2013-12-01

Score Voting vs. Approval Voting

A common criticism of Score Voting is that it is strategically identical to Approval Voting. For instance, one member of the German Pirate Party recently responded on Twitter to a Score Voting election using a -3 to +3 scale:
Best strategy for assessment choice by the way: Favorites to +3, all other -3. Otherwise, voting power is wasted.
The basic idea is that it's always strategically optimal to use the maximum and minimum scores (we often refer to this as "polarization"), which seems like an argument for using Approval Voting instead of Score Voting. There are a number of reasons why this argument is flawed.

First, it's not always true. There are some instances in which honesty is a better strategy than polarization. Having said that, I acknowledge that those are exceptions to the rule, which I point out purely to be thorough. So let's continue with the premise that polarization really is the best tactic, since it's approximately true. In that case, we must look at the pros and cons of using Score Voting instead of Approval Voting.

One major advantage of Score Voting is that it's more expressive, which many voters enjoy. For example, in the 2000 USA presidential election, polls show that about 10% of the people who preferred the Green Party voted for their nominee, Ralph Nader. They knew Nader had virtually no chance to win, and they could have made the tactical decision to vote for their favorite of the two major party candidates. But expressing their opinion was just so important to them, that they chose to "throw their votes away" on the Green Party.

This principle is actually at work within the very act of voting! Because in the vast majority of elections, a voter's odds of affecting the outcome are so incredibly small that it is economically irrational for him to waste his time voting. This is concept is actually called the Paradox of Voting. So if our Pirate friend from Twitter votes, that is proof that he actually agrees with us.

But there is more benefit here than mere self expression. It turns out that when voters are honest, they tend to "donate" more utility (aka welfare/satisfaction/happiness) to the other voters than they sacrifice, resulting in a net welfare increase. You can see this clearly in Bayesian regret figures. The more voters are honest, the greater the average satisfaction.

Critics will often respond that this only addresses those voters who consciously chose to be honest. What about those voters who simply didn't know any better, and were then unfortunately victimized by the tactical voters? There are a number of counter-arguments to this concern:

  • Those voters presumably are very few in number, meaning we should be skeptical about giving up the significant benefits of Score Voting simply to protect them.
  • One can make the argument that any voter so naive as to be unaware of strategy would actually be better off casting a sincere Score Voting ballot than an Approval Voting ballot. This is based on analysis of the effectiveness of these respective behaviors. I.e. observe that the values in column C tend to be greater than those in column D in the first table here.
  • It turns out that if there's enough sincere voting, then even the "naively honest fools" who vote sincerely do better with Score Voting than with Approval Voting. See table two from this page on the "Shentrup-Smith Experiment".

Summary

The bottom line is that if even one voter decides to sincerely use the intermediate scores, then Score Voting produces better average voter satisfaction that Approval Voting. And if you prevent sincere voters from using intermediate scores in order to protect the naive ones, you possibly hurt them, and you definitely hurt the voters who wanted to be expressive. Is it really worth it, just to make the voting procedure a little simpler? Score Voting is a little more complex than Approval Voting, but it is still much simpler than any ranked voting system. 

Approval Voting is a fantastic system, but a rational voter will want to take Score Voting instead, if he can get it.

5 comments:

Matt said...

As a "rational voter" I must beg to differ. Score voting requires me to spend time identifying *all* the candidates I abhor and give them the lowest possible score. This is highly irritating, especially since I can't be sure I got them all or I may accidentally give someone a minus three that I would have been okay with leaving neutral at zero.

The only election where score voting makes sense is in a completely non-contentious election and those are rare.

If the default score is -3 then for me score voting would drop from highly irritating to irritating.

The twitter poster is right. Anything other than a polarized vote is strategically a bad choice. The additional cost of implementing a score vote (from the point of view of US elections) buys only irritation for most voters and maybe a bit of feel good for a minority who have the time and energy to articulate nuances in their vote at the cost of strategic advantage.

I do think that score voting might encourage voters to put more effort into voting but most people are busy and their attention is spread thin. Under these conditions voting becomes yet another burden and keeping it as simple as possible outweighs any benefit of the system to manipulate better behaviour.

Clay Shentrup said...

> Score voting requires me to spend time identifying *all* the candidates I abhor and give them the lowest possible score.

You have unwittingly made an argument *in favor* of Score Voting. All voting systems require some evaluation of all the candidates. Plurality Voting, for instance, is effectively a variant of Score Voting where you give one candidate a maximum score, and give all others a minimum score. Any ranked system either requires you to rank all the candidates, or treats unranked candidates as "tied for last place".

