Yee Paper on Visualizing Voting Methods

Just a quickie (I know, I haven't posted that Egypt piece I promised; turns out, just because you don't know a lot about a foreign country's politics, doesn't mean they're simple) and not something that's new if you've been following us closely, but Ka-Ping Yee has a nice, simple, short paper based on his previous work, titled "Disadvantages of Transferable Vote Systems". This one is restricted to just plurality, IRV, and approval, and comes out strongly for approval. Also, the pictures look pretty sweet, so check it out.

Looking@Democracy Step 2: Vote with your Vote

Thanks again to all of you who contributed funds to have CES make their approval voting video. Now for step two! Voting for the public choice award for the Looking@Democracy has now opened, so please visit the page for CES's approval voting entry and vote for us!

Honestly guys, we may have an unfair advantage. The video is about approval voting, and the contest is being decided by approval voting! Not plurality, not instant-runoff (can you imagine having to rank all 347 entries?), but approval. How is that even fair? But who cares, go vote us up!

Video: What Is Approval Voting?

It's been just about 5 weeks since the end of The Center for Election Science's successful fundraiser, and the video is ready!

It will now be entered in the Looking@Democracy contest. But in the meantime, spread the word!

C.G.P. Grey is Wrong (on One Important Thing at the End of His IRV Video)

You've probably seen a couple of the snappy, well-enunciated videos produced by C. G. P. Grey; he's done pieces on the evil of pennies, the problems with copyright, and various aspects of British history, as well as a number of videos on political theory. I want to talk about his video The Alternative Vote Explained. The Alternative Vote is the British name for what Americans may better know as instant runoff voting, or perhaps as ranked choice voting, which are all mechanically identical; I will refer to it as IRV here. The first three minutes of the video are an excellent explanation of the method, including cute fuzzy animals in an easy-to-follow example. But right at the 3:00 mark, Grey makes an egregious mistake.

Grey claims that IRV's crowning achievement is that, unlike plurality voting, IRV doesn't have spoilers, but that isn't true, and it's very easy for me to show it. Consider first his "spoiler-proof" example. Gorilla and Leopard are running for office; Gorilla is about to receive 45% of the vote, and Leopard 55%; Leopard is going to win. But at this point, Tiger enters the race, and 15% of voters move from Leopard to Tiger, making the vote totals Gorilla 45%, Leopard 40%, and Tiger 15%:

Under plurality, that makes the winner change to Gorilla, and that's bad. Grey's claim, and this much is true, is that under IRV, those 15% of Tiger-favoring voters can have their votes reassigned to their second choice, Leopard, putting everything right with the world by making Leopard the winner again.

Persuasive Tiger

But what happens if Tiger is a bit more convincing? Consider the case where Tiger convinces not just 15% of Leopard voters to rank him first, but 30%. That makes the standings Gorilla still at 45%, Leopard 25%, and Tiger 30%:

This leads us into some uncharted territory, because now it's Leopard who is eliminated, and we don't know where Leopard's voters would now go for their second choices. But we can make some educated guesses. Taking a look at the video's earlier example (at the 1:47 mark):

We can see that there is a large contingent—amounting to 25%—of Owl-loving voters, who find themselves torn between Gorilla and Leopard. (Pedantic aside: You can imagine that Leopard gets 15% and Tiger 30% if you want to align this example with our alternate "persuasive Tiger" scenario.) If Owl were running in this race, those 25% of voters would have listed him first. But since he is not, they instead voted for other candidates. It seems that 3 out of 5 owls chose to vote for Gorilla (Turtle's 5% plus Gorilla's 25%, plus 15% from Owl, equals the 45% Gorilla is currently enjoying) while the other 10% are supporting Leopard. There is clearly a split in the Owl community about who the best non-Owl choice is. Suppose that the remaining 10% of Owl supporters, after the elimination of Leopard, re-join their brethren by supporting Gorilla as their second choice in this election, while the other Leopard voters all throw in with Tiger:

