Maskin monotonicity

{{Technical|date=February 2024}}

Maskin monotonicity is a desired property of voting systems suggested by Eric Maskin.{{cite journal|doi=10.1111/1467-937X.00076|title=Nash Equilibrium and Welfare Optimality|journal=Review of Economic Studies|volume=66|pages=23–38|year=1999|last1=Maskin|first1=Eric|citeseerx=10.1.1.122.2734|s2cid=16282419 }}

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 $P\_1$ with a chosen alternative $A\_1$, there is another preference profile $P\_2$ such that the position of $A\_1$ relative to each of the other alternatives either improves or stays the same as in $P\_1$. With Maskin monotonicity, $A\_1$ should still be chosen at $P\_2$.{{cite journal|doi=10.1007/s00355-014-0835-6|title=Maskin-monotonic scoring rules|journal=Social Choice and Welfare|volume=44|issue=2|pages=423|year=2014|last1=Doğan|first1=Battal|last2=Koray|first2=Semih|url=http://repository.bilkent.edu.tr/bitstream/11693/12509/1/7936.pdf|hdl=11693/12509|s2cid=253844286 |hdl-access=free}}

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.