The incompatibility of the Condorcet winner and loser criteria with positive involvement and resolvability

We prove that there is no preferential voting method satisfying the Condorcet winner and loser criteria, positive involvement (if a candidate x wins in an initial preference profile, then adding a voter who ranks x uniquely first cannot cause x to lose), and n -voter resolvability (if x initially ties for winning, then x can be made the unique winner by adding some set of up to n voters). This impossibility theorem holds for any positive integer n . It also holds if either the Condorcet loser criterion is replaced by independence of clones or positive involvement is replaced by negative involvement. • Condorcet winner and loser, positive involvement, and resolvability are jointly incompatible. • Condorcet loser can be replaced by independence of clones. • Positive involvement can be replaced by negative involvement. • Resolvability can be weakened to n-voter resolvability.