Multiseat Range method proposal (feedback requested)

[Lonán Dubh]

Working name of the method is "Apportioned Range Voting," but I'm open to suggestions.

Reason: All of the multi-seat range methods I've seen are pretty decent, but require a calculator or spreadsheet to compute (as cited in the "Book-club voting" thread), especially for more than a few "seats."  Anything that complicated isn't likely to be supported by the populace, which is (IMO) the biggest obstacle to actual reform, the biggest advantage Ranked Choice has right now: that people can understand the algorithm (if not the repercussions).

To solve this, I took a page out of STV's book, and instead of multiplying scores by some calculated coefficient, I propose to "set aside" ballots when they are "satisfied" (ie, used to seat winning candidates).  That way, the hypothetical book club can literally set aside ballot papers and calculate the next winner, rather than having to pull out a spreadsheet program

Using Score ballots, while there are still unfilled seats:

1. Find candidate top candidate as normal with Range voting

2. Set aside a Hare Quota of ballots provide the greatest contribution to that contribute most to the seated candidate as "belonging" to that seat and not influencing later seats.

"Contributes most" is (provisionally) defined as having the largest difference between that ballot's score for the candidate in question and the mean of the scores on that ballot.

For transparency, the ballots associated with each seat could (should) be tallied, so that the people can see the relative support each candidate got, and which other candidates their supporters liked/disliked.

Notes:

• For validity of calculation, a score needs to be predefined (and published) for unscored candidates.
• Non-discriminating ballots (all candidates receiving the same score) should be pre-apportioned evenly across all ballots, so as to prevent a scenario where the final seat is elected by fewer discriminating ballots than the earlier seats.  They could be simply simply tossed out as void, but I believe they should be included in the final reporting, for transparency.
• If multiple voting blocs tie in support (eg, 9/6/0 vs 9/0/6 vs 9/3/3, etc) apportionment should be proportional to the size of their voting blocs
• Alternately/additionally, there could be some form of apportionment tiebreaker, to ensure that the most discriminating ballots are left in the main ballot pool.  Perhaps the smallest set of scores?  Largest Z-Score of seated candidate's support? Smallest StDev of remaining scores? I'd love suggestions for this, or any aspect of "Contributes Most to Candidate"
  
• If fractional ballots are to be used in apportionment, recommend displaying results for each seat as Mean scores rather than Sums of scores, because the public expects averages, but not sums, to contain decimals
• Because of the (simulation) demonstrated benefits of STAR, and because many voting pathologies seem to occur predominantly (if not exclusively) in the last seat in any election, I would personally recommend that any application of this method treat the last seat as a form of STAR election, but using this method for selecting the runoff candidates.
  

Voting Criteria compliance (as best I can figure):

• Proportional: Yes?
  
• Monotone: Yes (Range)
  
• Cloneproof: ?
• No Favorite Betrayal: Yes (Range)
  
• Consistency: ?
• Participation: ?
• Later No Harm: Fails (Range)
• Later No Help: Passes single seat definition (Range)
  
• The Diff from Average method of ballot apportionment means that higher you rank L, the more likely that your ballot will be used for L's seat, instead of F's, but it also means that higher you rank L, the more likely that  your ballot will not be used for F's (secured) seat, but "survive" to help seat L
• Combined these two aspects of Diff from Average should promote honest scoring, because while the danger of not seating F provides pressure to artificially lower L's score, the possibility of additionally seating L provides counteracting pressure.
• How hard to understand: Harder than STV (requires math), but Simpler than RRV (the math is easier).

I'm pretty sure that's the entirety of the idea, and my analysis of it to date.
Questions?  Comments? Criticisms?

Ciaran

[parker friedland]

First of all, because your definition of "contributes the most" involves the mean of scores a voter gave to each candidate in the race, this voting system fails the independents of irrelevant alternatives criterion and is also heavily vulnerable to cloning.

You are also wrong about it passing the favorite betrayal criterion.

Consider the fallowing election:
51 honest voters give 5 stars to the Independent, 4 stars to the Democrat, and 0 stars to the Republican.
50 honest voters give 5 stars to the Independent, 4 stars to the Republican, and 0 stars to the Democrat.

In this election, the Independent is elected first, and the Democrat is elected afterwords. However, if some of the Republican voters strategically give 0 stars to the Independent, less of the Republican vote would contribute to electing the Independent and as a result, the Republican would be the second winner instead of the Democrat.

