“Allais paradox”的概念、定义、翻译、参考文献-科学参考

Allais paradox

Philosophy

A paradox in decision theory. Suppose you are offered a choice between two gambles:
1. Gamble 1: $500,000 with probability of 1
2. 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:
1. Gamble 3: $500,000 with probability 0·11; $0 with probability 0·89
2. 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 expected 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.
http://www.sfb504.uni-mannheim.de/glossary/allais.htm An account of the paradox’s theoretical context, with links to related issues
http://cepa.newschool.edu/het/essays/uncert/choiceref.htm A bibliography of scholarly articles on the paradox and related issues

Economics

An example of choice under uncertainty where the outcome for most experimental subjects violates the axioms of expected utility theory. In the first experiment subjects are requested to choose between winning £1 million for sure and a gamble in which the prizes are £1 million with probability 0.89, £5 million with probability 0.10, and nothing with probability 0.01. Most experimental subjects would choose the option of £1 million for sure. In the second experiment the choice is between two different gambles. For the first gamble the prizes are nothing with probability 0.89 and £1 million with probability 0.11. The second gamble has prizes of nothing with probability 0.90 and £5 million with probability 0.10. Most subjects choose the second gamble. These typical choices violate the independence axiom of expected utility theory: if the first option is chosen in the first experiment then the first option should also be chosen in the second experiment. The Allais paradox and other similar examples have motivated the search for alternatives to expected utility theory. See also anomalies; behavioural economics; decision theory; prospect theory.

单词	Allais paradox
释义	Allais paradox Philosophy 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 expected 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. http://www.sfb504.uni-mannheim.de/glossary/allais.htm An account of the paradox’s theoretical context, with links to related issues http://cepa.newschool.edu/het/essays/uncert/choiceref.htm A bibliography of scholarly articles on the paradox and related issues Economics An example of choice under uncertainty where the outcome for most experimental subjects violates the axioms of expected utility theory. In the first experiment subjects are requested to choose between winning £1 million for sure and a gamble in which the prizes are £1 million with probability 0.89, £5 million with probability 0.10, and nothing with probability 0.01. Most experimental subjects would choose the option of £1 million for sure. In the second experiment the choice is between two different gambles. For the first gamble the prizes are nothing with probability 0.89 and £1 million with probability 0.11. The second gamble has prizes of nothing with probability 0.90 and £5 million with probability 0.10. Most subjects choose the second gamble. These typical choices violate the independence axiom of expected utility theory: if the first option is chosen in the first experiment then the first option should also be chosen in the second experiment. The Allais paradox and other similar examples have motivated the search for alternatives to expected utility theory. See also anomalies; behavioural economics; decision theory; prospect theory.
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