Johan E. Gustafsson
University of York
Independence is the condition that, if X is preferred to Y, then a lottery between X and Z is preferred to a lottery between Y and Z given the same probability of Z. Is it rationally required that one’s preferences conform to Independence? The main objection to this requirement is that it would rule out the alleged rationality of Allais and Ellsberg Preferences. In this paper, I put forward a sequential dominance argument with fairly weak assumptions for a variant of Independence (called Independence for Constant Prospects), which shows that Allais and Ellsberg Preferences are irrational. Hence this influential objection (that is, the alleged rationality of Allais and Ellsberg Preferences) can be rebutted. I also put forward a number of sequential dominance arguments that various versions of Independence are requirements of rationality. One of these arguments is based on very minimal assumptions, but the arguments for the versions of Independence which are strong enough to serve in the standard axiomatization of Expected Utility Theory need notably stronger assumptions.
Keywords independence  the Allais Paradox  the Ellsberg Paradox  money pumps  expected utility theory
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DOI 10.1111/phpr.12669
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Risk and Rationality.Lara Buchak - 2013 - Oxford University Press.
Rationality and Dynamic Choice: Foundational Explorations.Edward Francis McClennen - 1990 - Cambridge, England: Cambridge University Press.
Infinity, Causation, and Paradox.Alexander R. Pruss - 2018 - Oxford, England: Oxford University Press.

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