[EM] STV version of VoteFair Representation ranking

[Richard, the VoteFair guy]

Excellent insights!  Once again, thank you Kristofer for your wisdom.

Richard Fobes
The VoteFair guy


On 2/10/2022 5:15 AM, Kristofer Munsterhjelm wrote:
> On 09.02.2022 20:51, Richard, the VoteFair guy wrote:
>> In the new "Hare clustering MAM-based PR, and a tie problem" thread,
>> Kristofer Munsterhjelm wrote:
>>> .... It's based around the idea of making a
>>> number of virtual constituencies (one for each seat), and
>>> then trying to allocate voters to each so that the case for
>>> the winner (according to the Ranked Pairs method run in
>>> that constituency) is as strong as possible, i.e. the
>>> choice of winner or winning order is as justified as
>>> it can be.
>>> ...
>>> Then both Kemeny and RP, in the absence of ties, calls an election by
>>> producing the social ordering that maximizes its respective score
>>> function. That is, Kemeny chooses the one whose sum of consistent
>>> pairwise victories is maximized, and RP the one whose largest pairwise
>>> victory is maximized, and among these, the one whose next largest
>>> pairwise victory is maximized, and so on.
>>
>> Kristofer, what you're describing sounds similar to the STV version of
>> VoteFair Representation ranking:
>>
>> https://electowiki.org/wiki/VoteFair_representation_ranking#STV_version
>
> It is, sort of, but I would say that there are some differences.
>
> - Your method is house monotone. Since the first seat is chosen with a
> Condorcet method, it must therefore fail Droop proportionality, see
> https://electowiki.org/wiki/Left,_Center,_Right.
>
> - The deweighting method seems a bit ad hoc, where it tries to reduce
> the influence of voters who got the candidate they wanted, but uses a
> heuristic to determine just who that is. In contrast, my method doesn't
> make up its mind about who the first group of voters (who deserve the
> first candidate) is, until it's done finding a candidate for that group;
> and once it has done so, it knows exactly who they are.
>
> Your method seems more consistent with the Droop quota than the Hare
> quota, as in: mine tries to find a group of voters, then remove them,
> while yours tries to find a group of voters and then reweight them (like
> ordinary STV).
>
> My method could be made Droop-style, and this would (I think) help
> attenuate the tie problems. Instead of the LP step choosing a Hare quota
> that's consistent with the defeat magnitudes locked in, it would choose
> to magnify a group of voters' weights so that a Droop quota becomes a
> majority. Then the mutual majority criterion of original RP (that Kemeny
> also passes, by the way) would translate directly to the Droop
> proportionality criterion.
>
> Let's say every voter's weight is 1 before we do reweighting, and there
> are v voters in total. Then the Droop quota is v/(s+1), so suppose
> everybody in this Droop quota gets a weight w, and everybody else
> retains the weight of 1. Then we have
> 	wv/(s+1) = 1/2 (wv/(s+1) + (v - v/(s+1)))	majority blowup
> which gives the solution w=s.
>
> So the LP would set: let each voter's weight be between 1 and s, so that
> the total weight distributed is exactly 2sv/(s+1), and set the weights
> so that the given pairwise preference's strength is maximized. This is
> an additive weights solution, similar to Warren STV. Presumably
> multiplicative weights (like Meek) are also possible, but this post is
> already long enough :-)
>
> This attenuates tie problems because now the unweighted ballots have
> some say in breaking the tie; the chance of a tie would be low even with
> very small virtual constituencies because (in effect) the ballots who
> are not participating help drag the outcome in their direction.
>
>> I added this section to Electowiki recently because there is growing
>> interest in using STV to elect city councils, yet STV is overly
>> simplistic, and has flaws similar to IRV flaws (especially ignoring
>> valid ranking data that's very relevant).
>>
>> This STV version of VoteFair Representation ranking extends the two-seat
>> version of it that I designed for partisan elections.  The result is an
>> STV-like non-partisan method.
>>
>> Of course it's based on the Kemeny method rather than Ranked Pairs.
>> That's my bias for the reason you mention, namely that locking in a
>> pairwise win can block additional info.  This is similar to the way IRV
>> blocks lower-ranked preference info from being looked at.
>
> Well, if you're willing to pay the NP tax, then Ranked Pairs can also be
> made to optimize its particular metric.
>
> As for Kemeny vs RP, I would say that "taking into account every
> candidate" sounds good, but if it's not done with proper insight, the
> method can get confused about how much information is available to each
> candidate.
>
> That's how Borda gets its teaming incentive: by cloning A, you make the
> "weight of evidence" that's about A stronger, relative to the other
> candidates, and so the method gets pulled in the direction of A. Because
> Kemeny takes the sum of preferences, it's also vulnerable to this sort
> of confusion. And sure enough, it's not cloneproof.
>
> In any case, the idea of my method is to generalize Condorcet methods
> like RP to proportional representation in a way that's clearly based
> around that Condorcet method and not on a candidate elimination method
> (like IRV-based STV is). It doesn't *completely* satisfy this as winners
> are still eliminated after winning, and so probably isn't monotone, but
> there are no remnants of IRV left. And unlike Schulze STV etc., it's
> polynomial time -- barely.
>
> (Now there's a thought: don't eliminate any candidates, but skip past
> already elected candidates when choosing the winner for the kth
> constituency based on its RP social ordering. It would probably still be
> non-monotone, but it should be better behaved.)
>
> -km
>