[Ciaran Dougherty]

Thread necromancy!  I'm still looking for comments, and especially suggestions, regarding this method.

First, I have found a scenario in which it would be beneficial to have a backoff step.  Specifically, when I was running simulations, the ballots associated with one of the seats for Candidate X actually preferred Candidate Y.  That doesn't seem right, so I have modified the algorithm as follows:

1. Find candidate top candidate, X, as normal with Range voting

2. Set aside a Hare Quota of ballots that contribute most to X being seated as "belonging" to that seat and not influencing later seats.

A. Calculate the winner of the ballot associated with that seat.  If that winner, Y, is not the same as X, put the ballots back in the pool, and continue with 2, seating Y instead.

As to Parker's assertion about it failing No Favorite Betrayal, the scenario describe is not favorite betrayal, it's Hylland Freeriding, a different problem.

While both can (will?) trend towards candidates having less expressed support than actual support, the difference is that Favorite Betrayal happens when a candidate is expected to lose (thereby causing them to lose, creating a vicious cycle that I believe a major driver of Duverger's Law), while Hylland Freeriding happens when a candidate is expected to win.   The result of this difference is that iterative FB will trend towards a candidate always losing, while iterative HR should trend towards them receiving as many seats as they are expected to win.

So, does anybody have any other comments?  I'd like more feedback than simply "You're wrong" without any suggestions, especially since I explicitly stated that "Contributes most" was only provisionally defined...

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[Ted Stern]

I played with such ideas back in 2011-2012.  My efforts at that time can be seen here:

https://github.com/dodecatheon/range-transferable-vote

IMO, taking out full ballots to make the quota is a bad idea, since it would increase the incentive for freeriding.

[Toby Pereira]

If a candidate is "over-supported" - i.e. has over a Hare quota, then by taking out actual ballots rather than doing a fractional reduction, a lot of that candidate's supporters will continue at full strength for later rounds, while some will be wiped out. You might have several voters that have given this candidate the highest rating, but then their support for other candidates is split. But they might be equal in terms of "contributing most" to their favoured candidate.

Also, people might give high ratings to non-entities so that their ballot "contributes less" to their favoured candidate. I know your definition of this is provisional, but as I understand this could be a problem right now.

I get the feeling generally that once you iron everything out, it won't be that simple!

[Ciaran Dougherty]

I agree that ballot removal does give incentive for freeriding, though I am less concerned with that (fewer votes for candidates/parties with seats) than I am with the majoritarian aspects of RRV, for example (fewer seats for candidates/parties with votes).

You say it would increase incentive for freeriding... increase it compared to what?

[Warren D Smith]

"1. Find candidate top candidate as normal with Range voting
2. Set aside a Hare Quota of ballots provide the greatest contribution
to that contribute most to the seated candidate as "belonging" to that
seat and not influencing later seats."

--my first comment is: that was not the English language you were using.

My second is, if it were approval ballots, not range, then it sounds
like this system would
indeed be PR. Therefore there is a sense it is PR with range ballots.

Third, you do not say what happens when it is no longer possible to
give anybody a
Hare Quota from the remaining ballots, so your description is
incomplete? And key
is some sort of tie-breaking, e.g. select the ones to set aside at random if
more than one such set-aside set is possible? Then it is a randomized
election method.
One could avoid randomness by partially setting aside ballots, i.e.
deweighting them,
which leads to weighting going on.



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Warren D. Smith
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[Warren D Smith]

Comment #4:
if you did weighting it would be pretty similar to RRV.

Comment #5:
However with range ballots there would be an annoying "discontinuity."
If I vote 6 for Joe, and you score Joe 7, then I contribute nearly
as much to Joe's victory as you do, but maybe my ballot is not deweighted or
set aside at all, while yours is. Which is kind of peculiar.

If you decided to correct for that flaw (if thought to be a flaw) then
your system would end up looking even more like RRV.

... So I'm not terribly in love with RRV, but it seems like
your system sounds intuitively like it is worse than RRV, since when
you start fixing apparent flaws in your method, it becomes more and
more RRV-like (maybe at
the end of the fixing process you'd actually then have RRV exactly).

[Ciaran Dougherty]

Oh, thank you, I had considered totally non-discriminatory ballots ("full ballots" under approval), but I had not considered ballots that were non-discriminatory after a candidate had been seated (and thus no longer a consideration).  

Now the question is whether those should be apportioned ahead of the still-discriminatory ones (of the same contribution), or merely distributed among the remaining seats (as fully discriminatory ones are).

