Arrow's theorem
Named by 2 essays across 2 fields — each of them below, with the objects they name alongside it.
Also named here as decisive set — the same set of essays touches all of them, so they are one junction rather than several.
Four conditions, and no rule that has all of them
Five reasonable rules can return five different winners on one set of ballots, which invites the obvious question of which one is right. The answer is that the conditions anybody would write down cannot all hold at once — and here each named rule's own violation is found by search rather than quoted.
An electorate too large for a dictator
Arrow proved that a voting rule with his four properties must have a dictator, and his proof uses the finiteness of the electorate exactly once. With infinitely many voters the dictator can vanish: the sets of voters who get their way form an ultrafilter, and every free ultrafilter is a rule with all four properties and nobody in charge. The catch is that no such rule can be written down. Its existence is a fragment of the axiom of choice.
Named alongside it
The objects these essays reach for when they reach for this one.
Decisive setIndependence of irrelevant alternativesAxiom of choiceCondorcet cycleDictatorshipExhaustive searchInfinityPairwise majorityPreference profileProof by contradictionVoting rule