Friday, June 26, 2009

"Best" Picture?

Between reading all that politics-stuff out there, you might have heard that the Academy of Motion Pictures has decided to expand the number of nominees in their "best picture" category from five to ten. This is, of course, the perfect time to talk about voting methods!

Okay, I'd probably say that about almost anything... but really this is a great example. And liberal blogger Matthew Yglesias almost puts his finger on why: "[B]ut if they want to make this switch they also need to reform the voting procedure to something with ordered preferences or something." But here's the thing, Matt: they already do. Kind of.

The Method

That article explains the current (until just now) method used to vote for best picture. According to that article, it goes like this:

  1. All Academy members can submit an ordered ballot of up to 5 movies
  2. Any movie which gets at lest 20% of 1st-place choices becomes a nominee
  3. The movie with the fewest 1st-place preferences is eliminated, and those ballots are re-allocated to their next choice
  4. Repeat until there are 5 nominees
  5. Then, a simple plurality vote on the nominees determines the actual winner
The first half is a (a very-poorly described version) of the single transferable vote method for multi-winner elections. And then, of course, we follow this up with a round of the worst voting method known: plurality.

Now, there's a funny thing about plurality; as shown by this graph from Brian Olsen's voting and elections page, the average performance of plurality (assuming honest voters) increases the more candidates there are... until you get beyond five candidates. So increasing the number of nominees to 10 might not actually help much.

But back to STV: it's not a terrible method, but it's not exactly great, particularly for this use: it's not designed to pick the best set of options out of a group, it's designed to pick a set of options that (more or less) evenly covers the voter's opinions. What I mean by that is, if there are, for instance (assuming we're picking 5 nominees) two very good movies that a very well received by a particular niche of voters, but those voters account for less than 40% of the electorate, then they can only get one of them to be nominated; STV will tend towards picking options strongly supported by other niches after one of these two is selected. STV tries to cover all the extremes, not pick 5 films that are all broadly well-liked. This is why it's used in political elections; if a region is 60% Democrat and 40% Republican, it's fairer to pick 3 Democrats and 2 Republicans than it is to pick 5 democrats (which is what would happen in 5 separate plurality elections for those same 5 seats.) This might explain why, sometimes, you get some really bizarre picks: the 20% of voters who hate everything popular randomly settle on some out-of-the-mainstream film. Addi tonally, it doesn't necessarily pick the favorite of each niche, either; like instant runoff voting (which is just STV with a single winner), if there are more than two strong competitors, you can run into problems with spoilers.

Still, STV-to-plurality is certain a better way to pick a winner than a simple plurality vote over a couple hundred candidates. But can we do better? You know what I'm going to say...

Score Voting!

That's right, the Academy should move to score voting. It's going to be a hard sell though. Hollywood (if any sci-fi film is evidence) absolutely hate math, logic, and science. So how do you go about convincing people that one method is better than another, when they have almost 80 years of examples for the old way and there's nothing to support the superiority of your new idea. Well, there's good news for us, because there is.

The Internet Movie Database allows its members to score any and every movie in their system, on 1 to 10 point scale and (barring some algorithmic scrubbing that we'll discuss in a minute), they sort them by average score. That's score voting. And IMDB has at least 430,000 "voters", who have voted on who knows how many hundreds (thousands?) of films. This is all the data we could ever ask for!

Now, about the scrubbing: IMDB doesn't used a simple arithmetic average. First, they work very hard to try to eliminate ballot stuffing (one person, one vote!), but that's probably impossible to do completely. Furthermore, Academy voting all takes place within a single year, whereas IMDB lets members vote years and years after the fact, and that may screw results as tastes change over the years. We'll just have to deal with all that in this analysis. Secondly, they realize that, since most people won't vote on most films, some films will have very few votes, and it'd be foolish to, for example, let a film with only 1 vote of 10 stars be listed as the greatest film of all time. So they do some math to correct for that, not unlike the quorum rule that suggests. Their quorum is around one-third of one percent of the number of votes received by the most-voted on film; not a large number, but enough to quell the "lunatic with a fanatic following that no one else has heard of wins" fears.

