Bring Approval Voting to Oregon!

In the last few years, legislative efforts to enact approval voting have been stymied in Arizona, Colorado, and New Hampshire. But there's an exciting new possibility opening up in Oregon, where there's an effort under way to get approval voting up through a ballot initiative.

Actually, it's an approval top-two-primary, and I've never been a fan of top-two primaries, but since it will be carried out using approval voting, this will still likely be a huge boon to the people of Oregon, if the initiative proves to be successful. If you're in Oregon, please get involved (or if you're willing to go visit; out-of-state petition circulators are legal in Oregon.)

So visit their website, like them on Facebook, follow them on Twitter, and get the word out. I'm hoping there will be a lot less friction moving this through with an initiative process rather than with a legislative process, so fingers crossed!

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In an entirely unrelated personal aside, this marks my first success with managing to post something at least once per month for an entire calendar year. Next year's resolution will be for at least two per month.

Alaska Statute 15.15.360(a)(4)

I moved to Alaska a little over 3 and a half years ago, about a year after I decided to take up Poundstone's challenge and work to enact approval (or maybe even score) voting in my city. Needless to say, changing localities tends to disrupt those kind of local efforts, and I've been hesitant to start, from scratch, again. But it's time I stop making excuses.

Alaska statute, section 15.15.360, part a, line 4. This is my enemy:

"If a voter marks more names than there are persons to be elected to the office, the votes for candidates for that office may not be counted."

These 27 words are the greatest legislative obstacle standing in my way for fairer electoral outcomes. All I would need to do in order to make approval voting the law of the land for elections across my entire state, is to change that line to something like:

"If a voter marks more names than there are persons to be elected to the office, a vote shall be counted for each candidate properly marked."

...which is copied, word-for-word, from the preceding sentence of the statute, about what to do if a voter marks fewer names than there are persons to be elected to the office.

It's such a small change. But it has such profound implications, and will (I'm sure) see so much resistance. Time to get to work.

From the Top

Cross-posted to my lovely wife's Web Librarian blog. The American Library Association is currently having a discussion about how they elect their Council, and she figured "Hey, I know a guy who loves to talk about election stuff!" This is a good back-to-basics introduction to our topic:

It has been said that democracy is the worst form of government, except all the others that have been tried. And the essential component for democracy is voting. So it seems reasonable that a better way of voting would lead to better democracy. That’s the motivation behind the Center for Election Science, the book Gaming the Vote: Why Elections Aren’t Fair (and What We Can Do About It), and this post.

Let’s break voting down. You have 1) a group of mutually-exclusive options to choose from. We don’t have to be talking about candidates for office; we could be deciding between different pizza toppings, or names for your new band. You have 2) a group of people with opinions about those options. Finally, you have 3) a system which takes those opinions and uses them to select one of the options. Actually, you have a whole lot of different systems, and you get to choose one. Your system could be “pick one of the options at random.” That’s not a good system, since you could end up with an option that everyone hates. Or, you could pick one of the people at random, and let them choose. That’s a little better—you know you’ve picked an option that at least one person thinks is the best—but what if everyone else thinks they’re wrong? Shouldn’t we consider everyone’s opinions?

Okay, so what if we let each person name their favorite option? And then, whichever option the most people choose, that’s the one we go with. This is the system you’re probably most familiar with. It’s called “plurality” or sometimes “first past the post.” And since you’re familiar with it, you’re probably also familiar with some of its shortcomings. For example, sometimes you might really like one of the options, but you also know that there are two other options where almost everyone else thinks one of them is the best. If you also have a strong opinion between those two, you need to decide if you’re actually going to support your real, no-hope favorite, at the risk of getting something popular that you don’t like. Or perhaps, there are two options which both seem equally good to you, and another popular one that you think is terrible. It can be difficult to determine which of the two good ones to get behind, and if people split evenly between them, it’s quite likely both will lose. You shouldn’t have to distort your opinions in order to vote effectively. Instead, you could use a voting system which collects more information about the voters’ opinions on the options, and incorporates as much of that as possible into the process.

It turns out, there are many other systems to choose from that are better than plurality. Some of them ask you to rank the options in order from your favorite on down. However, every single one of those methods suffers from at least one of the same shortcomings we identified for plurality: either there will be situations where you have a compelling reason not to vote for your real favorite first, or multiple too-similar options will stomp on each others’ support. Or both! This problem is a consequence of a very famous (and Nobel-prize-winning) theory from economics called Arrow’s Impossibility Theorem. Arrow’s theorem is usually pithily summed up as “There is no perfect voting system.” The whole truth is, of course, much more complicated than that. And while actual perfection probably is impossible, there has recently been a push in favor of voting systems which achieve what Arrow proved to be unachievable. Arrow wasn’t wrong; rather, his proof simply—and intentionally—ignored another class of voting systems, a class that doesn’t ask voters to rank the options, but rather, asks them to rate them.