That would be a logical assumption. And it means that the final standings are now Gorilla 55%, Tiger 45%:

Let's take a look at that again: If just Gorilla and Leopard run, then Leopard wins. But if Tiger chooses to run, and is able to convince a few more Leopard voters to vote for him, then not only does Tiger still fail to win, he makes it so that Leopard doesn't win either. He actually makes it so that Gorilla wins, which is the exact same problem that we saw with plurality. In other words, we have a candidate who doesn't win, but by entering the race, can change the winner. This is the very definition of a spoiler and it (yes, once again) shows that IRV does, in fact, have spoilers.

Calling C.G.P. Grey

Let me thank Grey for his enlightening videos and his clearly-superior-to-my-own abilities with graphic arts (images not used with permission, but I assert that my usage would qualify as Fair Use.) But this portion of his video is promoting a demonstrably wrong version of the facts, but one which has nonetheless gained a large amount of mindshare and garnered a frightening number of repetitions, both before Mr. Grey's video and more so since. I call on Mr. Grey to address this error, and if he is interested in creating videos to promote actually spoiler-free election method reforms, I would like to point him to approval voting.

Pro-Approval Video from NYU Professor

Steven Brams, Professor of Politics at New York University, runs down the advantages of approval voting and refutes many of the arguments against it, in this video. Worth the five minutes.

Start With the Primaries?

Enacting meaningful election reform is going to be an uphill battle. But perhaps there's an easier way to get a foot in the door. Currently, the national Republican party is reconsidering the rules for its presidential primaries. The plan coming from the national party would require that the states--at least those earliest in the primary season--divide their delegates in some proportion based on the percentage of votes each candidate receives in the primary, rather than using a winner-takes-all approach.

Presumably, this is coming as a response to John McCain's "win" in the Florida primary, way back in January of 2007 (seems like forever ago, doesn't it?), where he got 36% of the votes, but 100% of the delegates. Allegedly, this led to McCain's nomination, despite most Republicans wanting someone else. (The first post to LoAE was about this very issue. Oh my, I was still planing to advocate for Condorcet methods then!)

This will be a difficult process to implement. While there could be some potential improvement in national outcomes if every state delegation went with a proportional division, this is in opposition to the fact that each individual state can improve it's own power by sticking with winner-takes-all. It's the same reason that only a couple states divide their electoral college votes: by dividing your effort, you weaken the effect you have on the outcome. It may be possible for the national party to convince the state parties to give up this power, but someone, somewhere, is going to lose out in this transition.

But let's take a step back: the deeper problem here is that the national Republican party is trying to find a better way to make plurality votes decide an outcome among more than two possible choices. Whether or not to divide delegates up is missing the forest for the trees; the problem is that plurality voting sucks when there are more than two options.

The answer (which you've already guessed if this isn't your first time here) is approval voting (or score voting). Under approval, rather than have each voter vote for one, and then divvy those up somehow among several delegates who will also each vote for one, a better result can be obtained by having each voter approve of as many candidates as they want, and then assign a proportional number of delegates to submit approval for those candidates, potentially even having some delegates approve of multiple candidates. If 55% of the voters approve of A, have 55% of the delegates approve of A; if 65% also approve of B, have 65% approve of B, even if that means that (at least) 20% will have to approve of both. A similar procedure can work with score voting; if a candidate's average score is 5.5/10, have 55% of the delegates approve of A, and so on.

This process will require a larger change than perhaps the party can manage (it will require changes in all states, not just a Florida and a few others), but it will lead to much better results than any proportional-division plan based on plurality ballots could.

In the larger sense, entering the political system via party primaries is potentially a much better way to get approval (or score) voting adopted: while in the general elections, alternative voting methods could only hurt major parties (to the benefit of third parties), in a primary election it could only help, by delivering better candidates into the general election whenever more than two candidates vie for the nomination (where "better" is determined by whatever the voters think it means).

