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
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Source Duggan-Schwartz theorem (Wikipedia)
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1. Duggan-Schwartz theorem (Wikipedia)
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.
In Branch: Game Theory, Lead
The Duggan-Schwartz theorem (named after John Duggan and Thomas Schwartz) is 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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