Theory and Decision 67 (2):123-144 (2009)

Abstract
We consider the problem of extending a (complete) order over a set to its power set. The extension axioms we consider generate orderings over sets according to their expected utilities induced by some assignment of utilities over alternatives and probability distributions over sets. The model we propose gives a general and unified exposition of expected utility consistent extensions whilst it allows to emphasize various subtleties, the effects of which seem to be underestimated – particularly in the literature on strategy-proof social choice correspondences
Keywords preferences over sets  expected utility consistency  strategy-proofness
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DOI 10.1007/s11238-007-9066-y
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Even-Chance Lotteries in Social Choice Theory.Peter C. Fishburn - 1972 - Theory and Decision 3 (1):18-40.

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