[EM] Sequential Best Assigment (multiwinner method)
Richard Lung
voting at ukscientists.com
Sun Jul 30 00:39:23 PDT 2017
A generalised STV (which is what is my invention of Binomial STV [BTV])
does not have a residual FPTP in the last round.
By including a rational exclusion count, BTV [Binomial Transferable
Vote] avoids the problem of excluding candidates, which seems to be what
much of the discussion on this forum is about.
from
Richard Lung.
On 26/07/2017 16:12, Andy Jennings wrote:
> I think you're right that this matches BTV in the major details. Is
> http://rangevoting.org/BucklinTV.html the best reference for BTV? It
> doesn't have a page on Electowiki, yet, right? We should add one.
>
> There aren't many good, simple, rated-ballot, multiwinner systems, so
> it deserves to get talked about more, no?
>
> I wasn't suggesting to change the name, but if you are...
>
>
> Regarding the quota: I see what you're saying about the crumbs. I
> just have reservations about a quota that's not even going to try to
> represent 1/(s+1) of the population. I realize that STV does it and
> STV has a track record. But STV does it because it might come down to
> a one-on-one at the end and you want to say that a majority in the
> final round is the same as the quota for all the other rounds. A
> rated system doesn't have that restriction. I kind of like approval
> voting in the last round, even if the winner only gets 30-40%.
>
> If we choose one quota for the default, I'd hope we could add a
> footnote that the other one was a possible alternative.
>
>
> Tiebreaker and deweighting: I don't feel strongly about these, but
> it's good that we're considering different options, looking for
> simplicity but also looking for corners that cause adverse
> incentives. I think it's better to recommend good defaults than just
> including a bunch of options.
>
> Tiebreaker: If we were to use Hare quota (and "approval voting" in the
> last round), then the critical grade for the last round is going to be
> 0(F), so a GMJ tiebreaker or "most votes at or above critical" are not
> going to help break ties. We'd either have to have a different rule
> for the last round, or a second tiebreaker. "Most votes strictly
> above critical" would do it.
>
> Deweighting: If we wanted to, we could "assign" voters to the
> representatives for whom they were deweighted. In that case, it would
> be advantageous to deweight in chunks as large as possible. So
> subtractive deweighting would be better than multiplicative and rules
> that "deweight completely" are good. But multiplicative is probably
> simpler.
>
> ~ Andy
>
> On Tue, Jul 25, 2017 at 8:58 AM, Jameson Quinn
> <jameson.quinn at gmail.com <mailto:jameson.quinn at gmail.com>> wrote:
>
> This is a good idea.
>
> But on thinking about it further, I'm not sure whether it's not
> the same as BTV.
>
> BTV, like Bucklin, works by gradually lowering a "pseudo-approval
> threshold", and electing and deweighting candidates as they reach
> a quota of "pseudo-approvals". Andy's proposal, like MJ, works by
> directly looking at the "quota-th" highest rating, and electing
> and deweighting the candidate who's highest by that measure.
>
> But of course, we know that, aside from tiebreakers, MJ and
> Bucklin are the same thing. So the more I think about it, the more
> I think that (aside from quota choice, tiebreaker, and deweighting
> scheme; none of which are really specified by the label "BTV")
> Andy's proposal and BTV are the same thing.
>
> I could be wrong about this... can anybody else check my logic here?
>
> Still. Even if this is just a new name for BTV, it's a good excuse
> to discuss that system.
>
> We could talk about how good it is. Pretty excellent! I like that
> it avoids the horrible center-squeeze breakage of STV. Even though
> the problems with center squeeze are much less in a multiwinner
> setting than in IRV, it's still ugly.
>
> When designing GOLD
> <http://wiki.electorama.com/wiki/Geographic_Open_List/Delegated_%28GOLD%29_voting>,
> I chose STV rather than BTV as a substrate. That wasn't because I
> prefer STV theoretically; it's just because of its longer track
> record.
>
> Also, we could talk about the ancillary design decisions: quota
> choice, tiebreaker, and deweighting scheme.
>
> Quota choice: I tend to prefer Droop, or a compromise V/(S+.5),
> over Hare. Basically, when you're assigning the last seat, you're
> left with the voters who are most atypical; the "crumbs" of the
> party system. If you use a Hare quota, then at best you'll find a
> candidate with some appeal to a full quota; but realistically, you
> might just find the biggest of a group of crumbs, who could easily
> have support from just 35-40% of a quota (based on 1/e, my SWAG
> for this kind of situation). If you go with a Droop quota, on the
> other hand, the entire pool is 2 quotas; and 2/e is 70-80% of a
> quota, much closer to fair.
>
> Andy's suggested deweighting scheme might help encourage bigger
> crumbs, but I'm not sure about that.
>
> Tiebreaker: I don't have a lot to say about this. GMJ-style seems
> like a good choice.
>
> Deweighting: This is where things get interesting. You don't want
> to have too much of a free-riding incentive, but you do want to
> deweight the votes which are "more satisfied" with the winners and
> not-deweight those which are "less satisfied" with the future
> potential winners.
