One of the candidates for the poll is Majority Judgement  (a "category" ). A few months ago I posted something about a version of Bucklin that is also a Median Ratings method. I reproduce it  here to explain why in the poll I will be voting it below Hare and all the reasonable Condorcet methods: I think it is now generally agreed that least bad is to use some sort of limited-slot grading/rating ballot, with voters There has been more than one version of Bucklin that has been used or proposed. free to give as many or as few candidates as they like the same grade and to skip grades if they want.(So it is just a version of Average Ratings) If ranking ballots are used then above-bottom equal ranking should get the whole (not fractional) votes interpretation, but if say a ballot equal top-ranks 3 candidates that ballot gives a whole vote to each in the first "round" but then "sits out" rounds 2 and 3. (Not doing that was shown to make the method fail mono-raise). If we are talking about one of these versions then we are talking about a method that meets Favorite Betrayal and Majority for Solid Coalitions and Later-no-Help. But there is a very strong incentive for voters to just submit approval ballots, and in a competitive election with informed voters the extra complexity versus simple Approval doesn't seem to buy much. 40 A>B 30 B 09 C 02 X 81 ballots. This example highlights the method's disadvantages compared with Hare (aka IRV). I don't consider meeting Majority for Solid Coalitions to be an adequate standard of majoritarian representative goodness. I propose the "Dominant Coalition" criterion: *If a the number of ballots on which a set S of candidates is ranked/voted all below no outside-S candidate is greater than the maximum pairwise opposition that any inside-S candidate gets from any outside-S candidate, then the winner must come from set S.* The single-candidate version (that could be relevant for a method that fails Clone-Winner) is "Dominant Candidate". *If the number of ballots on which candidate X is ranked/voted below no other candidate is greater than X's maximum pairwise opposition, then X must win.* Another criterion I like (and I think I coined) is Irrelevant Ballots Independence: adding or removing ballots that contain no information relevant to any of the remotely competitive candidates should not change the result. Another criterion met by IRV/RCV but not Bucklin is Mutual Dominant Third : "if a set S of candidates that pairwise beat all the outside-S candidates are voted above all the outside-S candidates on at least one third of the ballots then the winner must come from S." In the example A is the Dominant Candidate and the Mutual Dominant Third candidate (and so of course the CW) but the Bucklin winner is B. (A lot of people like Hare's compliance with Later-no-Harm. Of course here if the A>B voters had truncated then A would have won.) But if we remove the 2 X ballots the winner changes from B to A, (because the majority threshold lowers from 41 to 40, so now there is no second round) a failure of Irrelevant Ballots independence. Chris B.

On 2024-04-10 15:36, Chris Benham wrote: > But there is a very strong incentive for voters to just submit approval > ballots, and in a competitive election with > informed voters the extra complexity versus simple Approval doesn't seem > to buy much. I think there's a more general result: Say we have a method that elects the candidate with the highest quality, and the quality of a candidate A only depends on each ballot's information about A (not on A's position relative to any other B). Suppose that the quality function f(A) is weakly monotone in the sense that if a voter raises (lowers) A, then f(A) can never decrease (increase). Then with complete information, Approval strategy is optimal. This covers both Range and MJ, and the most obvious way to make a general cardinal method pass IIA. -km

This is probably true under much weaker conditions. It feels like every good (FBC, monotone?) method converges to approval with strategic voters. (And approval converges to Smith//Approval.) On Fri, Apr 12, 2024 at 9:21 AM Kristofer Munsterhjelm <km_elmet@t-online.de> wrote: > On 2024-04-10 15:36, Chris Benham wrote: > > > But there is a very strong incentive for voters to just submit approval > > ballots, and in a competitive election with > > informed voters the extra complexity versus simple Approval doesn't seem > > to buy much. > > I think there's a more general result: > > Say we have a method that elects the candidate with the highest quality, > and the quality of a candidate A only depends on each ballot's > information about A (not on A's position relative to any other B). > Suppose that the quality function f(A) is weakly monotone in the sense > that if a voter raises (lowers) A, then f(A) can never decrease (increase). > > Then with complete information, Approval strategy is optimal. > > This covers both Range and MJ, and the most obvious way to make a > general cardinal method pass IIA. > > -km > ---- > Election-Methods mailing list - see https://electorama.com/em for list > info >

