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Multi-winner elections

Some of the content of the voting talk I gave January, aimed at the application of anime club, in which we typically have a few dozen nominated series, from which we select 6 to watch the next term. This is, in the jargon, a multi-winner election, as opposed to the single-winner ones we almost always use in the United States.

The first question is what do you want: majority rule, or proportional representation (PR)? For political purpose I strongly favor PR -- we all live here, like it or not; the legislature is meant to represent the people, but make better decisions than them due to small size and increased information; PR helps it actually represent the people.

But for a club with free and open membership, majority rule might work better, keeping the character of the club stable against random newcomers, so e.g. a club doesn't have to watch Naruto if there's a surge to 1/6 Naruto-favoring membership, possibly driving out old-timers and going into a death, or at least change, spiral.

So I've gone from thinking club should obviously be PR, to thinking maybe it should have two stages: a majoritarian one, filtering the nomination list for candidates acceptable to the majority or at least a lot of the club, followed by PR within that. This is actually close to what we've ad hocced up in the past.

Various options:


* Bloc voting, or at-large. N slots, so each voter has N votes, non-stackable.
* Approval voting: N *candidates*, and each voter has N votes, non-stackable. Basically a voter can vote up or down (approve) every candidate. Good for single-winner elections, very majoritarian for multi-winner.
* Range/score voting: one can give a score to every candidates. Approval is a degenerate case, where one only has 1 or 0 as options.

These give proportional results if the proportions of candidates match the voting blocs, and/or voting is decently coordinated.

* Limited voting. N slots, voters have fewer than N votes, non-stackable. If minority votes aren't split over many candidates, they can get representation. The fewer the number of votes, the more proportional it is, down to one vote, which is called single non-transferable vote (SNTV). OTOH, if a candidate gets more votes than it needs to win, those are wasted; if a group of allied candidates gets enough votes to win, but no individual does, those votes are wasted and none wins.
* Cumulative voting: voters have multiple votes, but they *are* stackable. If everyone stacks all their votes it's like SNTV, so one can think of it as SNTV with the option of splitting up a vote among many candidates you like.

Less relevant to us, but included for completeness

* Single transferable vote (STV): really complicated to describe or count
* Re-weighted range voting: range (or approval) voting, the top winner is selected, then all the ballots are given the weight of 1/(1+ sum of weights given to winners), so someone who voted fully for the first winner now has a ballot of 1/2 weight. Easy to program, hard to count by hand.
* Party-list: like SNTV or cumulative, one vote (or splittable), but the candidates are in party groups and can share votes. E.g. if a series needs 10 votes to win, and sports animes gets 4, 4, and 3 votes, and are acknowledged as a group, then one of them should win.

How this applies to us

What we used a few years ago was everyone voting on each series in turn, yes half-yes abstain or no, and we recorded the sum of yes and half-yes, and nos. This is close to score voting, except that something with a large net total might still have been vetoed for having a bunch of no votes. I think this is even more majoritarian: range voting + ad hoc minority veto. After that I think we had a round of limited voting, 6 slots 4 votes, but it's been a while.

Last time we had a weird superbloc vote -- 8 votes -- followed by several rounds of limited voting. All sped up by us voting directly on the blackboard, thus in parallel. That can have the effect of erasing votes you've case which are useless or unnecessary, which actually helps proportionality -- votes cycles around, but ideally it would settle down with the votes evenly distributed over six series.

For the past movie night, we had 3 stackable votes -- cumulative -- but then we took the top four winners, and had an SNTV round to pick the 3 winners. I'm not sure this repeated use of semi-proportional systems makes sense. It definitely doesn't if, say, we picked 3 winners, then had a second around to pick the other three: that would let the majority or plurality get its way, then have a second chance to have its way. Repeated votes to winnow down the pool might make sense, I'm not sure.

Still, my current recommendation would be approval voting, let everyone vote on everything, ad hoc the finalists -- definitely anything with a majority of votes, followed by others do get a decent list of candidates -- then a cumulative round, perhaps explicitly letting people change their votes until it settles down, for proportional choice within the majority-approved finalists.



( 2 comments — Leave a comment )
Apr. 24th, 2010 08:41 pm (UTC)
Score Voting hybrid?
I think it's pretty clear that Reweighted Score Voting ("Reweighted Range Voting") is superior to STV in pretty much every way. But you're absolutely right about the problem of having pure P.R.

What if you used Score Voting and took the top n movies by score, and then selected from within those with RSV?
Apr. 25th, 2010 04:19 am (UTC)
Re: Score Voting hybrid?
Problem with RRV/RSV is that it seems about as hard to actually count as STV. STV is like every voter being able to define their own party list; RRV gives a comparable amount of information. Doesn't really work for people voting by hand in an hour.

We ended up doing approval voting on 40 nominees, selecting about 24 top winners and doing a round of cumulative voting with 5 votes (5 slots, plus one pre-determined as FMAB 2nd season), starring the top winners of those, and then having a second cumulative round from those. Not my choice; our fearless leader's instincts or habits. Similar for the summer, but the final round there was limited, non-stackable; he didn't like that one series was pushing through mostly with two people putting all their votes on it, even though allowing that is part of the point. Also, hmm, 16-17 initial people making nominations, and only people present for the summer could vote for the summer, 2/12 would be 1/6th...

Oh well. Decent results in the end, and went relatively quickly.
( 2 comments — Leave a comment )


Damien Sullivan

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