So, how does score voting stack up against STV+Plurality? Compare and contrast for 2000-2008.

2008Slumdog MillionaireThe Dark Knight1
2007No Country for Old MenNo Country for Old Men
2006The DepartedThe Lives of Others1,3
2005Crash2Sin City1
2004Million Dollar BabyEternal Sunshine of the Spotless Mind1
2003The Lord of the Rings: The Return of the KingThe Lord of the Rings: The Return of the King
2002Chicago2City of God1,3
2001A Beautiful Mind2The Lord of the Rings: The Fellowship of the Ring
  1. Not nominated by Academy
  2. Not contained in IMDB's "Best/Worst '2000s' Titles"
  3. Listed in IMDB under original foreign title

Okay, so what does this tell us? I'll tell you my thoughts in the next post, but for now, I'd like to know your thoughts? Which method do you agree with more often? What films are you favorites that don't make either list? What do you think this years best picture is and–different question!–what film do you think the Academy will pick?

Tuesday, June 16, 2009

25% Majority: The Census, Governors and Gerrymanders (Oh My!)

I want to take a little side trek from my usual focus on election methods, to put them in a larger context.

The census is coming up shortly, and while it provides all sorts of interesting trivia to pour over, its main purpose has always been to determine how seats in the House of Representatives will be apportioned among the states, although the Constitution leaves most of the details for filling those seats up to the states themselves. In general (although this is not universal), each state's legislature writes up a proposal for the new district boundaries, which must be approved by the governor. And it's usually assumed that, if the legislature and the governorship are all controlled by the same political party, that the party can pretty much get away with even the most absurd boundaries. FiveThiryEight covered the where's-and-what-have-you's of these redistricting battlegrounds last month.

Of course, this isn't because of an appreciation for fractal geometry or for modern art, but in order to maximize the party's performance in future elections. Under a system of proportional representation, if an electorate's support is divided 40% for one party and 60% for another, than approximately 40% of legislative seats will be filled by the first party and 60% by the other; not so if you have single-winner districts and free-reign for drawing district boundaries! Depending on how much wiggle-room you want to leave yourself, you can fill 100% of the seats with members of your own party as long as you have a sliver more than 50% of the voters. And even if you have less than 50%, effective gerrymandering can double your seating percentage; which means that even if only 25%-plus-one of the electorate supports you, you can still have 50%-plus-one of the congressional seats.

This leads to a very strong self-reinforcing system, where a thin pseudo-majority can artificially inflate its political power for many years down the road, or one where a real, but small, majority can effectively remove all opposition. Occasionally, something of an unsteady balance is found, which you could positively think of as a "bipartisan compromise". Or, if you're more cynically minded, you could think of it as the parties agreeing to systematically disenfranchise about a third of the electorate; but it's okay, because this way, both of them save equally as much money by not having to buy ads in nearly as many markets (well, except for the primaries); and since it's equal, who can complain? Some states have gone so far as to remove the elected legislature and elected governor from this decision-making process, to replace them with a "bipartisan committee", whose equal number of Democrat- and Republican-appointed members would have control over the boundary lines.

Somewhere between 20 and 40 percent of Americans don't think of themselves as Republicans or Democrats, and yet, 99.9% or more of elected officials do. These sorts of games are yet another of the ways that this imbalance is made to continue. We could throw our hands up in the air and say "It's terrible, but what can you do?"; or would could take the approach I always do here and ask if there's a better system, one that everyone (not just party-faithful) could agree is fairer. There are a lot of different suggestions for algorithmically-defined solutions (I'm currently enthralled by the third in that list), but like score-voting, effecting change will be an up-hill battle.

Just something else to think about when you're voting for governor next year, or filling out your census questionnaire.

Friday, June 5, 2009


Recently, I gave a brief presentation to the local chapter of the Green Party. I wouldn't call the following a "transcript", but it does hit the same points.

