Approval Voting is superior to Plurality Voting, even for multi-winner races

[Clay Shentrup]

Steve Brams recently told me over lunch in San Francisco, that he doesn't agree with trying to switch multi-winner systems from at-large Plurality Voting to Approval Voting. (To be clear, I'm not talking about Proportional Approval Voting; I mean, you can vote for as many candidates as you want, and the n highest vote getters are the winners.)

Here's why I strongly disagree. First imagine these preferences for the smallest possible multi-winner race—a two-winner race:

35% R1 > R2 > C1 > C2 > L1 > L2

33% L1 > L2 > C2 > C1 > R2 > R1

32% C1 > C2 > L2 > L1 > R2 > R1

Where the letters stand for Right, Left, and Center, and the numbers represent different candidates, e.g. "Republican 1" and "Republican 2".

If everyone votes for their two favorite candidates, then R1 and R2 win.

But a huge 65% majority of the voters would take any other candidate over those two! This is a horrendously undemocratic outcome!

But imagine we used Approval Voting. Then we would likely elect C1 and C2, the centrists, who are also the Condorcet winners. This is obviously a far more democratic outcome. One could argue that an even better outcome would be to elect R1 and L1. That would be more "proportional". I agree! And that's why I think Proportional Approval Voting ("Sequential Proportional Approval Voting") would be a further improvement. But that should not keep us from making the upgrade to Approval Voting to start with.

Brams's concern is that you'd get the opposite. Say C1 and C2 weren't running in this race, and instead you had a couple more leftists. Then Plurality Voting would likely elect a Leftist and a Rightist—due to the Leftists splitting their huge 65% majority. Thereby leading to "better representation". Whereas, in that situation, Approval Voting would not suffer from the vote splitting, and therefore would elect two Leftists.

I think this is an absolutely horrendous argument, because:

A) Approval Voting created the niche for the centrists. It incentivized them to run. If they don't, that's not the fault of the voting system! Approval Voting does the right thing.

B) This effect only looks at representation in terms of ideology. It doesn't consider quality. E.g. if you just happen to get a roughly proportional outcome in terms of party, but it happens due to the random chaos of vote splitting, then you may get the worst representatives of each party. In which case, having two centrists could easily be an improvement—particularly if they were chosen not because of vote splitting, but because they were the most competent and therefore the most broadly appealing.

C) If you rely on this chaos to get you your approximate representativeness, then you have to be aware that it could happen in the complete opposite direction. E.g. you might have a situation where you were going to get a reasonable outcome (like a Rightest and a Leftist or even two Centrists) but vote splitting caused you to get two Leftists, or two Centrists.

It just seems incredibly obvious to me that at-large Approval Voting is a significant improvement over at-large Plurality Voting.

But even if you don't believe that, I think Approval Voting could still be advantageous as a stepping stone toward Proportional Approval Voting. That is, say Approval Voting theoretically ended up being slightly worse than Plurality Voting in e.g. 4-person city council races. But then say this enabled you to get Proportional Approval Voting in 10-20 years. Isn't it plausible that the net effect of that would be quite positive? I certainly think so. But again, this is just for the sake of argument. I strongly believe Approval Voting would be an improvement even prior to adding proportionality.

[Clay Shentrup]

On Monday, May 6, 2013 10:19:03 PM UTC-7, Clay Shentrup wrote:

C) If you rely on this chaos to get you your approximate representativeness, then you have to be aware that it could happen in the complete opposite direction. E.g. you might have a situation where you were going to get a reasonable outcome (like a Rightest and a Leftist or even two Centrists) but vote splitting caused you to get two Leftists, or two Centrists.

I meant "but vote splitting  caused you to get two Leftists, or two Rightists."

[Clay Shentrup]

On Monday, May 6, 2013 10:19:03 PM UTC-7, Clay Shentrup wrote:

But even if you don't believe that, I think Approval Voting could still be advantageous as a stepping stone toward Proportional Approval Voting.

Oh, and, duh, also as a precedent for Approval Voting, making it easier to get it adopted in other single-winner elections, where there's broad consensus about it being an improvement. 

[Jameson Quinn]

If clones within a given party tend to follow a rank-size distribution, then the actual result would be proportional. So the empirical question is, would they come closer to that distribution under plurality or under approval? If each party had equal number of clones, I suspect that plurality would be better (and limited voting, with a one vote per seat limit, would be even better). If the parties have different numbers of clones, then I suspect that approval would be better. In the end, I don't think there is a general rule; some cases would fall on either side. But I'd still support an actual initiative to use approval voting for multiwinner races (like the top-two initiative in Arizona, where it is used for the first, two-winner, round), purely out of solidarity.

2013/5/6 Clay Shentrup <cl...@electology.org>

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[Clay Shentrup]

An exchange between myself and Brams, but with his comments only paraphrased, because he didn't want me to share his email.

Brams thinks that I favor centrists, whereas he wants to see the major factions represented.

That's not what I said at all. My point is that getting two centrists is preferable to getting two leftists or two rightists. More specifically, the order of preference in the trivial 2-winner case would be:

1. leftist and rightist
2. two centrists
3. two leftists or two rightists

Approval Voting would tend to get high quality broadly appealing centrists. Plurality Voting may, due to its extreme randomness, tend to elect e.g. a leftist and a rightist more often, but it can also elect two from the same side, due to chaotic/arbitrary vote splitting effects.

Besides proportional AV and SAV, cumulative voting (CV) has worked well in a number of small US cities to produce an outcome, with minority representation, that is consistent with the makeup of a city.

Cumulative voting has a similar problem that it is extremely vulnerable to vote splitting effects. It is semi-proportional, merely as a result of chaotic/random vote splitting effects. This means it picks results that are heavily influenced by "noise" rather than just actual voter preferences.

Brams cites cities that adopted Cumulative Voting and saw increased support for minorities

The utility efficiency of an electoral system is affected by more than just "the extent to which ideological diversity is represented". The other critical vector is competence (or "quality"). Say you could have two partisan ideologues on the left and right, or two highly intelligent and experienced centrists in our hypothetical micro-legislature.

The benefit of having the partisans is that they're able to advocate for their positions, which can help reveal truths that transcend ideology. E.g. the leftist might make a case about the importance and severity of climate change, which actually changes the rightist's mind, resulting in better legislation.

But it's completely possible that two highly competent centrists could produce even better legislation, by weighing the facts objectively and engaging in a pragmatic dialectic.

Both of these vectors play a critical role! If you have two voting systems which are roughly equal in quality, then presumably the one that is more proportional will lead to better legislation, because advocates of different positions may actually improve the knowledge of their peers. Essentially they're able to reduce the amount of ignorance that serves as "noise" in the decision-making process.

But if you use some horrendously chaotic system like Plurality or Cumulative Voting, then it may be that the quality of the winners is so poor that the added diversity cannot make up the difference. And I strongly suspect that's the case.