"Reweighted" methods are second rate (medium article)

[Jameson Quinn]

I just published "Reweighted" methods are second rate. This is of course my own personal opinion only, but I'd welcome comments either here or on Medium.

Jameson

[Warren D Smith]

It would be better to actually state theorems.

As it is, you have a vague claim about a
vaguely defined class of voting methods.
The claim seems to be the "reweighted" PR methods,
whatever they are exactly, suffer from "free rider" strategic voting
pathologies, whatever that means exactly.
And what about other PR methods (not branded as "reweighted")?
Do they suffer same problem, and/or other problems?

And maybe just this one problem, is not enough to justify calling
something "second rate." Not until we have considered a lot
of other possible problems. I.e. your conclusion may be premature.

I have a general argument that all PR methods inherently suffer badly
from strategy in the sense that the number of possible winner-sets
can be exponentially large (e.g. 50 candidates, 25 winners)
causing the quality-gap between the best and 2nd best winner-set
to usually be very small, causing any single voter usually to be able to
alter conclusion. This is unlike single-winner methods, where
usually no single voter can alter conclusion.

There is no escape from this problem. It perhaps suggests as a moral
lesson, that PR methods should not be used unless the
cardinality of the winner set is small. How small? Well, as a rough bound,
perhaps demand
C^W < W! * V
where C=#candidates, W=#winners, V=#voters, 0<W<C<V.
This bound also, incidentally, causes the benefit that
even "brute force" PR methods which examine every possible
winner set, become feasible.

There is no easy fix of JQ's essay from my complaints -- the
whole area of multiwinner methods
is a big area which remains to be comprehended. But it likely
does not help much to make premature and vague claims
without much comprehension...



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Warren D. Smith
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[Anthony O'Neal]

I'm the article, you seen to imply that "apportioned" methods that use an STV and largest remainder like method of reweighting did not suffer from the same flaws as standard reweighted methods that use a highest averages like method (I.e. reducing the weight of the ballots by a droop/hare quota, rather than a fixed 1/k). 

However, they do. Minor parties associated with larger parties are still going to be punished if they don't downrate their allies. They will just be slowly drained of droop quotas rather than having their ballots value cut. I think this kind of downrating is probably better for most non-list pr methods, but it's not really a solution to these problems.

[Anthony O'Neal]

I'm working on a method of range PR right now that I don't believe sufferers from that issue though, I'm calling it "Affinity Grouped Range". It basically relies on data clustering methods (here, K-means) to group ballots into n-groups based on which ballots have the most affinity to one another, and runs a single winner election within those affinity groups. I think it's basically an approximation of Monroe's method.

Affinity here is defined as Euclidean distance, with each candidate being its own dimension, and the range scores for the ballots defining a point in n-dimensional space. Ballots are grouped based on distance in this place. You could probably swap this out for pearson affinity, but I'm not sure it would do any better.

It probably sufferers from a bunch of other problems I haven't considered yet though. This is just a proof of concept, I'm compsci and not particularly good at mathematical proofs.

This is my current bare bones implementation, a command line program that accepts election data in the form of spreadsheet csv's and prints the election results and some other data in the console.

https://github.com/Markwater0ff/AffinityRangePR

On Saturday, June 30, 2018 at 9:25:11 AM UTC-5, Jameson Quinn wrote:

[Sara Wolf]

Interesting article and good explanation of that strategy. I forget who else made that case to me recently. I don't really see most or many voters figuring all that out, but it's worth considering. It seems like for STAR-PR, and especially with voters already familiar with single winner STAR Voting, the strategy to show your honest preference order would win out. I expect that the runoffs in STAR-PR would make that strategy less effective, and also just less enticing or decipherable. 

Anthony, I'm also interested also in how this scenario plays out for STV, and others, as well as if other methods (STV and less expressive options like PAD and PLACE) have other problems instead. The article felt like it dropped of quick at the end there. I bet Jameson has a lot more to say on all this. Looking forward to the next installment. 

All of this just underscores a huge need for PR-VSE. No system is perfect so identifying a weakness isn't super meaningful unless we can gauge how often it happens, how much it effects voter honesty, if at all, and how it effects accuracy overall. 

Jameson seems super focused on strategic resilience. That is obviously important, but after seeing how many voters aren't engaged at all, how many have super limited bandwidth, and how many are already maxed out just trying to find info on the candidates I'm not sure this is as critical as it might seem, past a certain point. 

Maximizing honest, expressive voting is key to collect the data we need for accurate results. Honest voting and strategic resilience are correlated, but are not exactly the same thing. Most people want to be honest and most will be unless presented with a super clear compelling reason not to. Unless a strategy is particularly transparent and obvious I don't see it as likely that many will do it. 

My preliminary conclusion; sacrificing ballot expressiveness to prevent strategy seems like it will backfire overall, even if it helps in that one area. 