On 2024-04-12 19:41, Closed Limelike Curves wrote: > This is probably true under much weaker conditions. It feels like every > good (FBC, monotone?) method converges to approval with strategic > voters. (And approval converges to Smith//Approval.) I seem to recall someone saying that MMPO is a method that passes FBC and monotonicity yet doesn't behave like Approval. (Then again, its Plurality criterion failure is really a bummer.) There might also be methods that converge directly to something that passes Smith without going through Approval first. It's difficult to say since so few methods' equilibria are known. Finally, I'm not sure if Approval converges to anything useful in the presence of a sincere cycle. I would imagine that the strategic voters would chase each other through the cycle. For Condorcet, everybody who prefers the Condorcet winner W to the current Approval winner A could (theoretically, given continuously updating polls) place their cutoff between W and A, which would then stabilize the result there. But if they do that when there's a cycle, they would just end up chasing each other through it. E.g. with 36: A>B>C 34: B>C>A 32: C>A>B then suppose we start with everybody approving the first two. Then the winner is B. So the A>B voters compensate: 36: A>|B>C 34: B>C>|A 32: C>A|>B Then the winner is A. So the C>A voters compensate: 36: A>|B>C 34: B>C>|A 32: C>|A>B Then the winner is C. So the B>C voters compensate: 36: A>B|>C 34: B>|C>A 32: C>|A>B round and round and round it goes. Where it stops, nobody knows! The actual outcome would be heavily influenced by polling access and timing. So it doesn't seem like the "induced" Smith//Approval method would mean much. If I'm wrong, it would be interesting to take a leaf out of the revelation principle book and create a ranked method that does directly what Approval would do through strategy, and see what its characteristics are. E.g. is it monotone? It's only fair, if the purpose of Approval is to enact a higher order distributed algorithm that uses the polls as state data, to analyze this algorithm, whatever it is. That's why I keep coming back to the "manual DSV" objection. -km

> > Finally, I'm not sure if Approval converges to anything useful in the > presence of a sincere cycle. I would imagine that the strategic voters > would chase each other through the cycle. In real life, or in models? The answer to "what will approval actually do" depends on which (if any) of those models is correct. I'd conjecture every well-designed voting system converges, under plausible models of strategic voting, to something that looks basically like a maximal lottery. The perfect-group-strategy model predicts a maximal lottery. I'm not sure what other models predict, but I'm guessing they'll say approval (or score, or most Condorcet methods) will produce very similar results. But if nothing else, every strategic model of voters is clearly incomplete, because some voters are honest. My main reason for supporting score is that if we add in some honest voters, it can give us better results than Condorcet. round and round and round it goes. Where it stops, nobody knows! Funnily enough, that's also how a maximal lottery behaves. ;) Choosing candidates at random from a sincere cycle probably wouldn't be that bad a system. (Hell, it's arguably better than breaking the ties deterministically—less bias, so it'll tend to cancel out across election cycles or within a legislature!) > If I'm wrong, it would be interesting to take a leaf out of the > revelation principle book and create a ranked method that does directly > what Approval would do through strategy, and see what its > characteristics are. E.g. is it monotone? > Unfortunately, maximal lotteries aren't monotone. :( On the plus side, they somehow satisfy participation, which I count as a miracle. On Fri, Apr 12, 2024 at 3:59 PM Kristofer Munsterhjelm <km_elmet@t-online.de> wrote: > On 2024-04-12 19:41, Closed Limelike Curves wrote: > > This is probably true under much weaker conditions. It feels like every > > good (FBC, monotone?) method converges to approval with strategic > > voters. (And approval converges to Smith//Approval.) > > I seem to recall someone saying that MMPO is a method that passes FBC > and monotonicity yet doesn't behave like Approval. (Then again, its > Plurality criterion failure is really a bummer.) > > There might also be methods that converge directly to something that > passes Smith without going through Approval first. It's difficult to say > since so few methods' equilibria are known. > > Finally, I'm not sure if Approval converges to anything useful in the > presence of a sincere cycle. I would imagine that the strategic voters > would chase each other through the cycle. > > For Condorcet, everybody who prefers the Condorcet winner W to the > current Approval winner A could (theoretically, given continuously > updating polls) place their cutoff between W and A, which would then > stabilize the result there. But if they do that when there's a cycle, > they would just end up chasing each other through it. > > E.g. with > > 36: A>B>C > 34: B>C>A > 32: C>A>B > > then suppose we start with everybody approving the first two. Then the > winner is B. So the A>B voters compensate: > > 36: A>|B>C > 34: B>C>|A > 32: C>A|>B > > Then the winner is A. So the C>A voters compensate: > > 36: A>|B>C > 34: B>C>|A > 32: C>|A>B > > Then the winner is C. So the B>C voters compensate: > > 36: A>B|>C > 34: B>|C>A > 32: C>|A>B > > round and round and round it goes. Where it stops, nobody knows! > > The actual outcome would be heavily influenced by polling access and > timing. So it doesn't seem like the "induced" Smith//Approval method > would mean much. > > > If I'm wrong, it would be interesting to take a leaf out of the > revelation principle book and create a ranked method that does directly > what Approval would do through strategy, and see what its > characteristics are. E.g. is it monotone? > > It's only fair, if the purpose of Approval is to enact a higher order > distributed algorithm that uses the polls as state data, to analyze this > algorithm, whatever it is. That's why I keep coming back to the "manual > DSV" objection. > > -km >

