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score runoff voting

Yesterday I discovered a a new voting system which is growing on me as I think about it.

With basic score voting, you rate each candidate on some scale -- 1-10, or 0-1 (which is called approval voting), say. Add the ratings up, and the winner is whoever has the highest total. Or average, in some variants. If voters vote honestly then it's pretty expressive; however, there are strong incentives to not do so. I'll use a standard G D R example, where D and R are the most likely winners, and D is in between G and R.

A G voter rates G top, of course. But, knowing that the winner will likely be D or R, she has reason to also rate D top, to maximize her influence on the real contest. If she hold backs, she's just handicapping herself.

Meanwhile a D or R voter is already voting for a likely winner, and they have no incentive to bother rating anyone else. So you end up with a mix of bullet voting from the top two parties, and simple approval ballots from the others. The strategy is simple: "give a max rating to your favorite candidate, and also to your preferred front-runner if not the same as your favorite." It avoid spoiler effects, but is pretty centrist.

And if G becomes competitive, it's possible everyone just approves their own party, and we're back to the instability of plurality voting.

So, score runoff. Despite the name, there's no separate runoff election, just another round of counting. You use the same ballots, but pick the top two winners based on score total. Then the winner of those two is decided by relative preference. So if G and D end up in runoff and I gave a 10 to each, my ballot is a wash. But if I gave (10,9,0), then my ballot is a G vote in the runoff, while if I gave (1,10,0) my ballot is a D vote. The exact numbers don't matter, just whether one is higher than another.

Going back to the examples: if the G voter rates G and D max, then if they get lucky and have a G,D runoff, their ballot won't count. So there's reason to rate D at least a bit less -- (10,9,0) say. This way they'll still count as a G vote in the runoff. As the equal.vote people say, you give up a bit of influence in the first around in return for getting influence in the second round.

(Dark strategy: suppose the voter thinks G is more likely to beat R than D in a runoff. Could she vote (10,0,9), hoping to force a G-R runoff? Yes she could. But our premise is that D and R are the likely winners, so mostly likely she would end up casting an R vote in the runoff. Bad plan.)

As for a left-wing D voter, she doesn't have much to lose by giving G a bit of a rating: she's giving her max score to a front-runner already, a bit of score to a third party won't hurt. This lets her influence a G-R runoff properly, while even if lots of D voters accidentally combine to give G a higher total than D, as long as it's a G-D runoff they're still fine: their ballots will still be D votes in the runoff, fixing their 'mistake'.

How about an R voter? She really does have reason to think R>G is more likely than R>D in a runoff, as in the former case some D voters will crossover to R, whereas in the latter there's a solid G+D coalition againt R. So maybe she should vote (9,0,10). It's a gamble, though: if G ends up beating R anyway, then she's helped her worst outcome. So I think this might actually be unlikely. Conversely, a more cautious voter has no reason not to vote (0,1,10) -- it's not hurting R chances at ending up in the runoff at all, while ensuring (as insurance) a say in the event of G-D runoff.

So, while I see no incentive to be exactly honest, there is an incentive to at least moderate one's ratings and use some of the middle numbers. You give only a top rating to your real favorite (or favorites, if genuinely indifferent) so as to win runoffs, a high rating to a preferred front-runner if different, or a low rating to "insurance" choices. And while I can't rule out really perverted voting as being strategic, so far it seems bad or risky for the voter, which is a lot better than outright compelled as with plurality or IRV.

I *think* it's better to have a wide scale; if the scale is just 0-1-2, then the moderate choice seems to be giving up or granting more influence than a voter might be comfortable with, vs. numbers above.

One note on practicality. Score voting is easy, you just add up scores and pass on the totals. The 'runoff' round takes more information, but not a lot: yuseou the relative ratings to fill in a pairwise comparison matrix, a la Condorcet. So (10,9,0) would mean incrementing G>D, D>R, and D>R; (9,0,10) would mean incrementing G>D, R>D, and R>G. A district's ballots can be aggregated as the candidate totals plus a matrix, both of which can be added to the totals and matrices from other districts. Far simpler than IRV, which needs centralized counting of all the ballots to do the instant runoffs.

So is this better than Condorcet? I don't know. The ballots are theoretically more expressive. It's not guaranteed to elect a Condorcet winner, because such winners aren't guaranteed to make it into the runoff. But with ratings, arguably we have reason to identify situations when that's a good result; ranked ballots can't do that. It doesn't have to pick a Condorcet cycle tie-breaking method, which makes it much simpler to describe in full. It seems maybe harder to game, but that's said based on little analysis. Right now I'd be happy to try either.

