Let's Talk

First, let me say that I still get absolutely thrilled whenever I get comments; I've only been at this for a few months, and I've been really squeamish about publicizing it. I got one comment though in response to my last post about how IRV fails to fix the spoiler problem or grant success to third parties. And it really got me thinking. So let's talk:

IRV has elected Progressive Bob Kiss as the mayor of Burlington, VT and Ross Mirkarimi, a Green, to the San Francisco Board of Supervisors. While score/range voting is a worthy system, third parties in this country have enough problems with credibility without trying to advocate for a voting system that has never been used anywhere in the world.
--Anonymous

I Owe It All to IRV?

This comment bring up two points, and they're both worth responding to. The first is the assertion that IRV does fix the spoiler problem and allow third parties to succeed, as evidenced by Bob Kiss of the Vermont Progressive Party winning the election. I have three responses to that. One, if that's true, than plurality voting also fixes the spoiler problem, because plurality elected Bernie Sanders mayor of Burlington, VT in 1981 when he was the Progressive candidate. Obviously, that's ludicrous; if plurality was immune to spoilers, none of us would be wasting our time trying to fix the problem. No, the truth is, that Burlington (and San Francisco as well) is something of an exception in American politics, in that it has a very strong "third" party that is already capable of winning elections. But IRV has virtually nothing to do with their success.

My second response to this first point is a bit more flippant, but makes the same point: in Burlington, the Republicans are the third party; something that I went into more detail with in the too-long post I referred to in the previous post. (Mental note: maybe I should try to turn Burlington's Republicans on to score voting. Or would that be overly antagonistic?)

Third, and more substantive, if IRV were actually any help to third parties, then you would expect a country that has used IRV for years, like Australia, to actually have some in their legislature. But of the 150 Australian legislators, currently every last one is a member of one of two parties. (Technically, the Liberal party and the National party are different, but the two have been in a tight coalition since 1922, and are currently working on a merger plan that has already succeeded in the state of Queensland. In the minds of virtually every Australian, they are a single party. Furthermore, the three "independent" representatives were all, at one time, members of the National party, before leaving over intra-party disagreements; a situation very similar to "independent" US Senator Joseph Lieberman's position with the Democratic party.) And let's not forget senator Bernie Sanders; the same Progressive who won a plurality election to become mayor of Burlington also won a plurality election to become a senator from Vermont; by this logic, plurality is better for third parties than IRV!

But It's Doing Nothing Right Now!

The commentator's second point is that, even if IRV isn't helpful at fixing the spoiler/two-party problem, it's still a better idea than anything else out there because it's actually being used already. This is, one, foolish, and two, a bit disingenuous. It's foolish to put all of this effort into making a huge change, knowing that it doesn't actually fix the problem. Besides being a clear waste of effort, it creates a hostile environment for any future real improvements; once an electorate has been bitten by a false "fix-all" solution like IRV, they become much more shy about trying some other solution. Many locales that try IRV find themselves slipping back into the even-worse world of plurality; North Carolina, for instance, has a pilot program that is facing some strong motions this week to go back.

Besides, the truth is score voting has been used for a very long time, and is a system people are already quite familiar with: from Olympic judging, to movie and restaurant reviews, to Hot or Not. We use it every day; we just haven't used it to democratically elect our leaders. At least, not recently. But the two longest-running democratic governments in world history did. For 500 hundred years, Sparta used a (loud and very analog) score voting method for all their elections, and for another 500 years, Venice used a three-valued (+1, -1, 0) score voting method. IRV, on the other hand, was first used in 1893. Call me in three or four centuries.

The Real Winner

But really, it's not important which idea is older, or was used for longer. Even clearly showing that IRV can't completely fix the spoiler problem doesn't show that it's, overall, no good. Taken alone, each of these arguments can be brushed off as simple anecdotes, and we want data (and the plural of anecdote is not data!) Spoilers are bad, because it means a lot of people get something they strongly don't want; two-party domination is bad, because it restricts voter's choices to "the least of two evils" and we often don't want either. But how bad? Which is worse? How often is it a problem? Warren Smith's insight was to try to side-step all the anecdotes, and directly measure "how bad"; that's the idea behind Bayesian regret. And even he was honestly surprised at just how overwhelming the data was.

Now, maybe the simulation is flawed. But maybe it's not. But it's certainly compelling enough to suggest that score voting would be something worth trying. Meanwhile, everything CRV has said would happen with IRV, has happened, including spoilers and continual failure for third party candidates. So again, I would urge you: if you're supporting IRV because of spoilers, or because of third parties, you should STOP supporting IRV. Other options do a better job of fixing the issues you care about.

But if you're still not convinced, I'm game to continue the debate, so keep the comments coming!

