The Ellsberg paradox is a paradox in decision theory in which people’s choices violate the postulates of subjective expected utility.[1] It is generally taken to be evidence for ambiguity aversion. The paradox was popularized by Daniel Ellsberg, although a version of it was noted considerably earlier by John Maynard Keynes.[2]

The basic idea is that people overwhelmingly prefer taking on risk in situations where they know specific odds rather than an alternate risk scenario in which the odds are completely ambiguous—even when mathematically the odds are identical.[3][unreliable source?] That is, given a choice of risks to take (such as bets), people “prefer the devil they know” rather than assuming a risk where odds are difficult or impossible to calculate.[4]

Ellsberg actually proposed two separate thought experiments, the proposed choices which contradict subjective expected utility. The 2-color problem involves bets on two urns, both of which contain balls of two different colors. The 3-color problem, described below, involves bets on a single urn, which contains balls of three different colors.

Generality of the paradox

Note that the result holds regardless of your utility function. Indeed, the amount of the payoff is likewise irrelevant. Whichever gamble you choose, the prize for winning it is the same, and the cost of losing it is the same (no cost), so ultimately, there are only two outcomes: you receive a specific amount of money, or you receive nothing.

A modification of utility theory to incorporate uncertainty as distinct from risk is Choquet expected utility, which also proposes a solution to the paradox.

Alternative explanations

Other alternative explanations include the competence hypothesis [7] and comparative ignorance hypothesis.[5] These theories attribute the source of the ambiguity aversion to the participant’s pre-existing knowledge.

Allais paradox

Ambiguity aversion

Subjective expected utility

Utility theory

References

Jump up ^ Ellsberg, Daniel (1961). “Risk, Ambiguity, and the Savage Axioms”. Quarterly Journal of Economics 75 (4): 643–669. doi:10.2307/1884324. JSTOR 1884324.

Schmeidler, D. (1989). “Subjective Probability and Expected Utility without Additivity”. Econometrica 57 (3): 571–587. doi:10.2307/1911053. JSTOR 1911053. edit

Categories:

Economics paradoxes

Economics of uncertainty

Decision theory

Decision theory paradoxes

Utility

Statistical paradoxes

Paradoxes

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This situation poses both Knightian uncertainty – how many of the non-red balls are yellow and how many are black, which is not quantified – and probability – whether the ball is red or non-red, which is ⅓ vs. ⅔.

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