Intermediate Condorcet Winners and Losers

The conditions of strong Condorcet winner consistency and strong Condorcet loser consistency are, in essence, universally accepted. However, there are many situations in which they are silent. The weak counterparts of these properties suffer from the fatal flaw that a weak Condorcet winner can be a weak Condorcet loser at the same time. We propose a new notion of Condorcet-type winners and losers that is intermediate in strength between these two extremes. A feasible candidate is an intermediate Condorcet winner if this candidate wins against or ties with each other feasible candidate in a pairwise contest, with at least one instance of a win. Likewise, a feasible candidate is an intermediate Condorcet loser if the candidate loses against or ties with each other feasible candidate, with at least one instance of a loss. Our intermediate variants of Condorcet winner consistency and Condorcet loser consistency share the intuitive appeal of strong Condorcet winner consistency and strong Condorcet loser consistency, and they do not lead to the counterintuitive conclusions of the consistency conditions defined in terms of weak Condorcet winners and losers. We provide a thorough examination of the properties of our proposal and compare it to earlier attempts to modify the traditional Condorcet conditions.