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A weak version of Barberà-Kelly's Theorem

Abstract:

Lifting preferences over candidates to preferences over sets of candidates allows us to give a very natural notion of manipulability for social choice functions. In particular, we give simple conditions over the liftings entailing the manipulability of reasonable social choice functions. Our result is a weak version of Barbera and Kelly's Theorem, indeed it can be obtained from this last Theorem. However, we give a direct and very natural proof of our manipulability Theorem which is informative about the nature of the liftings allowing manipulability.