A Glossary (For Terril Bouricius)

Like any field, discussion of voting methods has developed a language all its own, full of jargon and technical terms that, while clearly defined for those well-versed in the field, are sometimes confusing or completely opaque to those on the outside. So I don't fault Terril Bouricius for his repeated failures to understand the lingo. I hope he will find this short glossary of voting-method terms useful.

non-mon·o·ton·ic: adj. 1. In reference to a method, a property meaning it is possible in that method to construct a scenario where either a. by improving a winning candidate's rank (or score) on some ballots, the candidate becomes a loser, or b. by lowering a losing candidate's rank (or score) on some ballots, the candidate becomes a winner. 2. In reference to an election, an example where either of the scenarios in 1. is in evidence.

spoi·ler: n. 1. A a non-winning candidate such that, if they are removed from all ballots, the winners of the election change.

By these well-accepted definitions, instant runoff voting is a non-monotonic method (whereas score voting and even plurality are monotonic), and Burlington's recent mayoral election was non-monotonic; instant runoff voting is susceptible to spoilers (plurality is too, but score voting is not), and Kurt Wright was a spoiler for Andy Montroll. These are easily-proven, in-arguable facts, and so are not up for discussion. So please, stop arguing from a position of ignorance, and learn the definitions.

Non-Monotonicity: Part II

In Part I, we defined non-monotonicity, showed that Instant Runoff Voting is a non-monotonic voting system, and that the recent mayoral election in Burlington Vermont suffered from non-monotonicity.

Here in Part II, I'll talk about why monotonicity matters, and do my best to refute all arguments to the contrary.

What happened?

To understand why it's important, first we should try to understand what happen to make an IRV election display non-monotonicity; we'll use what happened in Burlington's IRV election to showcase. I mentioned that "monotonicity" is an idea borrowed from algebra, but let's make that more clear: rather than move just 8 votes from Wright to Kiss, as we did in the example in Part I, let's make a function out of it, so we can see what it's like to move any number of votes over, and graph it against the vote-tallies in the final IRV round. A picture should make this clear:

You can see the huge discontinuity at 8 votes, where the IRV algorithm changes which candidate is eliminated. You can also see that, at 14 votes, the election switches back into Kiss' favor. So there's a limited window where this sort of manipulation will work. Foremost, obviously, is that there must be at least three candidates in the election. As candidates are eliminated, when only three are left, they must each have more than 25% of the vote. Finally, the eliminated candidate (the one with the fewest first-place votes) must be the "beats-all" (or "Condorcet winner") candidate, meaning that, in any one-on-one race, they would win. We can determine this by, for each pair of candidates, removing all but that pair from every ballot, and seeing who would win. For the Burlington election, check, check, and check.

Under these circumstances, IRV exhibits non-monotonic behavior, and eliminates the Condorcet winner. In fact, you could say that because it eliminates the Condorcet winner, it has exhibited non-monotonic behavior. But so what? Well, there's a hidden implication in the elimination of a Condorcet winner, and that is that the Condorcet winner is the moderate candidate, the compromise candidate. Meaning that, by eliminating them, we've chosen an extremist candidate.

In the Burlington election, in addition to the nationally-familiar Democratic party (with candidate Andy Montroll) and Republican party (with candidate Kurt Wright), we also had the eventual IRV-winner, Bob Kiss of the Vermont Progressive Party, which is just a bit more left-leaning than the Democrats. There is a model of voting behavior, appropriately refered to as the "1D" model, where candidates and voters are arrayed on a line, left to right, and voters always more-prefer the candidate closer to them. In the 1D model then, we should expect that all Kiss-first or Wright-first voters would have had Montroll second (ignoring, for now, candidates other than these three). And that's almost the case: among those who expressed a preference, Wright voters prefered Montroll 3:1 over Kiss, and Kiss voters prefered Montrol 7:1 over Wright. 1D isnt' perfect, but it's often pretty close (how much of this is feedback from our two-party dominated political process is an article for another day), and in my "simplified" example of the election, I moved all the "wrong" votes to their "proper" 1D vote. If the purpose of an election is to choose an appropriate candidate to represent a body of people, it's logical to say that you want the winner to come from the center of the spread of voters' opinions; it's a compromise.

But IRV doesn't always pick the compromise candidate; instead, it picks one of the two extremes. The Center for Range Voting has some excellent graphical representations of this, using a 2D political spectrum and many more candidates (which is more realistic than our 1D, 3 candidate example). At a glance you can see how extremist candidates encroach on the territory of more moderate candidates.

