Talk:Dominant mutual third set: Difference between revisions
→Practical Importance and Justification for DMTBR
(→Practical Importance and Justification for DMTBR: new section) |
|||
| (2 intermediate revisions by one other user not shown) | |||
Line 42:
Why is DMTBR important or a valuable criterion to fulfill? I get that DH3 is bad, and it would be better to avoid it, but inventing a criterion for this one specific pathology seems a bit like strategic whack-a-mole; every time we fixed one kind of strategy, another strategy for a different set of candidates opens up. What's the endgame? --[[User:Closed Limelike Curves|Closed Limelike Curves]] ([[User talk:Closed Limelike Curves|talk]]) 01:22, 22 February 2024 (UTC)
: A common objection to Condorcet methods is that they are vulnerable to burial. If a method passes DMTBR, it bounds the degree to which burial can affect them: basically it means that voters can't use fringe candidate as patsies to get their favored candidate elected. Now you might say that that's just one strategy of many, but consider James Green-Armytage's strategy simulations.
: He defines strategic susceptibility as that a method is strategically susceptible in an election if there exist some way for people who all support a candidate who didn't win, and who know how the others would vote, to modify their ballots so that the candidate does win. And his simulations suggest that Condorcet methods that fail DMTBR have a strategy susceptibility approaching 100% in the limit of the number of voters going to infinity, under impartial culture, whereas for methods that pass, this susceptibility approaches some finite level below 100% that depends on the number of candidates. See for instance tables 2 and 6 in his paper, [https://mpra.ub.uni-muenchen.de/32200/1/MPRA_paper_32200.pdf Strategic voting and nomination], pp. 16 and 18; and table 2 of [https://citeseerx.ist.psu.edu/document?repid=rep1&type=pdf&doi=49dba225741582cae5aabec6f1b5ff722f6fedf1 Four Condorcet-Hare Hybrid Methods for Single-Winner Elections], p. 7. Hare (IRV) and the Hare hybrids pass DMTBR, the other methods do not.
: Impartial culture is very punishing (the proportion of elections with Condorcet cycles also approaches 100% in the limit), and so may be entirely unrealistic. It's a valid objection to say that elections aren't ever going to get that messy and something like [[Minmax]] will suffice for real elections. But if DMTBR does create a finite fraction of strategy-immune elections in impartial culture, that does make DMTBR something more than "just another strategy resistance criterion", and would be of interest if you need as much strategy resistance as you can get.
: I guess intuitively you could say that Condorcet patches up compromise incentive and DMTBR patches up burial incentive, and the latter patch-up holds even in elections with tons of near-ties. ''Very'' roughly.
: Simple DMTBR methods like [[instant-runoff voting]] have much too high compromise incentive, so I prefer Condorcet methods.
: My own simulations suggest that what's actually important to get a nonzero fraction of strategy-immune elections in impartial culture is [[resistant set]] compliance. In that case, DMTBR's interest would broadly be as a clone-resistant generalization of resistant set. But I haven't proven this beyond a few burial immunity results for the resistant set. [[User:Kristomun|Kristomun]] ([[User talk:Kristomun|talk]]) 12:38, 22 February 2024 (UTC)
:: "Bounding the (IAC) probability that an election can be manipulated" seems like a ''great'' justification! It's intuitive and important. Maybe this should be placed front-and-center in the article?
:: I don't think I have the experience or game-theory knowledge to prove results like this, but I've wanted a table of P(manipulation) values for a long time. Even better would be something like VSE lost to manipulation; ideally these would select the utility lost in the worst-case Myerson-Webb or Strong Nash equilibrium. (Condorcet seems to reduce the number of elections that voters can manipulate, but might make the outcome worse when they ''are'' manipulated; so probability methods are going to be somewhat, but not totally, convincing.) The issue is that tackling all these issues by creating separate criteria (Chicken, DMTBR, etc.) one-by-one is going to take, well, literally forever by Gibbard's theorem. --[[User:Closed Limelike Curves|Closed Limelike Curves]] ([[User talk:Closed Limelike Curves|talk]]) 18:47, 23 February 2024 (UTC)
| |||