[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.
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
>         ----
>         Election-Methods mailing list - see http://electorama.com/em
>         for list info
> ----
> Election-Methods mailing list - see http://electorama.com/em for list info

Richard Lung.
Democracy Science series 3 free e-books in pdf:
E-books in epub format:

-------------- next part --------------
An HTML attachment was scrubbed...
URL: <http://lists.electorama.com/pipermail/election-methods-electorama.com/attachments/20170730/ce99393b/attachment-0001.htm>

More information about the Election-Methods mailing list