Condorcet winner
Named by 2 essays across one field — each of them below, with the objects they name alongside it.
The fewest swaps to a winner
When no candidate beats every other head to head, Charles Dodgson proposed in 1876 to elect the one that is closest to doing so — the candidate that the fewest swaps of neighbouring names on the ballots would turn into a winner of every contest. The rule is easy to state and hard to compute: the count needs a search, and deciding the winner is provably among the hardest problems of its kind. A much simpler count, the votes still to be won, usually agrees, more often the larger the electorate.
How often the rules find the majority favourite
When one candidate beats every rival head to head, a voting rule ought to elect it. Plurality does about three times in four when every ranking is equally likely, the runoff between the top two 96 times in a hundred, Borda's count 90. Every profile of up to 51 voters is counted exactly, the limit is sampled, and adding candidates pulls plurality down below one half.
Named alongside it
The objects these essays reach for when they reach for this one.
Borda countExhaustive searchVoting ruleApproximationCondorcet cycleMajority ruleNormal distributionNP-hardSimulation