>
> I like Andy's concept of subtractive, rather than multiplicative,
> deweighting. It makes things a little bit harder to describe, but
> it does mean that somebody who is "halfway decisive" twice will be
> fully deweighted, rather than keeping 1/4 of their voting weight;
> that seems fair to me.
>
> I think that Andy's rejected idea of "for those who only gave the
> new winner the threshold rating, deweight them last" was doing it
> wrong, so I'm not surprised that he decided it led to too big of a
> free rider incentive. If you're doing a GMJ tiebreaker anyway,
> then from a BTV point of view, those voters are essentially giving
> a fraction of an approval to the new winner. I think that only
> that fraction of their ballot should be at risk for deweighting;
> so their subtractive deweighting should be the minimum of their
> GMJ fraction and the overall deweighting.
>
> The other way to do things is to try to avoid deweighting voters
> insofar as they still have useful opinions about the remaining
> candidates. That's what Andy's proposed "completely deweight those
> who rate all remaining candidates at 0" rule would do. But this
> could still leave a very "crumbly" remainder at the end; imagine
> if the 100 candidates for the last seat each had 1% of the
> remainder giving them a top-rating.
>
> So I can imagine more complicated schemes to do this. For instance:
>
> 1. Find the R candidates with the highest quota-th ratings, where
> R is the remaining number of seats. In other words, the
> prospective winners if you proceeded from here on without any
> deweighting.
> 2. Of the deweight-able votes (counting only the GMJ subtractive
> portion ot threshold votes), find the Q which have the lowest
> max rating for those R candidates. Deweight these completely.
>
> Note that the incentive of the above is not so much to downvote
> early winners, as with traditional free riding (though of course
> that is still possible if you downvote them below their winning
> threshold), but rather to up-vote late winners. That creates a
> couter-free-riding incentive; a possibility I'd never considered
> before.
> ....
>
> But all-in-all, I think that Andy's suggested deweighting scheme
> is pretty good, and I'd rather go for "simple" than "theoretically
> awesome" here.
>
> Jameson
>
>
> 2017-07-24 21:58 GMT-07:00 Andy Jennings
> <elections at jenningsstory.com <mailto:elections at jenningsstory.com>>:
>
> Here's a multiwinner system that's so simple that it should
> have a name, but I don't think it does. Let me know if it does.
>
> It uses rated ballots. The goal is to repeatedly find the
> candidate whose top quota's-worth of grades are highest and
> elect that candidate, then de-weight a quota's-worth of
> voters. Some names worth considering:
>
> Sequential Best Assignment
> Sequential Constituent Matching
> Sequential Quota Allocation
>
> The method:
>
> N = Number of voters
> S = Number of seats
>
> 1. Every voter grades every candidate. (I'd say 4 or 6 grades.)
>
> 2. Each voter starts with weight 1.
>
> 3. Choose quota Q = N / S. (*)
>
> 4. For each candidate, calculate the minimum of their top Q
> grades. Let G be the highest minimum. Elect the candidate
> with that minimum. (Break ties as in GMJ: calculate for each
> candidate what fraction of their G grades are in their top Q
> grades, and elect the candidate with the smallest such
> fraction. Break further ties by choosing the candidate with
> the least number of G grades in their top Q grades.)
>
> 5. Deweight some voters to decrease the total voter weight by
> Q, in this manner:
> a) any voter who gave the minimum grade to all remaining
> candidates is deweighted to 0.
> b) for the voters not deweighted in (a) who gave this
> candidate a grade of G or above, find the deweighting D such
> that when the deweighting formula:
>
> W_new = max(W_old - D, 0)
>
> is applied, the total voter weight in this round is decreased
> by Q. (**)
>
> 6. Repeat steps 4 and 5, applying voter weights when
> calculating the top Q grades, until S seats are filled.
>
>
> (*) With this quota, when you are filling say, 4 seats, then
> 25% of the voting weight gets used up with each seat filled.
> 25% of the voting weight will remain when choosing the last
> seat. That last seat will be determined by the tie-breaker
> rule, so it is essentially equivalent to approval voting, with
> any above-bottom grade counting as approval.
>
> The other common choice of quota, Q = N / (S + 1), could also
> be considered. When filling 4 seats, then, 20% of the voting
> weight gets used up with each seat filled. 40% of the voting
> weight remains to choose the last seat, so the last seat is
> essentially filled with a median-based method (GMJ). 20% of
> the voters' opinions are, by design, left without a
> representative.
>
> (**) I thought about another step (a') where anyone who gave a
> grade strictly above G was deweighted completely, but I think
> it gives the voters too much incentive to down-weight
> candidates who they think can get elected without their help.
>
> I also considered another step (a'') where anyone who graded
> the chosen candidates strictly above all other candidates was
> deweighted completely, but I don't think there's much benefit
> for the added complexity.
>
>
> Any thoughts on which quota is better or on the right name?
>
> ~ Andy Jennings
>
>
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--
Richard Lung.
http://www.voting.ukscientists.com
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