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The Sequential Dominance Argument for the Independence Axiom of Expected Utility Theory
Author(s) -
Gustafsson Johan E.
Publication year - 2021
Publication title -
philosophy and phenomenological research
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.7
H-Index - 39
eISSN - 1933-1592
pISSN - 0031-8205
DOI - 10.1111/phpr.12669
Subject(s) - rationality , axiom independence , expected utility hypothesis , lottery , mathematical economics , independence (probability theory) , axiom , argument (complex analysis) , irrational number , subjective expected utility , economics , mathematics , philosophy , epistemology , microeconomics , statistics , biochemistry , geometry , chemistry
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.