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The Journal of Philosophy

Volume 114, Issue 1, January 2017

Luc Lauwers, Peter Vallentyne
Pages 33-42

A Tree Can Make a Difference

We show that it is not possible to extend the ranking of one-stage lotteries based on their weak-expectation (Easwaran 2008) to a reflexive and transitive (but possibly incomplete) relation on the collection of one- and two-stage lotteries that satisfies two basic axioms, the minimal value axiom and the reduction axiom. We propose an extension that satisfies only the first axiom. This ranking takes payoffs, their probabilities, and the tree structure into account.

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