﻿
A paradox in decision theory. Suppose you are offered a choice between two gambles:
Gamble 1: \$500,000 with probability of 1
Gamble 2: \$2,500,000 with probability 0.1; \$500,000 with probability 0.89; \$0, with probability 0.01.
Many people will prefer the first option. Now suppose you are offered a choice between another two gambles:
Gamble 3: \$500,000 with probability 0.11; \$0 with probability 0.89
Gamble 4: \$2,500,000 with probability 0.1; \$0 with probability 0.9.
Many people will take the second. The problem is that this pair of preferences is not consistent with any utility function. For from the first choice we have it that
U(\$500,000) > 0.1U(\$2,500,000) + 0.89U(\$500,000) + 0.01U(\$0)
and from the second choice we have it that
0.1U(\$2,500,000) + 0.9U(\$0) > 0.11U(\$500,000) + 0.89U(\$0)
but these are inconsistent: by the first equation
0.11U(\$500,000) – 0.01U(\$0) > 0.1U(\$2,500,000)
but by the second equation the inequality is reversed. Although the paradox can be used to attack the sure thing principle, another approach is to use it to educate choices, so that if one genuinely prefers gamble 1 to gamble 2, one learns to reverse the initial feeling that gamble 4 is a better choice than gamble 3.

Philosophy dictionary. . 2011.

### Look at other dictionaries:

• Allais paradox — The Allais paradox is a choice problem designed by Maurice Allais to show an inconsistency of actual observed choices with the predictions of expected utility theory. Contents 1 Statement of the Problem 2 Mathematical proof of inconsistency 2.1… …   Wikipedia

• Paradox — Ein Paradoxon oder Paradox (altgriechisch παράδοξον, von παρα , para – gegen und δόξα, dóxa – Meinung, Ansicht), auch Paradoxie (παραδοξία) und in der Mehrzahl Paradoxa g …   Deutsch Wikipedia

• Maurice Allais — Walrasian economics Born 31 May 1911(1911 05 31) Paris …   Wikipedia

• Maurice Allais — Pour les articles homonymes, voir Allais. Maurice Félix Charles Allais Maurice Félix Charles Allais en 2001 …   Wikipédia en Français

• Ellsberg paradox — The Ellsberg paradox is a paradox in decision theory and experimental economics in which people s choices violate the expected utility hypothesis.Citation |last=Ellsberg|first=Daniel|authorlink=Daniel Ellsberg|journal=Quarterly Journal of… …   Wikipedia

• Maurice Allais — A French economist who won the 1988 Nobel Prize in Economics for his research on market equilibrium and efficiency. He also won a prestigious French award, the Gold Medal of the National Center for Scientific Research; developed methods that… …   Investment dictionary

• Ellsberg-Paradox — Das Ellsberg Paradoxon ist ein aus der Entscheidungstheorie bekanntes Phänomen der Entscheidung unter Unsicherheit. Wenn Menschen sich zwischen zwei Optionen entscheiden müssen, und nur bei einer Option die Wahrscheinlichkeitsverteilung bekannt… …   Deutsch Wikipedia

• Behavioral economics — and its related area of study, behavioral finance, use social, cognitive and emotional factors in understanding the economic decisions of individuals and institutions performing economic functions, including consumers, borrowers and investors,… …   Wikipedia

• Disappointment — For other uses, see Disappointment (disambiguation). Disappointment expressed by a team of American football players commiserating after a defeat. Disappointment is the feeling of dissatisfaction that follows the failure of expectations or hopes… …   Wikipedia

• List of paradoxes — This is a list of paradoxes, grouped thematically. Note that many of the listed paradoxes have a clear resolution see Quine s Classification of Paradoxes.Logical, non mathematical* Paradox of entailment: Inconsistent premises always make an… …   Wikipedia