Talk:Gibbard's theorem

Merge

This should either be merged with Gibbard–Satterthwaite theorem or that article should be renamed to "Satterthwaite theorem".

About merging: I would advise against it. First, Gibbard's theorem seems to be for a more specialized audience than Gibbard-Satterthwaite. Second, merging the two would lead, I think, to a confusing article. About renaming: no, the Gibbard-Satterthwaite has been proven independently by these two authors and thus must be named as such; it is always named so in the scientific literature. --François Durand (talk) 14:47, 22 April 2022 (UTC)

'proven'

Is the use of this word justifiable? Notreallydavid (talk) 04:57, 8 January 2019 (UTC)

Yes it is; we're talking about a formal mathematical theorem that has been proven true. AxelBoldt (talk) 18:12, 5 August 2020 (UTC)

At the very least, you should clarify that “proven” is being used in a technical sense. And ideally, you wouldn’t use technical terminology that will mislead the non- mathematicians/economists/logicians for whom this article is supposedly written. — Preceding unsigned comment added by 98.218.180.156 (talk) 01:38, 2 September 2022 (UTC)

It is pretty common across many math-adjacent fields to take a concept, make a mathematical formalization that roughly captures the intuitive idea, and then prove rigorous theorems about the formalizations of these concepts, and finally to use this to gain intuition about the original concept. If something seemingly non-mathematical is called a "theorem" and it has an accompanying "proof", then this is what is meant. To otherwise call something a "theorem" would be dishonest. This idea isn't any more relevant to this wiki page than to pages about other examples of encoding intuitive ideas into formal mathematical expressions, so I don't think it deserves any explanation in this wiki page, but since this idea isn't known to many, I sort of agree that it might be worth putting a link to a page explaining what I just explained. There must already be a page that discusses this, but I can't find it. (Not to be confused with Hilbert formalism.) -Sam W 97.113.35.180 (talk) 05:14, 5 September 2022 (UTC)

Replace "strategyproof" by "straightforward"?

Hello! I think that the word "straightforward" should be used instead of "strategyproof". First, this is the word used in Gibbard's original article. Second, "strategyproof" only makes sense for what would be called nowadays a "direct mechanism" (= where people are asked to reveal their types), whereas "straightforward" is defined for all game forms (= where available strategies can be any sort of message). --François Durand (talk) 14:40, 22 April 2022 (UTC)

Statement of the theorem

In the original version of the page, the theorem was: "If a game form is straightforward and has at least 3 possible outcomes, then it is dictatorial", which is very close to Gibbard's wording. In the current version of the page, the theorem is: "If a game form is not dictatorial and has at least 3 possible outcomes, then it is not strategyproof." Of course the contraposition does not change the meaning, but are there prominent reasons for this wording? If not, I suggest sticking to the original version. --François Durand (talk) 14:52, 22 April 2022 (UTC)

Incomprehensible to non-economists

I was an econ undergrad and this is barely comprehensible to me. At a minimum, the article should be written so as to be approachable for the typical college graduate. This isn’t that. 98.218.180.156 (talk) 01:25, 2 September 2022 (UTC)