First and Second, or First and Last?

When I find myself trying to persuade others of the advantage of approval and score voting, I often end up arguing with proponents of instant runoff voting. And after debunking the claim that IRV is immune to spoilers, their typical follow-up response is to bring up "bullet voting".

Bang!

"Bullet voting" means that, even if a voter has the option in a voting system to rank or rate multiple candidates, they choose to only rank one. And so, their ballot is effectively equivalent to a plurality voting ballot. Since plurality is bad (a fact we can all agree on), any system that incentivizes it will also be bad.

My opponents argue that, if enough voters choose to approve of (or to give maximum points to) a second candidate—one other than their honest-favorite—that these voters could cause a worse result for themselves than if they had not done so. In other words, they could cause their true favorite to lose by approving multiple options; therefore, voters have an incentive to approve only one candidate, hence bullet voting, hence plurality-level results.

"You Missed"

The truth is, they've actually pointed out the greatest strength that cardinal voting systems (like approval and score) have over ranked voting systems (like IRV and Condorcet systems): you might accidentally cause your second choice to win. But how is this an advantage? Because in those other systems, the risk is that you might accidentally cause your last choice to win! That's what the existence of spoilers in these systems mean, that when voters choose to support their true favorite above all others, they risk throwing the election to the candidate the hate the most; that, or they can play it safe, by supporting an acceptable, but not fantastic, candidate, at the expense of removing all hope for their true-favorite to win.

Meanwhile, while you sit in the booth contemplating your approval ballot, trying to decide whether or not to "bullet vote", your fear isn't of your least-favorite candidate winning, but of your second-favorite candidate winning. Now, that's still not going to be an easy choice, but your prospects seem much better when your choice is between 1st and 2nd rather than between 1st and last.

Oscar Update

As we discussed last summer, the Oscar for best picture is moving from a field of 5 to a field of 10, and the vote is done by instant runoff. Here's the 2009 best picture nominees, vs. IMDB's "Top Rated Titles".

Academy	IMDB
Avatar The Blind Side District 9 An Education The Hurt Locker Inglorious Basterds Precious: Based on the Novel ‘Push’ by Sapphire A Serious Man Up Up in the Air	Avatar Up Inglorious Basterds District 9 Fantastic Mr. Fox Star Trek

The IMDB list is a little truncated, since they only list by decade, and only the top 50 of the decade, so its hard to find IMDB's best 10 films for any one year (maybe they don't want to step on the Academy's toes). You'll note, there's a good amount of overlap this year, which isn't too surprising since the nomination step uses a "name five" approval-style ballot, in which each voter names up to five films, without ranking them. The ten most-often-named films become the nominees. Top-5 is mathematically similar to IMDB's score-based voting system; at least, the two are more similar to each other than either is to the instant runoff voting (IRV) used for the final round.

But which picture will win? It's tempting to say Avatar, since it's IMDB's top rated film of the year, but we know that IRV has somewhere between a 5 and 15% chance to exhibit non-monotonic behavior, in which the true first-choice is eliminated before the final round. And that's with three strong contenders; the odds get worse the more there are, and I think at least four of these can be considered "strong contenders".

But what does "true first-choice" mean? For me, it means consensus. If you put all the Academy voters in a room and told them to watch a movie, which movie would engender the greatest total happiness for the crowd? That's the question that score voting (and IMDB) asks. But supporters of IRV instead speak of something they call "core support"; they say that it's most important for a winner to have a large following of fanatics, voters who like them best of all. They don't use the word "fanatic", but it's appropriate. Instant runoff repeatedly removes the choice with the fewest fanatic followers and shuffles them off to their next favorite group; it's fair to call them fanatics because other options that you may also like are never considered until your number-one is eliminated. In other words, IRV doesn't offer you much of an opportunity to offer a compromise, because its almost always the compromise that gets eliminated by non-monotonic behavior. So the question is, is Avatar a compromise? Does it make everyone mostly happy, or does it make only a few people very happy? Luckily, IMDB records that data too! Maybe we'll examine that next time.