On one hand, it's very strange for me to be damning this election, since it technically elected a third-party candidate, which I generally find to be a good thing. One of the reasons I find our current system so abhorrent is because third-party candidates actually damage their most closely-aligned major-party by acting as spoiler candidates. On the other hand, that's what happened in Burlington. Nearly two-thirds of Burlington residents are registered Democrats (click "voting" on that page to expose the data). And considering the Democratic wave that has been washing over the nation recently, in a vote between right, left, and lefter, the Republicans are the "third" party in Burlington. And as a third party, they operated as we would expect; they siphoned votes away from their nearest major-party candidate and gave the election to their most-hated opponent. Their nearest major-party candidate just happened to be the Democrats.

The "third party" Republicans opperated as a spoiler. Under the 1D model (and by a 7:1 margin in actuality) they would prefer the more-moderate Democrat, Montrol, over the further-left Progressive, Kiss. But their votes for Wright acted only as votes against Montroll in the final tally. This is exactly analogous to Nader spoiling Gore. Despite IRV proponents claims, IRV does not eliminate the effect of spoilers, it only delays their effect. Under our current plurality system, spoilers can have an effect with as little as one vote, if the other candidates are close enough. Under IRV, they only pop up when they have at least 25% of the vote. But the effect will ultimately be the same: fear of spoilers will tend to drive voters back towards the two major parties.

Both of these things—failure to elect a "beats all" winner and susceptibility to a "spoiler" candidate—are indicated by IRV's non-monotonic behavior. Non-monotonicity is the smoke to their fire, or the chink in the armor that lets them sneak in. As IRV advocates will claim, it doesn't matter that if some voters changed their votes they could change the outcome in a non-intuitive way; because they didn't. It matters because that possibility indicates that elections will tend toward extremism and towards two-party domination.

How often?

After being forced to admit that, yes, non-monotonicity is something to be concerned about, an IRV advocate's second round of defense will be that it doesn't matter because it doesn't happen that often. And I must admit, this one example is just one example; the plural of "anecdote" is not "data". Luckily, a host of very smart individuals have tried to calculate how often these things should happen, which CRV has taken the time to summarize. The first to make the attempt was Crispin Allard in 1996, and he calculated the chance as 1 in 40,000, and this is the number upon which IRV advocates have built their argument. Unfortunately, Allard's calculation was wrong. Very wrong. He only counted the more common of the two types of non-monotonicity, and he took advantage of a six-fold symmetry to simplify his calculations but forgot to multiply by six at the end, but worst of all made a serious arithmetic error. Over all, he was off by a factor of over 1,000.

Corrected calculations have found that, using Allard's model and his assumptions, the correct odds of an IRV election displaying non-monotonicity is closer to 1 in 7.

But, an IRV advocate might say, that's only one model. Yes, it is. Using a different model, the odds were calculated to be around 1 in 18, and in a third, a little less than 1 in 10. That, combined with the growing list of real-life IRV elections that have displayed non-monotonicity, it should be quite clear that these failures are predicted to happen often, and often happen in real life. Also, it's important to note that these values apply only when there are three strong candidates in a race. As the number of viable candidates increases, the odds only get worse, until the chaos is practically guaranteed.

What's it mean?

Ultimately, adoption of IRV will result in practically no change to the status-quo. Third parties will find they can gather more votes, but they still won't be able to win any elections, because of the fear of spoilers. Voters will still find themselves deciding between the least-evil of a pair of party-chosen politicians, and we'll continue to lurch back-and-forth between left-leaning policy and right-leaning policy, rather than pick a stable course. The divide between "red" and "blue" will continue to grow and our common ground will continue to wither away. And let's not ignore that this non-improvement comes at a high cost (another post for another day). Why not focus on a change that will actually change something?

I've come down hard on IRV here, but that's only because it's the loudest competitor. The truth is, every election method that uses ranked-order ballots (i.e., ballots of the type A > B > C) is susceptible to one of two failings, either "favorite-betrayal" (which IRV displays through its non-monotonicity) or something called "cloning" (which, briefly, involves proping up ideological copies of your opponent in order to split the votes of those who oppose you). IRV is immune to cloning, a fact that they proudly showcase in this video, while ignoring their non-monotonicity pitfall. ("Or something like that" indeed!) Now, cloning is a serious concern under our current plurality system; but why fix one problem by introducing another, when score voting is clone-proof and monotonic, not to mention cheaper to implement?

Non-Monotonicity: Part I

Since the results of Burlington's mayoral election were announced, battle has raged across the internet between advocates of instant runoff voting and those who have better ideas. Several points are being argued discussed, but the most confusing in the issue of non-monotonicity. What's that word even mean?

Monotonic, if you remember your algebra, means that a function, f(x), is either always increasing or always decreasing as x increases. A function that goes up for a little while and then goes back down is non-monotonic. You could think of it as "if more is better, than even more is even better". And that's (sort of) how the analogy comes over to voting methods: under a monotonic method, getting more votes is always better. So under a non-monotonic method, getting more votes is sometimes bad, or, getting fewer votes is sometimes good.

