithmic. He then proposed

that a sensible decision rule for choices that involve risk is to maximize the ex-

pected utility of wealth (the moral expectation). This proposition accom-

plished what Bernoulli had set out to do: it explained risk aversion, as well as

the different risk attitudes of the rich and of the poor. The theory of expect-

ed utility that he introduced is still the dominant model of risky choice. The

language of Bernoulli’s essay is prescriptive – it speaks of what is sensible or

reasonable to do – but the theory is also intended to describe the choices of

reasonable men (Gigerenzer et al., 1989). As in most modern treatments of

decision making, there is no acknowledgment of any tension between pre-

scription and description in Bernoulli’s essay. The idea that decision makers

evaluate outcomes by the utility of final asset positions has been retained in

economic analyses for almost 300 years. This is rather remarkable, because

the idea is easily shown to be wrong; I call it Bernoulli’s error. 

Bernoulli’s model is flawed because it is reference-independent: it assumes that

the value that is assigned to a given state of wealth does not vary with the de-

cision maker’s initial state of wealth.

2

This assumption flies against a basic

principle of perception, where the effective stimulus is not the new level of

2

What varies with wealth in Bernoulli’s theory is the response to a given change of wealth. This

variation is represented by the curvature of the utility function for wealth. Such a function 

cannot be drawn if the utility of wealth is reference-dependent, because utility then depends not

only on current wealth but also on the reference level of wealth.

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stimulation, but the difference between it and the existing adaptation level.

The analogy to perception suggests that the carriers of utility are likely to be

gains and losses rather than states of wealth, and this suggestion is amply sup-

ported by the evidence of both experimental and observational studies of

choice (see Kahneman & Tversky, 2000). The present discussion will rely on

two thought experiments, of the kind that Tversky and I devised when we de-

veloped the model of risky choice that we called Prospect Theory (Kahneman

& Tversky, 1979). 

Problem 2

Would you accept this gamble?

50% chance to win $150

50% chance to lose $100

Would your choice change if your overall wealth were lower by $100?

There will be few takers of the gamble in Problem 2. The experimental evi-

dence shows that most people will reject a gamble with even chances to win

and lose, unless the possible win is at least twice the size of the possible loss

(e.g., Tversky & Kahneman, 1992). The answer to the second question is, of

course, negative.

Next consider Problem 3:

Problem 3

Which would you choose?

lose $100 with certainty

or

50% chance to win $50

50% chance to lose $200

Would your choice change if your overall wealth were higher by $100?

In Problem 3, the gamble appears much more attractive than the sure loss.

Experimental results indicate that risk seeking preferences are held by a large

majority of respondents in choices of this kind (Kahneman & Tversky, 1979).

Here again, the idea that a change of $100 in total wealth would affect pref-

erences cannot be taken seriously. 

Problems 2 and 3 evoke sharply different preferences, but from a

Bernoullian perspective the difference is a framing effect: when stated in

terms of final wealth, the problems only differ in that all values are lower by

$100 in Problem 3 – surely an inconsequential variation. Tversky and I exam-

ined many choice pairs of this type early in our explorations of risky choice,

and concluded that the abrupt transition from risk aversion to risk seeking

could not plausibly be explained by a utility function for wealth. Preferences

appeared to be determined by attitudes to gains and losses, defined relative

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