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