Between 1996 and 2000, the Green party increased their share of the votes in the presidential election by over 400%. But between 2000 and 2004, despite flagging support for the incumbent Republican, a lackluster Democratic challenger, and an increase in public support for the Green stance on virtually every policy issue, the Green party share of votes dropped by 96%. How is that possible?

Because Nader, and the Green party, was branded as a spoiler. When you spoil an election, your support dries up as voters go back to voting for the lesser of two evils. This is a known problem with our current plurality election method, one that economists, mathematicians, and political scientists have known about for years, and they have also known for years of alternative election methods that don't suffer from this problem. And yet, it doesn't seem to come up as something worth fixing.

Thankfully, recently, there has been some movement towards trying different election methods. Unfortunately, one often-proposed method, instant-runoff voting, which is a plank in the Green party platform, does not fix this problem. I'm here to show you some methods, called approval voting and score voting, that do fix this problem. Allow me to show you some examples.

This is a simple example with just nine voters; four vote for option 'A', and five for option 'B'. B wins. But what if we add a new option, 'C', that appeals primarily to the B-voters.

C doesn't win, but now, neither does B, so C spoiled the election. This is basically what happened in Florida in 2000. Instant-runoff voting (IRV) claims that it can fix this problem. On an instant-runoff ballot, instead of listing only one choice, you can list several choices in order. The candidate with the fewest votes is eliminated, and votes for them are re-allocated to the voter's next choice in line, and you repeat this until one candidate has a majority of votes. So, in our example, C has the fewest votes, so it's eliminated, and the votes go to the voter's second choice, which we know from before is B. B now has five votes, and wins, as they should have all along.

This looks great; it looks like IRV fixed the problem. But you still haven't won any elections. Support for a new party grows slowly over time; you don't go from zero to victory. So let's give C one more of B's votes.

Okay, now, you're doing really well; you've actually got more votes than one of the major parties. But now, we have to ask a question that we haven't answered before: what's the second choice of these last two B voters? If one of them (let's call him "Al") has A as his second choice, we get this:

Now, A wins. Remember, without C involved in the vote, B would win. But because C is here, A wins. So C is, again, a spoiler. And here you'll still lose 96% of your support in the next election.

A better option is score voting or approval voting: I'll do an example with approval since it's a bit simpler. With approval voting, instead of indicating just one candidate, you can indicate as many or as few as you want. So, those first two votes for C can come without in any way diminishing B's five votes, as can the third; and as your support continues to grow, maybe you convince some of A's voters to approve you as well, until you win. Without ever being a spoiler.

Score voting is only slightly more complicated, in that it gives you the option to explicity state a willingness to compromise, by letting you give each candidate a score in some range, such as zero to ten. So you could say, for instance, I give C my full approval at 10, but I'd be pretty satisfied with B as well, so I give it an 8.

Either way—score or approval—no spoilers, no abandonment by the electorate, and so your support can continue to grow until you actually win.

Now, what I want from you is I'd like to promote this idea to the rest of your party; your national conference is in July, perhaps something there. Also, IRV has had some pilot programs conducted, in California, Vermont, North Carolina; I'd would like to ask for your support in getting some sort of pilot program using score voting here.

Then there was a brief question-and-answer period. I was asked to reiterate the example of how a spoiler happens under IRV (the important part is that not all B-first voters will vote C-second), to speak to IRV's "success" in San Francisco (before IRV: one Green elected to council, after IRV: one Green elected to council. Change: zero), and to discuss briefly proportional representation (also a good idea.)

Overall, I thought the experience was very positive, and I will be put in touch with some local Green party members who are also voting-reform advocates. It was also recommended that I contact Ralph Nader directly.

The presentation took just five minutes, with five minutes more for questions and discussion. If you would like to give a similar presentation in your area, feel free to use everything I've said; the images are quite easy to reproduce on a chalkboard or whiteboard.