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2004•RePEc: Research Papers in EconomicsRequires access

Minimal Manipulability: Anonymity and Surjectivity

Stefan Maus, Hans Peters, Ton Storcken

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Abstract

Gibbard''s (1973) and Satterthwaite''s (1975) result implies that anonymous surjective social choice functions on more than two alternatives are manipulable. Placing some mild constraints on the number of agents compared to the number of alternatives, we show what the minimal number of manipulable profiles of such social choice functions is. Moreover, all such social choice functions attaining the lower bound are characterized. They show a trade off between minimizing manipulability and treating alternatives neutrally.

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Gibbard''s (1973) and Satterthwaite''s (1975) result implies that anonymous surjective social choice functions on more than two alternatives are manipulable. Placing some mild constraints on the number of agents compared to the number of alternatives, we show what the minimal number of manipulable profiles of such social choice functions is. Moreover, all such social choice functions attaining the lower bound are characterized. They show a trade off between minimizing manipulability and treating alternatives neutrally.

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Available abstract

Gibbard''s (1973) and Satterthwaite''s (1975) result implies that anonymous surjective social choice functions on more than two alternatives are manipulable. Placing some mild constraints on the number of agents compared to the number of alternatives, we show what the minimal number of manipulable profiles of such social choice functions is. Moreover, all such social choice functions attaining the lower bound are characterized. They show a trade off between minimizing manipulability and treating alternatives neutrally.

Key concepts: Anonymity, Surjective function, Social choice theory, Mathematical economics, Mathematics, Upper and lower bounds, Social preferences, Computer science

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