On Fri, Apr 12, 2024 at 20:27 Closed Limelike Curves < closed.limelike.curves@gmail.com> wrote: Finally, I'm not sure if Approval converges to anything useful in the >> presence of a sincere cycle. > > Just the candidate or alternative liked by the most people. would imagine that the strategic voters >> would chase each other through the cycle. > > In real life, or in models? The answer to "what will approval actually do" > depends on which (if any) of those models is correct. > > I'd conjecture every well-designed voting system converges, under > plausible models of strategic voting, to something that looks basically > like a maximal lottery. The perfect-group-strategy model predicts a maximal > lottery. I'm not sure what other models predict, but I'm guessing they'll > say approval (or score, or most Condorcet methods) will produce very > similar results. > > But if nothing else, every strategic model of voters is clearly > incomplete, because some voters are honest. My main reason for supporting > score is that if we add in some honest voters, it can give us better > results than Condorcet. > > round and round and round it goes. Where it stops, nobody knows! > > Funnily enough, that's also how a maximal lottery behaves. ;) Choosing > candidates at random from a sincere cycle probably wouldn't be that bad a > system. (Hell, it's arguably better than breaking the ties > deterministically—less bias, so it'll tend to cancel out across election > cycles or within a legislature!) > > >> If I'm wrong, it would be interesting to take a leaf out of the >> revelation principle book and create a ranked method that does directly >> what Approval would do through strategy, and see what its >> characteristics are. E.g. is it monotone? >> > Unfortunately, maximal lotteries aren't monotone. :( > > On the plus side, they somehow satisfy participation, which I count as a > miracle. > > On Fri, Apr 12, 2024 at 3:59 PM Kristofer Munsterhjelm < > km_elmet@t-online.de> wrote: > >> On 2024-04-12 19:41, Closed Limelike Curves wrote: >> > This is probably true under much weaker conditions. It feels like every >> > good (FBC, monotone?) method converges to approval with strategic >> > voters. (And approval converges to Smith//Approval.) >> >> I seem to recall someone saying that MMPO is a method that passes FBC >> and monotonicity yet doesn't behave like Approval. (Then again, its >> Plurality criterion failure is really a bummer.) >> >> There might also be methods that converge directly to something that >> passes Smith without going through Approval first. It's difficult to say >> since so few methods' equilibria are known. >> >> Finally, I'm not sure if Approval converges to anything useful in the >> presence of a sincere cycle. I would imagine that the strategic voters >> would chase each other through the cycle. >> >> For Condorcet, everybody who prefers the Condorcet winner W to the >> current Approval winner A could (theoretically, given continuously >> updating polls) place their cutoff between W and A, which would then >> stabilize the result there. But if they do that when there's a cycle, >> they would just end up chasing each other through it. >> >> E.g. with >> >> 36: A>B>C >> 34: B>C>A >> 32: C>A>B >> >> then suppose we start with everybody approving the first two. Then the >> winner is B. So the A>B voters compensate: >> >> 36: A>|B>C >> 34: B>C>|A >> 32: C>A|>B >> >> Then the winner is A. So the C>A voters compensate: >> >> 36: A>|B>C >> 34: B>C>|A >> 32: C>|A>B >> >> Then the winner is C. So the B>C voters compensate: >> >> 36: A>B|>C >> 34: B>|C>A >> 32: C>|A>B >> >> round and round and round it goes. Where it stops, nobody knows! >> >> The actual outcome would be heavily influenced by polling access and >> timing. So it doesn't seem like the "induced" Smith//Approval method >> would mean much. >> >> >> If I'm wrong, it would be interesting to take a leaf out of the >> revelation principle book and create a ranked method that does directly >> what Approval would do through strategy, and see what its >> characteristics are. E.g. is it monotone? >> >> It's only fair, if the purpose of Approval is to enact a higher order >> distributed algorithm that uses the polls as state data, to analyze this >> algorithm, whatever it is. That's why I keep coming back to the "manual >> DSV" objection. >> >> -km >> > ---- > Election-Methods mailing list - see https://electorama.com/em for list > info >