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”.

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.

Advocate of Score Voting and Approval Voting. Software engineer. Father. Husband. American.

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