The Duggan-Schwartz theorem is a result about voting systems that select a nonempty set of winning candidates, rather than a single winner, from voters' ranked preferences over three or more candidates. It states that any such system must have at least one of several undesirable properties: it treats voters unequally, it ignores voter input for some candidates, every voter's top choice is always among the winners, or the system can be manipulated by a voter misrepresenting their preferences to obtain a more favorable set of winners.
Facts
StatementFor elections with three or more candidates, any voting system choosing a nonempty set of winners from ranked preferences must treat voters unequally, make some candidates unable to win, have every voter's top choice win, or be manipulable by optimistic or pessimistic voters. 1 Classification
Statement Form Connections
Has Statement Form
Entity-backed identity for the statement-form enum value this theorem already carries, resolved to a mathematics concept by an explicit value-to-entity map (phase 3 bucket conversion, docs\design_entity_backed_browse_buckets_20260928.md). The statement-form fact itself stays on the theorem unchanged.
Sources
1. Duggan-Schwartz theorem (Wikipedia)
Lead paragraphQuote, Lead paragraph
a result about voting systems designed to choose a nonempty set of winners from the preferences of certain individuals, where each individual ranks all candidates in order of preference.
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