Does anyone know any papers that look at Myerson-Weber equilibria for different systems? I know about Burt Monroe's "nonelection of turkeys" paper, but not much else. I'd be very interested in any work on calculating the regret for each method.

Myerson’s & Weber’s own original paper that introduced it. They showed that Approval’s MW equilibrium is at the voter-median (…where the CW is). They showed that Plurality (Vote-For-1) can have a MW equilibrium that keeps on electing any pair of parties, however unliked, forever. That sounds close to home. …though our MW equilibrium is getting a lot of help from the mass-media. It was published in an economics journal, a major one. Econometrica? Google Myerson & Weber, Voting Equilibrium. On Sat, Feb 24, 2024 at 11:44 Closed Limelike Curves < closed.limelike.curves@gmail.com> wrote: > Does anyone know any papers that look at Myerson-Weber equilibria for > different systems? I know about Burt Monroe's "nonelection of turkeys" > paper, but not much else. I'd be very interested in any work on calculating > the regret for each method. > ---- > Election-Methods mailing list - see https://electorama.com/em for list > info >

On 2024-02-24 20:39, Closed Limelike Curves wrote: > Does anyone know any papers that look at Myerson-Weber equilibria for > different systems? I know about Burt Monroe's "nonelection of turkeys" > paper, but not much else. I'd be very interested in any work on > calculating the regret for each method. There are some papers that analyze Nash and M-W voting equilibria for voting methods, but they're usually very specific, as calculating Nash over a multiplayer game with simultaneous moves is in general very hard. (By multiplayer I mean more than two distinct players or types.) Monroe's paper uses only two types of players, and I suspect that's the reason. Example of Nash equilibria in voting: https://webdoc.sub.gwdg.de/ebook/serien/e/CORE/dp9931.pdf https://www.nber.org/system/files/working_papers/w23898/revisions/w23898.rev0.pdf (Chicken dilemma situation with more constrained behavior on the voters) https://link.springer.com/article/10.1007/BF02425262 (sci-hub: https://sci-hub.se/https://link.springer.com/article/10.1007/BF02425262) https://link.springer.com/chapter/10.1007/978-3-642-02839-7_9 (sci-hub analogous) As for Monroe, I would further suspect that for some methods, modifying a method X to be Condorcet//X instead will preserve NIA, but not for all such methods. For instance, I'd imagine Condorcet//IRV passes and Condorcet//Plurality fails. But again, I haven't proven this. E.g. for Condorcet//IRV: Honest voting gives a tie between 1 and 2. If any voter raises 3 to second to try to set up a cycle, the method falls through to IRV, where 3 is still eliminated. This is basically DH3, and C//IRV resists DH3 so it passes in this case. Proving a single scenario doesn't prove the whole space, of course. It would be interesting to determine if DMTBR (or electing from the resistant set) implies Monroe's NIA, but I think doing so formally is a bit out of my grasp. The converse, NIA->DMTBR, is false (see Electowiki). Other interesting things would include proving e.g. DMTBR implying resistant-efficiency. In any case, it should be possible to analyze two-voter situations by using linear programming. But I don't know of any papers where that has been done more comprehensively. -km