Talk:Gibbard-Satterthwaite theorem: Difference between revisions

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:: "Whereas Satterthwaite's version only applies to ordinal voting systems, Gibbard's version applies to all deterministic voting systems, including non-ordinal ones. Combining Gibbard's version and a remark made by Satterthwaite" ... gives us G-S? Or Gibbard's theorem is a separate one from G-S? https://politics.stackexchange.com/a/14245 — [[User:Psephomancy|Psephomancy]] ([[User talk:Psephomancy|talk]]) 19:32, 16 April 2020 (UTC)

::: From Gibbard's paper:<ref>{{cite journal

|first=Allan

|last=Gibbard

|title=Manipulation of voting schemes: A general result

|journal=Econometrica

|volume=41

|issue=4

|year=1973

|pages=587–601

|jstor=1914083

|doi=10.2307/1914083

}}</ref> "I shall prove in this paper that any non-dictatorial voting scheme with at least three possible outcomes is subject to individual manipulation" ... "The result on voting schemes follows from a theorem I shall prove which covers schemes of a more general kind". So in his paper, Gibbard proves the result for (ordinal) voting methods as a special case of a more general result. The special result is G-S, since it was also independently discovered by Satterthwaite. However, the general result, which generalizes beyond ordinal voting methods, is not covered by Satterthwaite.

::: Thus (at least it seems to me), Gibbard-Satterthwaite is used to specifically refer to the result that both found independent of each other, which covers ordinal voting systems, and Gibbard's theorem refers to the more general result that Gibbard showed G-S is a corollary of. [[User:Kristomun|Kristomun]] ([[User talk:Kristomun|talk]]) 19:47, 16 April 2020 (UTC)

==References==