Gibbard–Satterthwaite theorem in the context of "Michael Dummett"

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👉 Gibbard–Satterthwaite theorem in the context of Michael Dummett

Sir Michael Anthony Eardley Dummett FBA (/ˈdʌmɪt/; 27 June 1925 – 27 December 2011) was an English academic described as "among the most significant British philosophers of the last century and a leading campaigner for racial tolerance and equality." He was, until 1992, Wykeham Professor of Logic at the University of Oxford. He wrote on the history of analytic philosophy, notably as an interpreter of Frege, and made original contributions particularly in the philosophies of mathematics, logic, language and metaphysics.

He was known for his work on truth and meaning and their implications to debates between realism and anti-realism, a term he helped to popularize. In mathematical logic, he developed an intermediate logic, a logical system intermediate between classical logic and intuitionistic logic that had already been studied by Kurt Gödel: the Gödel–Dummett logic. In voting theory, he devised the Quota Borda system of proportional voting, based on the Borda count, and conjectured the Gibbard–Satterthwaite theorem together with Robin Farquharson; he also devised the condition of proportionality for solid coalitions. Besides his main work in analytic philosophy, he also wrote extensively on the history of card games, particularly on tarot card games.

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Gibbard–Satterthwaite theorem in the context of Gibbard's theorem

In the fields of mechanism design and social choice theory, Gibbard's theorem is a result proven by philosopher Allan Gibbard in 1973. It states that for any deterministic process of collective decision, at least one of the following three properties must hold:

  1. The process is dictatorial, i.e. there is a single voter whose vote chooses the outcome.
  2. The process limits the possible outcomes to two options only.
  3. The process is not straightforward; the optimal ballot for a voter "requires strategic voting", i.e. it depends on their beliefs about other voters' ballots.

A corollary of this theorem is the Gibbard–Satterthwaite theorem about voting rules. The key difference between the two theorems is that Gibbard–Satterthwaite applies only to ranked voting. Because of its broader scope, Gibbard's theorem makes no claim about whether voters need to reverse their ranking of candidates, only that their optimal ballots depend on the other voters' ballots.

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