Re-weighted Approval Voting would lose summability, but it might be worth considering. To fill out your proposal, the Approval winner and the reweighted approval winner after reweighting are matched using the original ballot rank preferences. This amounts to a two-seat multiwinner primary (satisfying some PR rule) with pairwise instant runoff. I worry that introducing multiwinner strategy would still lead to two-party factionalism. Would this still satisfy IIA? Ted On Nov 10, 2016 11:45, "Jameson Quinn" <jameson.quinn@gmail.com> wrote: > It would be relatively easy to modify this method so that it was > reasonably cloneproof. To wit: "Rank preferences are inferred from > ratings, and the pairwise winner between the top two candidates from > reweighted approval voting (that is: pick the top approval candidate, > reweight all ballots which approved them at 1/2, and then pick the new top > approval candidate)." > > 1/2 (D'Hondt) could be replaced by 1/3 (Sainte-Laguë) if you preferred. > > > 2016-11-10 14:31 GMT-05:00 Monkey Puzzle <araucaria.araucana@gmail.com>: > >> Back in 2005, Russ Paielli proposed the following to this list: >> (https://www.mail-archive.com/election-methods-electorama.co >> m@electorama.com/msg06164.html) >> >> I'm up too late again, and I just had an interesting idea. If the >>> following method has been proposed before, please let me know. >>> The voters rank the candidates and specify an Approval cutoff. The >>> winner is then the pairwise winner of the top-two most-approved >>> candidates. >>> If it doesn't have a name already, let me tentatively call it ATTPR for >>> Approval Top-Two Pairwise Runoff. >>> A simpler variation would be to let the voter rank only the approved >>> candidates, thereby eliminating the need for an explicit Approval cutoff. >>> Good night, or good morning, whichever the case may be. >> >> >> I'd like to revive this proposal, in the following form, still basically >> what Russ proposed: >> >> Voters grade the candidates on a 6 level scale, A>B>C>D>E>F. >> >> Grades A, B, or C are approved; D, E, or F are disapproved. >> >> Rank preferences are inferred from ratings, and the pairwise winner of >> the top two approved candidates is the winner. >> >> I'd like to defend this method against the two objections posed at the >> time: >> >> Kevin Venzke raised the following objection: >> >>> This fails Clone-Loser pretty badly: if the faction commanding the most >>> approval runs two candidates, they can win regardless of the pairwise >>> comparison. >> >> >> My take on this is that you would have the same problem with straight >> Approval. The full pairwise comparison ensures that the least >> objectionable of the clones (to both winning and losing factions) is the >> one who wins. Since my primary metric is finding the candidate who >> minimizes variance, there is better variance-minimizing when those >> disagreeing with the top-two approved candidates are able to have a voice >> in the comparison between the two. >> >> Chris Benham responded with the following objection: >> >>> This would be a strategy farce. Voters who are only interested in >>> electing their favourite would all have incentive to approve, besides >>> their favourite, any and all candidates >>> that they think that their favourite can beat in the runoff. The net >>> effect of this strategising could be that that the two candidates in >>> the runoff could be the two *least* popular >>> (sincerely approved). >>> As well of course, as Kevin pointed out, well-resourced parties would >>> have incentive to each run two candidates to try to capture both runoff >>> spots. >> >> >> I disagree with the supposed strategic incentive. This seems to be a >> combination of pushover strategy plus Chicken Dilemma. The very fact that >> one might promote more than one sincerely disapproved candidate into the >> top-two set is itself a disincentive to the attempt, since you get only one >> coarse-grained shot at the top two. I think pairwise runoff is an >> incentive to avoid CD, but possibly not. >> >> And again, I'm not worried about a runoff between clones. The advantage >> of TTA is that if the larger faction is going to win anyway, the losing >> factions can at least have a voice in deciding the lesser of two evils. >> >> I'm primarily concerned about participation, monotonicity and >> independence from irrelevant alternatives. It seems to me that >> participation is satisfied as it would be with straight approval, since >> adding an approved vote