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Risk and Rationality$
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Lara Buchak

Print publication date: 2013

Print ISBN-13: 9780199672165

Published to Oxford Scholarship Online: April 2014

DOI: 10.1093/acprof:oso/9780199672165.001.0001

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(p.82) 3Representation
Risk and Rationality

Lara Buchak

Oxford University Press

This chapter provides a representation theorem for risk-weighted expected utility theory (proved in the Appendices). The theorem outlines a set of constraints on individuals’ preferences that are strictly weaker than the constraints of expected utility theory. It is shown that if an individual’s preferences meet these constraints, then we can represent her beliefs, her desires, and her attitude towards risk by precise numerical values. The dispute between expected utility theory and risk-weighted expected utility theory is characterized in terms of whether to accept an axiom known as Tradeoff Consistency or instead a combination of two weaker axioms: Comonotonic Tradeoff Consistency and Strong Comparative Probability. It is shown that this dispute corresponds to forbidding or allowing individuals to care about global properties of gambles.

Keywords:   representation theorem, tradeoff consistency, comonotonic tradeoff consistency, comonotonicity, strong comparative probability, risk-weighted expected utility, expected utility, risk

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