Generalizing the Gibbard–Satterthwaite theorem: partial preferences, the degree of manipulation, and multi-valuedness
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The Gibbard–Satterthwaite (GS) theorem is generalized in three ways: First, it is proved that the theorem is still valid when individual preferences belong to a convenient class of partial preferences; second, it is shown that every non-dictatorial surjective social choice function (SCF) is not only manipulable, but it can be manipulated in such a way that some individual obtains either his best or second best alternative; third, we prove a variant of the theorem where the outcomes of the SCF are subsets of the set of alternatives of an a priori fixed size. In addition, all results are proved not only for finite, but also for countably infinite sets of alternatives.
KeywordsEcon Theory Pareto Optimality Social Choice Function Strategic Vote Preference Domain
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- Barberà S, Bossert W, Pattanaik P (2004) Ranking sets of objects. In: Barberà S, Hammond P, Seidl C (eds) Handbook of utility theory, vol 2. Kluwer academic publishers, BostonGoogle Scholar
- Mas-Colell A, Whinston M, Green J (1995) Microeconomic theory. Oxford University PressGoogle Scholar
- Sen A (1970) Collective choice and social welfare. Holden-Day, San FranciscoGoogle Scholar
- Svensson LG (1999) The proof of the Gibbard-Satterthwaite theorem revisited. Working Paper Series 1999:1, Department of Economics, Lund UniversityGoogle Scholar