for your favorite would never decrease approval, >> and adding a preference between favorite and any other compromise should >> never hurt either favorite or compromise. >> >> IIA seems like it should be satisfied because adding or removing a >> non-top-two candidate should never have an effect on the top-two pairwise >> comparison. >> >> The latter is interesting to me because one would expect that a method >> with ranking would fall under Arrow Impossibility conditions. >> >> It is apparent that TTAPR can fail Condorcet when the sincere CW is not >> in the top-two approved, but there is less chance of that occurring than >> would happen in simple Approval, so I see an improvement. Of course, it >> would still fail Smith and other full set Condorcet criteria also. >> >> In an ideal world, I would like to reduce the weight of the pairwise vote >> between two disapproved candidates, but in a USA-type election, it seems >> like one has to ensure that ballot weight is always 1 when making candidate >> comparisons to satisfy constitutional requirements. >> >> Finally, I think this satisfies all the monotonicity criteria satisfied >> by Approval. Are there any counterexamples? >> >> Ted >> -- >> Frango ut patefaciam -- I break so that I may reveal >> >> ---- >> Election-Methods mailing list - see http://electorama.com/em for list >> info >> >> >

On 11/10/2016 09:19 PM, Monkey Puzzle wrote: > Re-weighted Approval Voting would lose summability, but it might be > worth considering. > > To fill out your proposal, the Approval winner and the reweighted > approval winner after reweighting are matched using the original ballot > rank preferences. > > This amounts to a two-seat multiwinner primary (satisfying some PR rule) > with pairwise instant runoff. > > I worry that introducing multiwinner strategy would still lead to > two-party factionalism. > > Would this still satisfy IIA? It should be summable with order n^2. For each candidate C, keep a "C-penalized Approval count" that is counted as usual except that where every ballot that approves of C only counts 1/2 (or 1/3), instead of a full point, towards the candidates that ballot approves. Then you use the unpenalized Approval count to determine the ordinary Approval Winner. Suppose the winner is x. Then you look up the winner in x's penalized Approval count (say it's y). Finally, you determine the pairwise winner between x and y based on non-penalized pairwise preferences. You can't do better than O(n^2) since you'd presumably need the full pairwise matrix anyway, so as far as asymptotics go, including the n C-penalized Approval counts is essentially free. Or am I missing something?

Thanks Kristofer, that does sound correct, and still O(n^2) as you note. This is looking quite interesting. You get clone independence from the PR round. Does it now avoid pushover strategy? Quite possibly, because elevating your weakest opponent could also weaken your hoped-for favorite. How about IIA and monotonicity criteria? Ted Frango ut patefaciam -- I break so that I may reveal On Thu, Nov 10, 2016 at 1:01 PM, Kristofer Munsterhjelm < km_elmet@t-online.de> wrote: > On 11/10/2016 09:19 PM, Monkey Puzzle wrote: > > Re-weighted Approval Voting would lose summability, but it might be > > worth considering. > > > > To fill out your proposal, the Approval winner and the reweighted > > approval winner after reweighting are matched using the original ballot > > rank preferences. > > > > This amounts to a two-seat multiwinner primary (satisfying some PR rule) > > with pairwise instant runoff. > > > > I worry that introducing multiwinner strategy would still lead to > > two-party factionalism. > > > > Would this still satisfy IIA? > > It should be summable with order n^2. For each candidate C, keep a > "C-penalized Approval count" that is counted as usual except that where > every ballot that approves of C only counts 1/2 (or 1/3), instead of a > full point, towards the candidates that ballot approves. > > Then you use the unpenalized Approval count to determine the ordinary > Approval Winner. Suppose the winner is x. Then you look up the winner in > x's penalized Approval count (say it's y). Finally, you determine the > pairwise winner between x and y based on non-penalized pairwise > preferences. > > You can't do better than O(n^2) since you'd presumably need the full > pairwise matrix anyway, so as far as asymptotics go, including the n > C-penalized Approval counts is essentially free. > > Or am I missing something? >