2011/7/26 Jameson Quinn <[email protected]> > > > 2011/7/25 Andy Jennings <[email protected]> > >> Jameson Quinn wrote: >> >>> - Would it work just as well with the Hare quota? >>>> >>> >>> Yes, but see my other message about your median-based system. For >>> contentious elections, I prefer the Droop quota. With the Hare quota, the >>> last candidate elected is likely to have about half the support of all the >>> rest. >>> >> >> I don't think that's necessarily true. It all depends how the voters are >> divided, how many candidates they approved, and the order in which they are >> eliminated. If we're electing ten candidates, there's really no reason >> that, out of the last two-elevenths of the population, exactly 50% will be >> happy with the last candidate and 50% won't. And I don't think we can >> decide beforehand that each candidate should represent one-eleventh of the >> population and one-eleventh of the population should be left unrepresented. >> >> Droop quota is natural in STV because it is the smallest number that can >> elect no more than the desired number of candidates. With a cardinal method >> I think Droop is just arbitrary. With one-winner approval voting, even 50% >> doesn't have any special significance. We just take whoever is the >> candidate with the most approvals. >> >> I guess I prefer a method like Monroe, that tries to get as close to Hare >> as it can, and if not, it does the best it can. Of course, it's not >> perfect... >> > > I definitely like a method which, all else equal, maximizes the quota. > That is, it should generally have a quota of at least Droop, and up to Hare. > But the thing is that the more information there is on each ballot, the less > likely it is to be the case that all else really is equal. Pretty soon > maximizing the quota must balance against other concerns. In that case, I'd > be happy to give it some weight if possible, but I would be suspicious of a > method that reduces to a minority veto in the single-winner case. > >> >> >> >>> Suggestions: >>>> - When a candidate is elected and you need to discard ballots, you could >>>> specify a more detailed preference order: >>>> 1. Ballots which delegated to that candidate >>>> 2. Ballots which bullet voted that candidate and didn't delegate >>>> 3. Ballots which approved two candidates >>>> 4. Ballots which approved three candidates >>>> 5. Ballots which approved four candidates >>>> 6. And so on. >>>> This eliminates ballots first which approve fewer candidates. You may >>>> still have to select randomly within these tiers, but it gives an incentive >>>> for people to approve more candidates, which helps the method work better. >>>> Right? >>>> >>> >>> Well, up to a point. The problem would be if people approved a "no-hope" >>> candidate, just to puff up the number of approvals on their ballot. This is >>> a form of "Woodall free riding", and it could lead to DH3-type pathologies >>> in the worst case. I'd rather not go there. >>> >> >> Good point. Although if there do happen to be any voters who bullet voted >> for that candidate but didn't delegate to him, then you should definitely >> eliminate those first (even before the delegated ones, I think). Once that >> candidate is elected, ballots which don't approve any other candidates are >> pretty useless, so you might as well get rid of them. >> >> But after that, I can see why you would be reluctant to incentivize >> approving more candidates. >> >> > Here's an idea. When you have elected a candidate, choose which of their > ballots survive, not which are eliminated; and do so in proportion to the > number of remaining hopeful candidates approved per ballot. This naturally > eliminates bullet votes. > > I just realized that this method makes an interesting RRV-like method. Instead of worrying about assigning ballots to candidates they approve, you worry about keeping ballots that contain plenty of leftover approval for later. I call it Remaining Ballot Weight. Dead-simple, two-step process:
Repeat: 1. Elect the highest range score 2. Reweight all ballots (from scratch) in proportion to their total range score over remaining hopeful candidates. On second thought, to prevent turkey-raising from being effective and safe, you'd have to add a step 3, taken when necessary to maintain the proportion (or, alternatively, the exponent?) between remaining seats and hopeful candidates: 3. Eliminate the lowest range score. Still, it's an unconventional system which I suspect could work very well with either honest or rationally-strategic votes. I also suspect, though, that humanly-irrational votes would tend to over-score/turkey-raise, so as to "maintain their weights", and so it would in practice lead to DH3. JQ
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