Definitions

Condorcet loser criterion

In single-winner voting system theory, the Condorcet loser criterion is a measure for differentiating voting systems.

A voting system complying with the Condorcet loser criterion will never allow a Condorcet loser to win.

A Condorcet loser is a candidate who can be defeated in a head-to-head competition against every other candidate. (Not all elections will have a Condorcet loser since it is possible for three or more candidates to be mutually defeatable in different head-to-head competitions.)

Plurality voting system

Plurality may elect the Condorcet loser. The simplest example is where two similar candidates split the vote.

100 voters 80 voters 60 voters
1. Concentrated Opposition 1. Divided Favorite 1 1. Divided Favorite 2
2. Divided Favorite 1 2. Divided Favorite 2 2. Divided Favorite 1
3. Divided Favorite 2 3. Concentrated Opposition 3. Concentrated Opposition

By Plurality, Concentrated Opposition has more first place votes than either of the divided favorites, and so he wins. But one-on-one, 140 voters prefer either of the divided favorites to Concentrated Opposition, whereas only 100 voters have the opposite one-on-one preference. Hence, Concentrated Opposition, which Plurality elected, is the Condorcet loser.

Ranked Pairs

Ranked Pairs work by "locking in" strong victories, starting with the strongest, unless that would contradict an earlier lock. Assume that the Condorcet loser is X. For X to win, Ranked Pairs must lock a preference of X over some other candidate Y (for at least one Y) before it locks Y over X. But since X is the Condorcet loser, the victory of Y over X will be greater than that of X over Y, and therefore Y over X will be locked first, no matter what other candidate Y is. Hence X cannot win, which was what we wanted.