There are three issues at stake here: first, is IRV non-monotonic? This is an unqualified "yes", although IRV advocates will claim that it's so rare as to be inconsequential in real-life elections. (More on that later.) Second, did the recent election in Burlington exhibit non-monotonicity? This is also an unqualified "yes", which one might think would give pause to those claiming that non-monotonicity is ultra-rare. (Rather, they have decided to argue that it didn't really happen.) And finally, does it matter? This is the only issue of the three which can be up for debate, which we'll do in Part II. But first, we'll pause to prove points one and two.

IRV is non-monotonic

The easiest way to show this, is to construct an example. First, the election needs to have at least three candidates; let's call them 'K', 'M', and 'W'. Secondly, we need to construct a set of ballots where one candidate, let's pick K, is the winner, but in such a way that if we improve K's ranking on some of the ballots, they instead lose. Easy enough:

29 ballots: K > M > W
25 ballots: M > K > W
32 ballots: W > M > K

M, with the fewest top-ranking ballots, is eliminated, and K defeats W by an impressive 54 to 32 margin. But! if we improve K's position on just eight ballots, like this:

29 ballots: K > M > W
25 ballots: M > K > W
24 ballots: W > M > K
8 ballots: K > W > M

Then instead candidate W, with only 24 top-ranking ballots, is eliminated, and M defeats K by a 49 to 37 margin. To repeat: by improving K's score on a small number of ballots, K went from being the winner to being the loser. Which is a very non-intuitive result. It's also possible to create a situation where decreasing a losing candidate's rank on some ballots can cause them to win (but I leave that as an exercise to the reader). If either of these cases is possible to construct for a given voting method, then getting more votes is not always better, and by definition the voting method is non-monotonic.

What about Burlington?

So clearly these situations can happen under IRV. The next question is if the Burlington election was one of those situations. The proof of this is almost trivial, since the numbers (and names) in the above example were pulled from the results of the Burlington election (with a few complicating but non-relevant omissions.)

The real question is, why do IRV's supporters insist that this is not the case? I wish I knew! It seems to stem from a lack of understanding of the words "if" and "could", as in "If the outcome of the election could be changed by...", as their argument is that this election "could" have been non-monotonic "if" some voters changed their ballots "but they didn't". No, no, no! If they could then it is non-monotonic! A lot of bad-blood is being spilled over this non-disputable point, and I don't understand why the opposition persists, as it only serves to distract us from the real discussion.

Which we'll cover in the next installment.

IRV Fails In Its Own Backyard

Burlington Vermont just elected their mayor, which wouldn't be big news, except that Burlington is the home town of one of IRVs largest proponents, Terrill G. Bouricius, and he has persuaded his town to use that system. Courtesy of the Center For Range Voting, we show how this election perfectly demonstrates the problems that IRV causes; the ones that Bouricius and Fair Vote insist are "unimportant", "unlikely", and "uninteresting". Namely:

• Failure to elect a majority winner: the eventual winner, Bob Kiss, would have lost to Andy Montroll in a one-on-one election. In fact, Montroll would have beaten any other candidate in a one-on-one election.
• Failure in the face of a spoiler candidate: if Wright hadn't been in the election, then Montroll would have won.
• Failure of participation: if a few hundred Wright voters had stayed home and not voted, they would have gotten a better outcome (their 2nd choice, Montroll, instead of Kiss.)
• Failure by non-monotonicity: if a few hundred Wright voters had instead voted for Kiss, Kiss would have lost (and Montroll wold have won).

The first, I can almost forgive; it's not as if Condorcet's method is perfect either, and IRV advocates can make a deliberate choice between simplicity and effectiveness. The second makes me furious, as IRV advocates prey on Democrat's fear of Gore-Florida-2000-like scenarios, claiming IRV will completely fix problems with Nader-like spoilers; but this election exemplifies how this is not the case. The third, considering the already embarassingly low voter turnouts in the US, is disgusting; we cannot allow people another excuse to stay home on election day. Finally, "non-monotonicity" gets brushed off by IRV advocates as being too "academic" to be concerned over; sure, it's a somewhat complicated concern, but it's a serious concern, which this election shows.

Considering all these failures--all the ones that the Center for Range Voting has warned about and Fair Vote has repeatedly brushed off--I'm disgusted that Fair Vote is pretending everything is fine. Why--how--could you continue to support IRV in the face of this overwhelming evidence from your own home town? Is it ego? Or maybe... it's the money? Yes, in addition to being a "senior analyst" for Fair Vote, Mr. Bouricius is one of the founders of Election Solutions, Inc., who sell the software that Burlington uses to run its elections.