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Concept

Borda count

A voting rule in which each ballot ranks the candidates and gives a candidate one point for every rival ranked below it, the highest total winning. It uses the whole of every ranking, and it can defeat a candidate whom a majority prefers to each rival.

Named by 2 essays across one field — each of them below, with the objects they name alongside it.

Five rules on one profile of 27 ballots, and 5 different winners. The ballot groups as columns beside a table of five voting rules with the winner each returns and the count that decided it.

Five rules and five winners

Twenty-seven ranked ballots, five entirely reasonable ways of counting them, and five different candidates declared the winner. Every count is correct, every rule is defensible, and the answer turns out to be a property of the rule rather than of the ballots.

applied · Voting rules Dodgson's rule: the fewest swaps that make a Condorcet winner. Profile of 9 ballots with no Condorcet winner; Dodgson scores A 1, B 2, C 3, D 6; Borda scores A 15, B 16, C 14, D 9; Copeland A 1, B 1, C 1, D −3.

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.

applied · Voting rules

Named alongside it

The objects these essays reach for when they reach for this one.

Voting ruleApproximationCondorcet cycleCondorcet winnerCounterexampleCounting argumentExhaustive searchInstant runoffMajority ruleNP-hardPairwise majorityPreference profile

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