Maskin monotonicity is a desired property of
voting system
An electoral system or voting system is a set of rules that determine how elections and referendums are conducted and how their results are determined. Electoral systems are used in politics to elect governments, while non-political elections ma ...
s suggested by
Eric Maskin
Eric Stark Maskin (born December 12, 1950) is an American economist and mathematician. He was jointly awarded the 2007 Nobel Memorial Prize in Economic Sciences with Leonid Hurwicz and Roger Myerson "for having laid the foundations of mechanism d ...
.
Each voter reports his entire
preference relation The term preference relation is used to refer to orderings that describe human preferences for one thing over an other.
* In mathematics, preferences may be modeled as a weak ordering or a semiorder, two different types of binary relation. One speci ...
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
with a chosen alternative
, there is another preference profile
such that the position of
relative to each of the other alternatives either improves or stays the same as in
. With Maskin monotonicity,
should still be chosen at
.
Maskin monotonicity is a necessary condition for implementability in
Nash equilibrium
In game theory, the Nash equilibrium, named after the mathematician John Nash, is the most common way to define the solution of a non-cooperative game involving two or more players. In a Nash equilibrium, each player is assumed to know the equili ...
. 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.
See also
*
Monotonicity (mechanism design) In mechanism design, monotonicity is a property of a social choice function. It is a necessary condition for being able to implement the function using a strategyproof mechanism. Its verbal description is:
In other words:
Notation
There is a ...
* The
monotonicity criterion in voting systems
References
{{reflist
Mechanism design
Voting