Median voter
Named by 3 essays across one field — each of them below, with the objects they name alongside it.
Agendas that cannot contradict themselves
A court voting on two unconnected questions never contradicts itself, and neither does one voting on a chain of thresholds. A court voting on two premises and their conjunction sometimes does. What separates them is the size of the smallest sets of judgements that cannot all be true: pairs are harmless, because two majorities always share a judge, and triples are not. The same count says exactly how large a supermajority has to be to stay consistent on any agenda.
Sellers on a street stand back to back
Put two ice-cream sellers on a beach and they end up side by side in the middle, though customers would walk half as far if they stood at the quarter marks. Three sellers never settle at all: whoever is squeezed in the middle leaps outside, for ever. Four stand in pairs, five in pairs with one alone in the centre, six in endlessly many ways. Let them set prices too, with travel costing the square of the distance, and the conclusion reverses: the two sellers move as far apart as the beach allows.
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 ruleAggregationBest replyCondorcet cycleCondorcet paradoxDiscursive dilemmaImpossibility theoremJudgement aggregationMixed strategyNash equilibriumPrice of anarchy