--

[Ciaran Dougherty]

It may not have been clear enough to suit you, but there's no reason to be insulting; you could have asked for clarification. I will attempt that now, which should also clear up your point 3

For a race with N seats, there are, by definition, N full Hare Quotas.

For the first seat, calculate the Range/Score winner of the N quotas as though it were a standard, single seat race.

Having found the winner of the first seat, find Hare quota that contributes most to their selection, and set them aside as being ballots apportioned as electing that first seat.

Repeat this process, calculating the second seat from the N-1 quotas not yet apportioned, the quota that most contributed to them, etc.

For the Nth seat, there is only one quota left, which is treated like any standard single seat range/Score election.

[Ciaran Dougherty]

I am specifically not doing weighting, because none of my previous attempts to tweak the RRV weighting were capable of overcoming RRV's majoritarian bias to a reasonable degree; with my test sets, every weighting I tried either gave the majority faction way too many seats, or way too few.

Re: 5. All else the same, you have the right of it.  ...but why should that be peculiar? By our own ballots, I declared that I would receive greater utility than you, the seated candidate is closer to my ideals than to your own. As such, by the declaration encoded on your ballot, you would be less "harmed" by your ballot being used to elect an alternative than I would.

On the other hand, if our ballots were different beyond just our scores for that candidate, it might be your ballot that is apportioned to that seat. For example, if your ballot were 6/2/0 and mine were 7/4/6, then our relative contributions, our relative utilities, would be +6/+2/+0 and +3/+0/+2. After all, a ballot of 9/9/9 contributes no more to A being selected over  B or C than a 0/0/0 ballot does.

So, no, I do not consider similar ballots being treated differently a flaw, because they are different.  By my design, the more similar the ballots are, the less likely they will be treated differently, but because every reweighting attempt I've seen ends up less proportional than STV or SNTV (unless people bullet vote, neutralizing the benefits of cardinal ballots), there needs to be some cutoff at some point.

It sucks, no question, but I'm at a loss as to what other options there are for cardinal ballot PR systems under party list/slate of clones scenarios.

[Toby Pereira]

Have you read what I put in this thread - https://groups.google.com/d/msg/electionscience/tyQFDrD3GR8/Nv0ogS2XAwAJ The majoritarian bias you found could be due not to the reweighting itself but due to how RRV deals with scores less than the maximum. Turning everything into approvals first (using the KP transformation) should make it less majoritarian.

[Toby Pereira]

One possibility to keep it simple and roughly fair is to use a random method to decide which ballots are used for each Hare quota. I'm not sure how well randomness will be perceived, but in big enough elections it should average out, and unless it's really close it won't normally make a difference. You'd still need to decide how the random process worked of course.

[Ciaran Dougherty]

If you randomly sorted the ballots into the quotas, each one would trend towards equivalent to the overall result, based on the math that makes sampling a valid concept. 

As such, the result would trend towards being functionally indistinguishable from Range-winner-takes-all in party list scenarios (e.g. presidential electors), and "top N scores" in all others. At that point, there's little benefit to splitting the ballots at all.

[Toby Pereira]

That's not what would happen. The ballots would be randomly drawn from those supporting the elected candidate (perhaps their weight in the random draw could be proportional to the score they have given the candidate or something) - I'm not talking about electing a candidate and then picking Hare quota of ballots at random from all the ballots in the election. That would be crazy! So in a party list scenario, when party A gets a candidate elected, the only ballots that are withdrawn would be those supporting party A. This would then reduce the number of party A ballots for the next candidate to be elected.

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[Ciaran Dougherty]

Okay, that makes way more sense than how I (mis)interpreted your suggestion.

So then, one has to ask whether a 3/5/1 ballot has equal probability of being selected for A as a 5/3/1 ballot does?  Perhaps you could have weighted probability, but that pushes us significantly towards "Computer required" territory.

Even if you do have the random selection weighted by score for A, would a ballot 5/1/1 have equal probability of being selected as a 5/3/1 ballot?  If the latter is selected, mightn't that turn the former from a "Bullet A" ballot into a "non-discriminating" ballot (assuming A is no longer eligible for seats), thus negating the relative advantage B had over C?

Once you start considering those questions, it sounds like the question of "How do you define 'shows support'?" that I had in my deterministic scenario, but with the added complexity of randomness.

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[Toby Pereira]

I suppose the main problem is that I can't see any way of making a reasonable PR method that doesn't require a computer when there are more than a handful of ballots.