Of course, I'd rather have a PR legislature than lots of single-winner elections.

***

Why IRV sucks:

31 G > D > R
18 D > G > R
11 D > R > G
40 R > D > G

D is eliminated in the first round, and R wins 51-49, despite D being the Condorcet winner. If G hadn't run, D would win 60-40, which is a result G voters would prefer, so their own candidate running hurt their cause. That's classic vote splitting/spoiler effect, exactly what advocates claim can't happen.

See the comment count unavailable DW comments at http://mindstalk.dreamwidth.org/459319.html#comments

Comments

( 3 comments — Leave a comment )
l33tminion
Nov. 23rd, 2016 08:14 pm (UTC)
The "IRV sucks" example you construct is still at least an example where it doesn't do worse than largest-plurality. And you admit you can construct similar examples for score-runoff.

Applying IRV only to members of the Smith set (the smallest non-empty set of candidates who win pairwise-majority contests with everyone outside of the set) has the Condorcet property, so I think that might be even better than pure IRV (and it doesn't add any extra complexity to the ballots relative to pure IRV).

I'm not sure I've thought enough about score-runoff voting to know if I prefer it over pure IRV, but the arbitrariness of the particular scoring system chosen makes me antsy (a second choice is worth 8/9 of a first choice in terms of who makes the runoff, you have to trade off between throwing your full weight behind/against a candidate getting into the runoff and expressing a preference in the runoff at all). The ballots are also very confusing to explain relative to IRV (which just requires voters to rank candidates in order).

I do kind of like the version of score-runoff that's like approval voting plus runoff (scores are 1 or 0 with ranking done separately). For one thing, that's easy to do by just having a single ranking of the candidates on the ballot (like IRV) with "nobody" thrown into the mix. Give candidates above "nobody" a score of 1 and those below a score of 0.

The details don't matter so much, though. Tere are so many systems that are strictly much better than largest-plurality that getting away from largest-plurality should be the priority.
mindstalk
Nov. 23rd, 2016 09:23 pm (UTC)
* I was thinking that when score systems don't elect a Condorcet winner, the ratings at least give voter-preference information such that you can argue the Condorcet winner isn't actually the best winner; I can't expand that into an example right now, but ranking systems definitely don't do that. And this line of argument would in extreme be a blow against SRV for me, not a rehabilitation of IRV.

* That's called Condorcet-IRV. I remember disliking it compared to Ranked Pairs or Schulze, though at the moment I forget why. It's not like any pure Condorcet system has any more complex ballots either.

* I don't think the ballots are any more complex than IRV. "Rate each candidate on a scale" is standard survey practice. Though here perhaps voters should be advised to give a max rating to their top choice, for effectiveness, even if flawed. There are also ideas about re-norming ballots, so if if someone didn't do that, you do it for them.

* If you're going to use approval voting, I don't see why you'd bother faking an IRV ranking; explicit approval ballots are simpler and don't need new machines. ...oh, you mean using the ranking in the runoff phase, like SRV? Hrm. I guess that works, though I'm not sure why that'd be better. Honest score voting is a great system, and the point of SRV seems to be to elicit somewhat more honesty in the ratings.

* AFAICT IRV is *not* "much better" than plurality. It's maybe slightly better.
l33tminion
Nov. 23rd, 2016 09:55 pm (UTC)
you can argue the Condorcet winner isn't actually the best winner

You could, but I'm skeptical. You could argue that for IRV, too. It would even be a similar argument (that a large number of first choices should outweigh a smaller number of first choices plus some second choices). You seem to be inconsistent about how much of a drawback not having the Condorcet property is, while mounting an argument in defense of a system you just heard about.

the point of SRV seems to be to elicit somewhat more honesty in the ratings

Also skeptical. I'd expect actual voters would choose between e.g. 9-8-0, 9-5-0, and 9-1-0 in a way that is more arbitrary than some objective measure of the relative strength of preferences. Even if it was, it is, I think, more in line with democratic principles to count numbers of relative preferences than to try to give stronger preferences more influence.

AFAICT IRV is *not* "much better" than plurality. It's maybe slightly better.

It is definitely better, given that you agree that "spoiler" scenarios are bad. How much is subjective, but I think IRV gets it right in many scenarios where largest-plurality gets it wrong.
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