Talk:Smith criterion

Smith "winner"?

I think something's wrong in this article. "it picks the winner from the Smith set" So who's "the winner of the Smith set"? --Chealer 21:03, 2004 Dec 4 (UTC)

I don't see the problem. The article doesn't say, "picks the winner of the Smith set" but "picks the winner from the Smith set". For example, a trivial voting system meeting the Smith criterion: determine the Smith set, and choose as the winner the first alphebetical member of the Smith set. CRGreathouse 21:44, 19 July 2006 (UTC)

Calculating the Smith set?

Is there an efficient method for calculating the Smith set given a Dodgson matrix? CRGreathouse 21:44, 19 July 2006 (UTC)

Yes, assuming a "Dodgson matrix" is a matrix from which all majorities of the round robin tournament can be calculated, and assuming "efficient" means an execution time bounded by a polynomial of the number of candidates (like n²). Here's an algorithm that suffices: Initialize C to be a list of all candidates and initialize S to be an empty list. Pick any ordering of the candidates (for efficiency, simply use the order in which the candidates are listed in C), calculate which candidate would win if that ordering were the agenda in Robert's Rules' sequential pairwise elimination method, and append that candidate to S. Then, for each candidate x in S and each candidate y in C-S, append y to S if a majority does not rank x over y. When done, S is the Smith set. SEppley (talk) 16:22, 22 November 2012 (UTC)

Sincere Smith set versus strategically manipulated Smith set

The language used in the article defines the Smith set according to voters' preferences, not according to the votes. This is an important distinction because votes can misrepresent voters' preferences. (See the Gibbard-Satterthwaite "manipulability" theorem, which shows that sometimes some voters have an incentive to vote in a way that misrepresents their preferences.) The purpose of the Smith criterion is to elect a candidate in the sincere Smith set (the Smith set defined according to voters' sincere preferences). That's more desirable than electing a candidate in a set manipulated by strategic voting. So the article is misleading where it lists voting methods that "comply" with the Smith criterion, since they really only comply with a different criterion defined according to votes, not preferences. (The same issue exists with the Condorcet criterion. The purpose is to elect the sincere Condorcet winner when one exists. The problem is that there can be situations where a sincere Condorcet winner exists but there is no Condorcet winner according to the votes, due to voters who misrepresent their preferences.)

The difficulty is compounded because voters' sincere preferences depend indirectly on the voting method. Most comparisons of voting methods naively assume the set of candidates who compete and their positions on issues don't depend on the voting method. But they do, and since voters' preferences on candidates depend on the set of candidates and the candidates' positions on issues, it follows that voters' preferences depend on the voting method. (This may seem like a minor point, but it's possible that the most important criteria for comparing voting methods involve desirable or undesirable effects of voting methods on candidates' positions. Those criteria won't be discovered by people who assume candidates' positions are independent of the voting method.) Thus the sincere Smith set depends on the voting method, even though sincere preferences are not defined according to the votes.

I recommend revising the article so it discusses both the sincere set and the voted set, and also references related criteria (examples: truncation resistance, minimal defense) that help distinguish voting methods that are closer to the spirit of the sincere Smith criterion and the sincere Condorcet criterion. SEppley (talk) 00:18, 23 November 2012 (UTC)

Merge with 'Smith set'

Wikipedia hardly needs both articles. I would suggest merging this one into Smith set, but the latter is a bit under-referenced so may need some work first. Colin.champion (talk) 13:01, 25 September 2021 (UTC)

Agreed. –Maximum Limelihood Estimator 03:40, 23 April 2024 (UTC)