Also, remember that the Academy hates science fiction, and animation. In which case, maybe Inglorious Basterds has a good chance...

Comics

I have two mostly-written posts waiting in the wings, but they have to take a back-burner to this.

I love the webcomic xkcd, and considering the topic of this blog, today's comic is very special to me. But then I read the hover text: "I favor approval voting or IRV chiefly because they mean we might get to bring back The Bull Moose party."

Okay; approval voting I'm in favor of. It's a minimalist form of score voting (score where the only allowed scores are 0 and 1), which is good, and since score voting is free of both candidate cloning and favorite betrayal, it could actually allow third parties, like The Bull Moose party, to have a real chance at victory.

But IRV is not good. IRV is strongly susceptible to favorite betrayal, and so is only a marginal improvement over plurality, in that all those third parties, like The Bull Moose party, will still be spoilers (yes, IRV has spoilers) before they become winners. (And that marginal improvement is before you start to account for the significant increase in complexity while counting the election, the potential cost of new machines, and non-intuitive results stemming from non-monotonicity issues.)

But, I have hope: xkcd's author and fans tend to be rather logical (you have to be in order to get all the jokes!) Hopefully this proof will convince them. And if not, this image might.

When You Poll, What Do You Poll About?

There's an interesting fact I've noticed about polling, especially at this point in time, when primaries for important state-wide offices are going by in some states (Virginia and New Jersey, for example), while in others, hats are being tossed into the ring well in advance of any primaries for next year's elections. And what I noticed is this: there are two separate classes of questions, and their proportions change as the primary passes.

The first class is the one people are probably most familiar with, and it completely dominates the post-primary polls. It follows the basic form of "If the election were held today, would you vote for A or for B?" Which is a fine question to ask, once the field has been narrowed such that there are only two candidates with any chance of winning (everyone knows, of course, that third parties can't win.) But there is a second question that, while it doesn't completely push the first out of the spotlight, gets at least equal billing before the primary has passed, when there are still more than two candidates who "have a chance", and it follows the form "Do you view candidate A favorably or disfavorably?"

The reason why is pretty clear: if there are 3 Democrats and 3 Republicans vying for the nominations of their respective parties, you would need to ask 3×3=9 questions to cover all the head-to-head match ups—and that wouldn't necessarily give you a clear impression of the likely outcome—but with the favorability question, you would only have to ask 3+3=6 questions to get, basically, the whole story (and there are proportionally even fewer questions the more candidates are added to each side). And it is basically the whole story: usually, the candidate with the highest favorability wins their party's nomination, and the candidate with the overall highest favorability wins the election.

There's only a few problems: First, a lot can happen in the time between the primary and the election, so who knows what may have happened if all the losers in the primary had just had more time to prove their case to the voters. Secondly, and more importantly, there's no place in this system for any third parties; there's no place to get in at all, actually, without going through one of the two major parties.

And that makes sense to: after all, we have to remember why the parties exist, which is to avoid the perils of vote-splitting by ensuring there's only a one-versus-one choice for any election. Sure, a few crazy folks floated the idea that the Democrats should have kept both Obama and Clinton in to election day, but you'd have to be insane (or angling for a Republican win) to think that would be a good idea: your unified-opposition would be almost guaranteed to win each state's plurality election, and both Democrats would lose. The only logical thing for all leftward-leaning voters is to pool their resources behind a single name; and the same is true for the right.

But what if vote-splitting weren't a concern, and you could rate each candidate, out of a field of three, four, or more, in a way that was completely independent of your rating for every other candidate, and the winner was simply the highest-rated candidate? Essentially, what if favorability polls were how the election was decided? Primaries would still be informative, but they would no longer be restrictive, eliminating most voters opinions before they even have the opportunity to express it; a second-place finisher in the primary could stay in the race as long as they'd like, withhout anyone saying they're ruining the parties chances. We would no longer even need the twin gatekeepers of the two major parties, which only 60% of voters even subscribe to despite their shared near-100% dominance of politics in this country, and those two would no longer be able to create a moral argument for the insanely restrictive ballot-access laws which they've created to keep third-parties from even making it to election day.

