Condorcet paradox
Named by 2 essays across one field — each of them below, with the objects they name alongside it.
How few voters any majority needs
Any pattern of head-to-head majorities whatever — cycles within cycles, a candidate who beats the winner of every other contest and loses to its loser — can be produced by voters who each rank the candidates sensibly. McGarvey's recipe needs n(n − 1) of them for n candidates. The truth is far fewer: every pattern on five candidates takes three voters at most, a counting argument shows the number must eventually grow, and it grows only like n divided by its logarithm.
A party that loses every issue can win
Two parties take opposite sides on three issues, and every voter backs the party they agree with on more of them. The party that wins the election can be on the losing side of all three issues — in a fifth of random electorates it loses most of them, and in about one in a hundred it loses every one. A majority of voters can even find themselves outvoted on most of the questions decided. Only when issues are settled by three-to-one majorities on average is that ruled out.
Named alongside it
The objects these essays reach for when they reach for this one.
Exhaustive searchMajority ruleAggregationCounting argumentDiscursive dilemmaMedian voterTournamentVoting rule