Multi-Seat range voting other than Reweighting?

[Ciaran Dougherty]

Hi everybody,

I've been looking at multi-seat range voting for a while, and while there are numerous solutions that work for Candidates, the behavior seems kind of weird to me when it comes to "Party List" elections (such as the Electoral College should be, in my opinion).
I spent a fair bit of time looking at various methods, trying to improve on the re-weighting algorithm, but every attempt I've made at re-weighting is worse than extant designs.

That got me wondering, though.  Are all extant multi-seat, score/approval voting systems re-weighting based?  Is there any that uses a different method?  Because I have what I think might be a viable alternative (if I could get the bloody thing coded to test it against multiple data sets in a reasonable time frame...)

Ciaran

[parker friedland]

Yes, there is a variety of multi-winner voting methods. I have put many of them on to a comparison table on Wikipedia: https://en.wikipedia.org/wiki/Comparison_of_electoral_systems#Compliance_of_multi-winner_methods_.28table.29

[Brian Langstraat]

Score Remainder Voting (SRV) and Approval Remainder Voting (ARV) are voting systems for multiple winners similar to Reweighted Range Voting (RRV) except votes retain power equal to the remainder of their contribution beyond the winning threshold for each winner.

Another interesting proportional voting system is Single Divisible Vote with Least-Popular Elimination (SDV-LPE).

I am not sure how "Party List" elections would integrate with range voting systems, since voters can give scores to every candidate (beyond a single party).

Perhaps, Geographic Open List/Delegated (GOLD) voting could be close.

It is funny to me that Bid Voting is in the comparison table, since I posted it as a thought experiment.

[Brian Olson]

Reweighting seems like a pretty obvious and pretty good general strategy for me for Proportional Representation election algorithms.

If you vote for a popular candidate with more than the PR election threshold, you should get some of your vote transferred further down on your ballot. Depending on the details of the algorithm you could be voting 70% 80% 50% 30% or whatever for your first choice at various intermediate steps in the election algorithm depending on the state of the rest of the candidates and your vote.

This doesn't bother me, it seems like a normal process to have intermediate state like this which settles on a pretty good final outcome.

Is the worry that this will be unpleasant sausage-factory stuff to the general voting populace?

Some other worry or distaste?

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[parker friedland]

Re-weighted range voting and proportional approval voting are unfortunately a lot more strategic then their single winner counterparts. They create participation paradoxes, fail the favorite betrayal criterion (which unfortunately may not be possible to avoid because Hylland free riding seems like a problem in all voting systems), and they fail the universally liked candidate criterion (http://scorevoting.net/QualityMulti.html#faildesid) which puts in to question how proportional these voting systems are to begin with.

I am however very interested in Monroe's voting system (http://scorevoting.net/MonroeMW.html) because it seems to be the most resistant proportional voting method to Hylland free riding and favorite betrayal. Consider the fallowing example:

There are three candidates running and there will be two. Every voter prefers the independent however half of the voter's second choice is either the democrat or the republican. Nearly every proportional voting system that I know of will encourage democrats or republicans to give less support to the indepndent in order to make their votes more powerful when determining whether the democrat or republican will win the second seat, except Monroe's system (and possibly Elbert's voting system as well however I don't understand his voting system). However there are other examples of Monroe's system failing the favorite betrayal criterion when there are more candidates, but in the case of three candidates and two winners, I don't think there is a scenario where there is an advantage to not giving your favorite candidate a maximum score.

Thus I believe that Monroe's voting system might be the proportional systems that is the most (or one of the most) resistant to strategic voting. And it is not very hard to implement in an election. In the approval version of Monroe's system, you can simply use this equation:


Where Va = the number of voters that out of a, b, and c, only approve of candidate a
Vb = the number of voters that out of a, b, and c, only approve of candidate b
Vc = the number of voters that out of a, b, and c, only approve of candidate c
Vab = the number of voters that out of a, b, and c, only approve of candidate a and b
Vac = the number of voters that out of a, b, and c, only approve of candidate a and c
Vbc = the number of voters that out of a, b, and c, only approve of candidate b and c
Vabc = the number of voters that approve of a, b, and c
Vx = the number of voters that do not approve candidate a, b, and c
Q = (Va + Vb + Vc + Vab + Vac + Vbc + Vabc + Vx)/3

Candidates a, b, and c can be substituted for any candidates and the three winners are the three candidates that when substituted for a, b, and c, produce the lowest value of P.

Note that I created my own box syntax: each box is equal to what is in that box when it is positive, and 0 when what is in that box is negative.

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[Lonán Dubh]

That's a really neat chart, but is there any centralized list of definitions for the Multi-Seat Criteria?  The ones that I don't quite understand specifically are what is meant in this context by:

• Independence of Core Support
• Majoritarian
• Smith-Set Winners (Does "Yes" mean a Smith Set is, or isn't, elected?)
• Universally Liked Candidates

Thanks for helping me get up to date on the more technical side of this.

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[parker friedland]

Majoritarian is not a criterion, it is simply a form of classification of the type of voting method just like Proportional was. I put that in there because some voting methods are neither majoritarian or proportional like SNTV (however it is proportional when all voters are 100% strategic) so I didn't want to give the wrong impression about those methods.

The Smith Set Winners criterion is simply intended for majoritarian methods, and is just a multi-winner version of the Smith criterion. A method passes this criterion if when the smith set is larger then the amount of winners, every winner will be from the smith set, and when the smith set is smaller then the amount of winners, every member of the smith set will be a winner. This is suppost to be the multi-winner version of the single winner Smith/ISDA criterion so I probably should of just called it Smith/ISDA in order to prevent confusion.

I linked the Universally Liked Candidates criterion to a page that defines the criterion. You could have just clicked on that link: http://scorevoting.net/QualityMulti.html#faildesid

The "independence of core support" criterion is just a way that I tried to spin the ability for a voting method to elect a candidate with 0 first preference votes as a positive. This is because Fairvote had a page up for a while that was eventually taken down and on that page, Fairvote's litmus test for whether a voting method is reasonable or not is if it only elects candidates with "core support" meaning candidates that are atleast one voter's favorite according to their ballot. In fact, they still mention that aspect on this page too (http://www.fairvote.org/alternatives) however it is not their main litmus test anymore. This is completely ridiculous. It should actually be a good thing for a voting method to be able to elect a candidate that has 0 first preference votes because when there are a 1,000,000 candidates, 999,999 voters, and every voter happens to have a favorite candidate, but they all have the same 2nd favorite candidate, then no matter what Fairvote says, that 2nd favorite candidate should win. period. This is a criterion that should be added to the single winner page instead because IRV and plurality are the only voting methods that fail the criterion, but the visual Wikipedia table editor will not let me edit the single-winner table and I can't edit the code because I don't even know what language Wikipedia codes it in so I just put it in the multi-winner table for now.

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