Maskin monotonicity
Maskin monotonicity
- Maskin monotonicity** is a desired property of voting systems suggested by [[eric-maskin]].
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.
For a preference profile <math>P_1</math> with a chosen alternative <math>A_1</math>, there is another preference profile <math>P_2</math> such that the position of <math>A_1</math> relative to each of the other alternatives either improves or stays the same as in <math>P_1</math>. With Maskin monotonicity, <math>A_1</math> should still be chosen at <math>P_2</math>.
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 equilibrium form if there are three or more voters.