Condorcet criterion and reduction of coalitional manipulability

Since any non-trivial voting system is susceptible to manipulation, we investigate how it is possible to reduce the set of situations where it is manipulable, that is, such that a coalition of voters, by casting an insincere ballot, may secure an outcome that is better from their point of view. We prove that, for a large class of voting systems, a simple modification allows to reduce manipulability. This modification is Condorcification: when there is a Condorcet winner, designate her; otherwise, use the original rule. If indifferences are possible, a notion of Condorcet winner based on absolute majority is used. Our very general framework allows to do this for all voting systems, including non-ordinal ones. As a consequence, when searching for a voting system whose manipulability is minimal (in a large class of systems), one can restrict to those that meet the Condorcet criterion.