[Ciaran Dougherty]

I think, if I understand Jameson's distinction, he's not proposing re-weighting the ballots by a fixed amount, or any degree of re-weighting, but actually removing some number of a Hare Quota of ballots, as being satisfied.

Just as STV links a quota of ballots to the candidate nominally representing that quota, I believe Jameson is referring (though not explicitly) to a method along the lines of my Apportioned Range method.

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[Jameson Quinn]

Yes, Ciaran is correct. I used the word "allocated" rather than "apportioned", but I was referring to the same basic idea. After each winner is chosen, 1 quota worth of ballots are removed. Typically you'd sort the ballots by some criterion, which would encompass their support for the winner and/or their lack of support for other strong candidates, and then remove the quota that came first in line. In some cases, there might be "ties" in the line, and then you might have to proportionally remove an equal amount of weight from all the "tied" ballots in the group that straddled the cutoff, so that a quota overall was removed. Or you could randomly choose "tied" ballots to remove, which generally speaking should amount to the same thing.

[Ciaran Dougherty]

To be fair, I spent a lot of time debating between "Allocated Range" and "Apportioned Range," but ultimately went with "Apportioned" in my case so as to avoid the confusion between that and allocation-based voting methods (e.g., you have 10 points to allocate among 3 candidates), but in this context, I think allocate and apportion are effectively equivalent.

PS, Jameson: Did you get the direct email I sent the other day?  I worry it might have been caught by the Spam filters.

[Clay S]

In general, I think it is important for voting systems to be continuous. RRV does this by gradually reducing the influence of voters who have a say. I think Apportioned Score Voting's approach of completely removing them produces big discontinuous jumps. Suppose you have quota (Q) worth of voters as follows:

Q: X=5, Y=3, Z=3

Q: X=5, Y=4, Z=2

Both these groups of voters have the same sum of (X - avg(others)), so based on slight variances (a voter is sick and stays home), you elect W and either remove the first quota of voters, or you remove the second quota. But this has a dramatically different effect on the contest between Y and Z!

RRV does something I consider to be dramatically more rational, which is to tax ALL supporters of X equally.

So on this issue alone, I'm pretty skeptical of Apportioned. I certainly don't think RRV is perfect, but I agree with Warren that, "There is no escape from this problem." Maybe it's better to say that there's no escape from failing at least one of this group of problems.

[Jameson Quinn]

That's precisely backwards! "Continuous" means "strategy always helps and only sometimes hurts". Specifically, in RRV, the people who support candidate X the most can strategically steal some of the voting power of X's weakest supporters, while still giving more support than the weakest supporters. In apportioned voting, strategic free riding can only steal voting power from other relatively strong supporters — people more likely to vote just as you do, so that stealing their voting power is more likely to be useless.

All else equal, "continuous" is something voting methods should actively avoid. Especially proportional ones.

...

Clay, we seem to be in complete disagreement on several issues here. Is there a chance we could "double crux" this? That is: what evidence would change your mind? The evidence that would change my mind would be if you could show your methods have better two-stage voter satisfaction efficiency in a realistic voter model (not impartial culture; possibly N-dimensional Gaussian ideology; but ideally, Dirichlet clusters in ideology space).

Jameson

--

[Clay S]

Jameson,

Regardless of the semantics around what "continuous" means, I've cited a clear problem. A tiny change in input has a drastic change in output. You elect X but only penalize half of his supporters, which just isn't mathematically/logically justified.

The alternative is to just erase information so it can't be exploited. It's like forcing Approval Voting instead of Score Voting so tactical voters don't get as much Advantage as with score voting. I think this is deeply flawed reasoning.

[Clay S]

having said this, there's probably a way that we could get the best of both worlds. If you go back and look at Ciaran's original flawed example for RRV, the problem is that you can add a constant to every score on a particular voter's ballot, and change the result. so one can imagine an rrv that Waits based on relative scores rather than absolute scores, similar to the ARV proposal, but without making the drastically distortionary move of eliminating some set of voters.

[NoIRV]

Asset Voting is better. We should make www.asset.vote for it.

[Toby Pereira]

You can use the KP transformation, which turns score ballots into approval ballots, and that might do what you want.

Let's say there are two parties, A and B, with a max score of 10, and you have the following ballots:

20 voters: A=5, B=0

10 voters: A=0, B=5

RRV I believe wouldn't award the seats in a 2:1 ratio because of how it handles scores below the max.

Using the KP transformation, you'd end up with (approval ballots):

10 voters: A

5 voters: B

And A would end up with twice as many seats as B. Then you could add a constant to the scores:

20 voters: A=10, B=5

10 voters: A=5, B=10

This transforms to:

10 voters: A

10 voters: A, B

5 voters: B

5 voters: A, B

Which cancels to:

10 voters: A

5 voters: B

15 voters: AB

Under PAV (which is what RRV with approval ballots becomes), the AB voters become irrelevant, so it's easy to see that the 2:1 ratio holds. Under normal RRV without the KP transformation, you'd end up with something horrible I think.