Peter Norvig on Allais Paradox - Dictionary of Arguments
Norvig I 619
Allais Paradox/Irrationality/Norvig/Russell: The evidence suggests that humans are “predictably irrational” (Ariely, 2009)(1).
Norvig I 620
Allais paradox: The best-known problem is the Allais paradox (Allais, 1953). People are given a choice between lotteries A and B and then between C and D, which have the following prizes: A : 80% chance of $4000 C : 20% chance of $4000 B : 100% chance of $3000 D : 25% chance of $3000
Most people consistently prefer B over A (taking the sure thing), and C over D (taking the higher expected maximum value, EMV). The normative analysis disagrees! We can see this most easily if we use the freedom implied by Equation (16.2) to set U($0) = 0. In that case, then B -> A implies that U($3000) > 0.8 U($4000), whereas C -> D implies exactly the reverse. In other words, there is no utility function that is consistent with these choices. One explanation for the apparently irrational preferences is the certainty effect (Kahneman and Tversky, 1979)(2): people are strongly attracted to gains that are certain. >Certainty effect/Kahneman/Tversky, >Ambiguity/Kahneman/Tversky, >Rationality/AI research, >Preferences/Norvig, >Utility/AI research.
Norvig I 638
The Allais paradox, due to Nobel Prize-winning economist Maurice Allais (1953)(3) was tested experimentally (Tversky and Kahneman, 1982(4); Conlisk, 1989(5)) to show that people are consistently inconsistent in their judgments.
1. Ariely, D. (2009). Predictably Irrational (Revised edition). Harper.
2. Kahneman, D. and Tversky, A. (1979). Prospect theory: An analysis of decision under risk. econometrica, pp. 263–291.
3. Allais, M. (1953). Le comportment de l’homme rationnel devant la risque: critique des postulats et
axiomes de l’´ecole Am´ericaine. Econometrica, 21, 503–546.
4. Tversky, A. and Kahneman, D. (1982). Causal schemata in judgements under uncertainty. In Kahneman,
D., Slovic, P., and Tversky, A. (Eds.), Judgement Under Uncertainty: Heuristics and Biases. Cambridge University Press.
5. Conlisk, J. (1989). Three variants on the Allais example. American Economic Review, 79(3), 392–407._____________Explanation of symbols: Roman numerals indicate the source, arabic numerals indicate the page number. The corresponding books are indicated on the right hand side. ((s)…): Comment by the sender of the contribution. Translations: Dictionary of Arguments The note [Author1]Vs[Author2] or [Author]Vs[term] is an addition from the Dictionary of Arguments. If a German edition is specified, the page numbers refer to this edition.
Stuart J. Russell
Artificial Intelligence: A Modern Approach Upper Saddle River, NJ 2010