Volume 114, Issue 1, January 2017
Luc Lauwers, Peter Vallentyne
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.