I contend that election results would be no worse—by which I mean, in aggregate the electorate would be at least as satisfied with the results of the election as they are today, and may possibly be more satisfied, given the larger field to choose from.

IMDB does at least as well as the Academy at choosing the best films of all time; and it can pick them out against a field of thousands, not just five. Favorability polls can pick an election winner out of a field of a half-dozen, not just two. And favorability polls are the same thing as approval voting. Some outfits even publish "net approval" ratings; the candidate's favorability minus their unfavorability. This system is precisely the same as the method used in the Republic of Venice's elections, which lasted under a Democratic system for over 500 years. We may do even better by including "strongly favor" and "strongly disfavor"—in essence, a score voting system from -2 to +2—which is an answer many pollsters already allow in their questionaires.

These last few post (I hope you've noticed) have a common theme: approval and score voting are all around us, we use them everyday, in mundane decisions and even, in limited capacity, with our current electoral system. It allows greater choice, and gives us better results. It's time we tried it on Election Day, not just in the polls leading up to Super Tuesday.

Award Season

I've been trying to come up with some sort of clear conclusion to draw about the Academy Awards vs. IMDB's Top 250, but I keep running into the problem that I don't know half the movies on both lists, and when I try to generalize anything from conclusions based on what I do know, I run into this wall of uncertainty (another reason that I was hoping for comments, but oh well.) But, before I give it all a rest, I'd like to talk about another award-slash-voting-system: science fiction's Hugo Awards.

According to their description, the Hugo Awards (like the Academy Awards) uses a two-step process; nominations and final voting. The nomination process for the Hugo's uses approval voting (good on them!) but with a limit of five titles on each persons ballot (oh well, no one's perfect) with the top five being nominated. The final voting step is instant-runoff (uh oh!) with one important exception.

In addition to the nominees, Hugo voters are allowed to rank "no award" anywhere on their ballot. After determining the IRV winner by the normal method, the potential winner is compared pairwise to "no award" (obviously, if "no award" was the IRV winner, there is no award). In other words, for each ballot it is determined whether that ballot ranks the potential winner higher or "no award" higher, irrespective of the rankings of all other nominees. If more ballots prefer "no award" than prefer the potential winner, then there is no award.

This "special case" highlights one of the more damning aspects of instant runoff: it does not, despite its advocate's claims, always pick a majority-preferred candidate, but rather, sometimes, one of the other candidates is preferred over the "winner" by a majority of voters. (This, among other issues, happened in Burlington, Vermont's most recent mayoral election.)

These sorts of pairwise comparissons—looking at a more-than-two way race as a series of one-on-one contests—is the heart of another ranked-order voting method (or rather, a family of such methods) called Condorcet's method; and as ranked-order methods go, based on Bayesian regret, Condorcet is better than IRV (not a tall order since IRV is the second-worst method, only ahead of plurality). If the Hugo awards are so fearful of "no award" getting an unfair pairwise chance against the IRV winner, I wonder why they don't use an entirely pairwise method; surely there must be some overlap with judges of a science-fiction contest (geeks) and open-source programmers (more geeks), and the programmers use Condorcet for their elections.

Of course, I recommend that both of them move to score voting; however, the approval-based nomination step is a great idea for the initial round of a two-step process (although on average the approval votes alone would likely get a better result than the final IRV round, barring the fact that the two-round process gives everyone a chance to go read any nominees they missed before the decisive round.)

Finally: I try to keep my personal views on any actual issues out of my writing here, and focus only on the process by which groups can make more-democratic decisions. But if Anathem doesn't win Best Novel, I will riot in the streets.