Score Voting, by contrast, is compatible with certain variations where you treat non-scores as "blanks" that don't affect a candidate's average. You can even use a quorum rule to get the best of both worlds between averaging and summing.
http://ScoreVoting.net/BetterQuorum.html

> The only election where score voting makes sense is in a completely non-contentious election

This is the exact opposite of reality. Bayesian regret calculations from Warren D. Smith find that Score Voting outperforms the other commonly proposed alternative voting methods with any proportion of strategic or honest voters.
http://scorevoting.net/BayRegsFig.html

This is extremely robust, and holds up even with one-sided strategy.
http://ScoreVoting.net/StratHonMix.html

There are also theorems about the mild (some would say "good") behavior of Score Voting in response to tactics:

1) Score Voting may be a better Condorcet method than real Condorcet methods.
http://ScoreVoting.net/AppCW.html

2) Score Voting maximizes "pleasant surprise".
http://scorevoting.net/PleasantSurprise.html

We cover tactical voting in great depth here:
www.electology.org/tactical-voting

> Anything other than a polarized vote is strategically a bad choice.

As I mentioned in my post, this is not correct.
http://scorevoting.net/RVstrat1.html

As I also pointed out, that's irrelevant even in cases where it's true, since a lot of voters prefer expressiveness (sincere voting) to optimal tactical voting. And for every voter who opts to be sincere, that increases the net welfare of the electorate, since the sincere voters sacrifice less utility than they "donate" to the tactical voters.

> If the default score is -3 then for me score voting would drop from highly irritating to irritating.

We generally advise a 0-based scale like 0-5 or 0-9, with a default score of zero. But I would question the merit of your complaint. If you're prepared to take issue with how "irritating" it is to have one particular default score vs. another, then:

1) That's not an argument against Score Voting in favor of some other method. That's an argument for a different default score.

2) That's a highly irrational prioritization of things, since by far the greatest impact of a voting system is "who got elected and what laws did they pass that affected you." Compared to that, any complaints about "the irritation I felt during the 10 minutes I spent in the voting booth" are minor.

> The additional cost of implementing a score vote (from the point of view of US elections) buys only irritation for most voters

It turns out we have some polling data about what "most voters" want, and it disagrees with you.
http://scorevoting.net/WhatVotersWant.html

Clay Shentrup said...

(continued)

> maybe a bit of feel good for a minority

No. You're not understanding what I said. Allowing a minority of voters to use intermediate scores improves the expected welfare of *the entire electorate*. In other words, YOU as someone who would presumably vote in the most tactical way possible, would be statistically better off with Score Voting, because that honest minority would be voluntarily ceding some power to you and making you better off. So if YOU oppose Score Voting, you harm your own interests. And those of society as a whole.

Further, if the sincere voting minority is big enough, then even *that minority* is better off with Score Voting. This comes from a rather esoteric simulation experiment Warren Smith performed at my suggestion.
http://scorevoting.net/ShExpRes.html

I mentioned all this in my post. It would be nice if you had read it.

> Under these conditions voting becomes yet another burden and keeping it as simple as possible outweighs any benefit of the system to manipulate better behaviour.

There is considerable evidence that Score Voting is effectively *simpler* than Plurality Voting. It reduces the rate of spoiled ballots, for instance.
http://ScoreVoting.net/Complexity.html

Virtually every criticism you waged here would have been unnecessary had you spent half an hour researching this subject matter.

Ares Olympus said...

The case that comes to me is when you dislike ALL the candidates, so perhaps on a -3 to +3 scale, I might vote -3,-3,-2 to express this.

So ignoring picking a winner, there's a message being conveyed, and I can see the value in expressing that.

However in terms of picking a winner, do I want a "full vote" on a -2 candidate, or am I really saying I want a 1/5 vote for him, and 0/5 for the rest? Do I really want to weaken my vote if I actually have a preference?

So this suggests to me the possibility of a normalization process - so a "full vote" used for picking a winner be scaled by each voter as their highest expressed preference.

So voting (+2,+2,+3) gives the same voting effect as (-3,-3,-2), both being (0,0,1) normalized.

The value of this normalization is you can report both the scoring preference AND normalized preference to pick a winner.

Of course the worst case is when there's only a single candidate running. If the single candidate wins with a scoring preference of -3, that's a clear message, either that he should figure out what's wrong, or other future candidates should be inspired to!

Ares Olympus said...

The interesting case that comes to me is when you dislike ALL the candidates, so perhaps on a -3 to +3 scale, I might vote -3,-3,-2 to express this.

So ignoring picking a winner, there's a message being conveyed, and I can see the value in expressing that.

However in terms of picking a winner, do I want a "full vote" on a -2 candidate, or am I really saying I want a 1/5 vote for him, and 0/5 for the rest? Do I really want to weaken my vote if I actually have a preference?

So this suggests to me the possibility of a normalization process - so a "full vote" used for picking a winner be scaled by each voter as their highest expressed preference.

So voting (+2,+2,+3) gives the same voting effect as (-3,-3,-2), both being (0,0,1) normalized.

The value of this normalization is you can report both the scoring preference AND normalized preference to pick a winner.

Of course the worst case is when there's only a single candidate running. If the single candidate wins with a scoring preference of -3, that's a clear message, either that he should figure out what's wrong, or other future candidates should be inspired to!