Is the Allais paradox due to appeal of certainty or aversion to zero?
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Is the Allais paradox due to appeal of certainty or aversion to zero? Elif Incekara‑Hafalir1 · Eungsik Kim2 · Jack D. Stecher3 Received: 24 June 2019 / Revised: 15 August 2020 / Accepted: 3 September 2020 © Economic Science Association 2020
Abstract We provide a novel but intuitive explanation for expected utility violations found in the Allais paradox: individuals are commonly averse to receiving nothing. We call this phenomenon the zero effect. Our laboratory experiments show support for the zero effect. By contrast, the evidence for the certainty effect is weak to nonexistent. Keywords Allais paradox · Certainty effect · Common consequence · Common ratio · Decision theory · Zero effect
1 Introduction The Allais (1953) paradox is a systematic pattern of choice under risk that violates expected utility theory. The pattern involves choosing a certain, strictly positive payment over a risky lottery that has positive probability of a zero outcome, then making the opposite choice if both alternatives are modified in an identical way such that both can yield a zero outcome. It is widely accepted that this behavior reflects Electronic supplementary material The online version of this article (https://doi.org/10.1007/s1068 3-020-09678-4) contains supplementary material, which is available to authorized users. * Elif Incekara‑Hafalir [email protected] Eungsik Kim [email protected] Jack D. Stecher [email protected] 1
Present Address: University of Technology Sydney, City Campus, Haymarket Dr Chau Chak Wing Building 8, Lv 9, Rm 012, Po Box 123, Broadway, Sydney NSW 2007, Australia
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Present Address: University of Kansas, Snow Hall 339, 1460 Jayhawk Blvd, Lawrence, Lawrence, KS, USA
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Present Address: University of Alberta, 340J Business Building, Edmonton, AB T6G 2R6, Canada
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an added appeal of a riskless decision, a phenomenon that Kahneman and Tversky (1979) call the certainty effect (defined precisely in Wakker 2010; Schneider and Schonger 2019 as an additional appeal of lotteries with zero variance). Our purpose in this paper is to challenge this interpretation. We argue that avoidance of zero, rather than attraction to certainty, is a more compelling explanation. We call our alternative explanation the zero effect, and note that it reflects a previously unrecognized confound. In all four lotteries in standard Allais-type tasks, the only lottery without a possible zero outcome is the certain lottery. Therefore, the certainty effect and the zero effect lead to the same pattern of choice. By getting participants to make additional choices, we are able to separate the certainty effect from the zero effect, and to test the ability of each to explain the Allais paradox. Before describing our experiments and analysis, we provide some illustrations. In the common consequence task Allais (1953) presents, participants choose between the following alternatives: { 1 million francs, with an 11% chance A= 0, with an 89% chance
vs. B=
{
5 milli
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