Tuesday, February 28, 2012

Voting Variants - Range Voting

Range Voting (RV) and its variants, including Approval Voting (AV) and Score Voting (SV), asks voters to rate each candidate independently within a given range or scale, like one to five or zero to ten, or for AV, 0 or 1. RV ballots are more expressive than either IRV or plurality, allowing members to express rather complex opinions. For example, I might want to say something like, candidate A is my slight preference, and either B or C would be okay with me, but D would be a total disaster in my opinion. On a scale of 0 to 100, I might assign candidate A a 100, B and C an 80, and D a zero. There is no requirement that the scores need to add to anything, or even that every candidate receives a score at all.

Calculating the winner of an RV election is straightforward. One simply adds the scores for each candidate across all voters. The candidate with the highest score percentage wins.

Pros and Cons

RV in the form of "star voting" has been used a lot recently on the Internet for things like rating movies (Netflix) or buyers and sellers (eBay). Reality TV uses RV when a show allows the same caller to vote multiple times for a candidate; the score for each candidate is just the number of votes it receives. It does not have as much of a track record in the political arena as either plurality or IRV. Like everything else, it is still vulnerable to strategic voters who know or think they can predict partial results about the election before they cast their votes.

From a technical viewpoint, RV does somewhat better against the standard criteria used by experts to judge voting procedures. It is both "consistent" and "summable," for example. Unlike IRV, it fails the "majority" criteria in that it does not always elect a candidate that clearly has a majority of first place votes. On the other hand, the concept of first place vote in RV is somewhat ambiguous, since you may assign your favorite a 100 and your second favorite a 10, while someone else says their second favorite is a 90, indicating there's not much difference between the two. In this example, there's a strong and a weak first place vote. Due to the simpliciy of the vote counting procedure, RV is also more transparent than IRV.

There is a practical drawback of RV that could be very important in the context of the Ethosphere. Many people have a hard time assigning a numerical value to something as subjective as the fitness of a given candidate. I know when a doctor asks me to rate my pain on a scale of 1 to 10 I often choose to respond with a verbal assault instead of a thoughtful opinion. This difficulty can result in some voters assigning 100 to their favorite candidate and not bothering to rate the others. This tactic, of course, degrades to simple plurality voting if enough members choose to adopt it.

Unlike plurality and IRV, RV tends to favor the centrist candidates a little more. Take an example similar to the one discussed in the IRV post. Candidate A receives a score of 100 from 51% of the voters while candidate C receives a score of 100 from only 49%. Both "parties" are comfortable with the centrist candidate, B, so it receives a score of 80 from all voters. In this case, RV will elect B, the compromise candidate. RV supporters claim this is a good thing because it minimizes a metric called "bayesian regret," a measure of how unhappy the teamspace as a whole will be with this outcome. In simple terms, it means the RV result produces the least unhappiness amongst the group. On the other hand, it should be pointed out that the winner ended up being a candidate that was nobody's first choice.

2 comments:

1. Nice work! I do have a few comments to add; clarifications really.

One, there have been a few psychological studies done on the issue, and while it's easier to _rank_ 3 or 4 choices, it's easier to _rate_ 5 or more (on average; individuals and situations will vary.) This is why IMDB, Amazon, etc. all use ratings; can you imagine being asked to rank your top 100 favorite books or movies in order (if not, go try it)? But you could probably rate them all into one of 5 "star" categories quite a bit faster, and millions do, every day.

Second, in practice voters do not tend to bullet vote (vote for just one) with RV. And strategically, this is often clearly a foolish choice anyway. Furthermore, exit polls have been conducted on "real" elections in France, Germany, and elsewhere, and a few small real-world elections have been done by RV (student bodies, professional organizations) all showing that voters tend toward scoring multiple candidates highly (and the more candidates there are, the more of them they score highly, with no apparent upper limit, at least up to about 10 candidates.)

That's why RV supporters refer to Bayesian regret: it not only considers what's _possible_ (e.g., it's possible that RV elects a candidate who is no-one's first choice), but what the likelihood is (how often does RV do that? Not often) and how damaging it is (when it does, does it pick a terrible candidate, or a good compromise? RV almost always picks a good compromise in those cases.)

2. Great point about the relative ease of ranking versus rating as the number of choices gets large. My thinking was stuck in the present context, where there is likely to be only a few choices, when I made that over-broad statement.