A strong Condorcet winner (SCW) is an alternative, x, that a majority of voters rank higher than z, for every other alternative, z. A weak Condorcet winner (WCW) is an alternative, y, that no majority of voters rank below any other alternative, z, but is not a SCW. There has been some confusion...

In voting theory, monotonicity is the axiom that an improvement in the ranking of a candidate by voters cannot cause a candidate who would otherwise win to lose. The participation axiom states that the sincere report of a voter’s preferences cannot cause an outcome that the voter regards as...