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

Abstract: 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 resolvability (if $x$ initially ties for winning, then $x$ can be made the unique winner by adding a single voter). In a previous note, we proved an analogous result assuming an additional axiom of ordinal margin invariance, which we now show is unnecessary for an impossibility theorem, at least if the desired voting method is defined for five-candidate elections.