Maskin monotonicity

Maskin monotonicity is a desired property of voting systems, suggested by Eric Maskin.

We are dealing with voting systems that work in the following way. Each voter reports his entire preference relation over the set of alternatives. The set of reports is called a preference profile. A social choice rule maps the preference profile to the selected alternative.

Maskin monotonicity is the following property of a social choice rule. Suppose that, for preference profile P1, the chosen alternative is A1. Consider another preference profile P2 such that, the position of A1 relative to each of the other alternatives either improves or stays the same as in P1. Then, A1 should still be chosen at P2.

Maskin monotonicity is a necessary condition for implementability in Nash equilibrium. Moreover, any social-choice-rule that satisfies Maskin-monotonicity and another property called "no veto power" can be implemented in Nash quilibrium form if there are three or more voters.

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