Think of it like giving “stars” to products on Amazon, or “liking” comments on social media. You don’t consider each product by directly comparing it against all other products you’ve ever purchased, or each comment by directly comparing it against every other comment you’ve read today. Instead, the process is more indirect. This book was about a 4. That banana slicer was definitely a 1. You like your aunt’s comment enough to say so, or you don’t. What are the best products? Probably the ones with the highest scores. What are the best comments? Probably the ones where more of the people who saw it, liked it.

Approval voting is the simplest of this class of voting methods. It’s exactly like “liking.” For each option, each voter can either approve of it, or not. The option with the most approvals wins. You can expand on the idea by using an idea like “stars.” Each voter gives each option as many points as they like, up to some limit, often 5 or 9 or 99. This method is called score voting. (And you can think of approval voting as score voting with a limit of 1.) Because you rate each option completely independently, similar options don’t ruin each others’ chances, and you can always give top mark to the choice that’s your true favorite. By fixing the problems that encouraged people to distort their opinions, by collecting more information from people about their opinions, and by incorporating it into the process in an intelligent way, a group is better-able to select the option that is the best choice for it. Approval voting is better democracy.

Further reading: What Do You Mean By "Best"?

Approval Voting Fundraiser

This last weekend, the Center for Election Science—the world's largest (only?) approval voting advocacy group—launched a fundraiser through Indiegogo. The goal is to raise $12,375 (a very precise amount; don't you love an organization run by math geeks?) in order to have a professional, high-quality video produced about the advantages of approval voting, which will then be entered in the MacArthur Foundation's Looking@Democracy contest. Or, in short, please watch this video for a fundraiser for a video for a fundraiser.

There are a number of perks available for different funding levels. I put in $100 in order to get a signed copy of Gaming the Vote, the book that first convinced me of the benefits of approval voting. I must have bought the book three or four times by now, but I keep giving my copies away to friends and local politicians. I'll definitely be keeping this one though!

Even if you can only contribute $1, it would be warmly welcomed, and it would mean a lot to me, personally. I've been at this for four years now (some CES supporters have been working towards this much longer!) and although one little video may not seem like much, it marks the difference between being just a bunch of people complaining about politics on the internet, and being real advocates for change. Help us do something important.

Maybe you haven't heard the advantages of approval voting, or maybe you could use a recap. Approval voting:

• Always lets you vote for your favorite
• Never has spoilers
• Is simpler than any rank-based voting method
• Encourages consensus winners
• Lets 3rd parties earn their true level of support

We have real-world and theory-backed evidence to support all of these claims. We just need a little bit of help from you to get the word out.

Pendulum Or Plumb?

An engineer, a mechanic, and a statistician go on an African hunting safari. They spot a lion in the distance, and the engineer aims, and fires... but misses five feet to the left. The mechanic scoffs, takes aim, and fires... but misses five feet to the right. So the statistician jumps up and shouts "We got 'em!"

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Since about WWII, congressional polarization has steadily increased. Over the last election cycle we've seen another wave of incumbent moderates forced from office, either by successful primary challenges (e.g. Richard Lugar), or via replacement with a more partisan candidate that's more in-line with the area's political leanings (e.g. Scott Brown or Ben Nelson). As a result, this month's election continues that trend and makes the US Congress yet more polarized than it already was.

With moderation virtually impossible to find in any one member of congress, many Americans have resigned themselves to the hope that, while political power will swing like a pendulum between too-far-left and too-far-right, the results will average out to be somewhere in the middle. (Or worse, they've resigned themselves to the despair that politics has become hopelessly and irrevocably polarized.)

But what if there's a better way? Plurality voting (as well as instant runoff voting) suffers from a problem known as "center squeeze", where if three candidates are running for office, the one in the center is at a significant disadvantage. And so overtime, despite the honest intentions of every voter, the political center is emptied of elected representation. But if we use a voting method that does not suffer from "center squeeze", such as approval voting, then we would see the opposite effect: Over time, more members of congress would be found in the center.

Alternative Voting Methods Experiment by OWS

The Political and Electoral Reform working group, a part of the Occupy Wall Street movement, performed an exit-poll survey experiment on alternative voting methods. It was conducted at a very Democratic-leaning precinct, but the results are still quite informative. By all three methods tested (approval, score, and instant runoff voting), the Green party won, and only under IRV did the Democrats even come in second. In the actual election, the precinct went heavily to the Democrats, of course.

Two New French Voting Studies

In the last couple days, two new voting studies have come out of France, following the Presidential elections there. One (translation to English) and two (and also in English.) The first included a look at approval voting, and the second score voting, with a range of -2 to 2, and both suggest that France would have gotten a different, and probably better, result if they had used either of these methods.

Specifically, the first study found that, if approval voting had been used in the first round, that the two candidates to advance would have been Hollande (the Socialist leader who advanced in the real election, and went on to defeat incumbent center-right President Sarkozy) and the original fourth-place finisher, François Bayrou. Bayrou is an interesting character; he came in third in the previous election, and his Democratic Union party is considered a centrist group. The study also showed that, in a head-to-head match up, Bayrou would have beaten Hollande. This is some real-world data supporting the theory that approval voting does a better job of electing centrist candidates than plurality. They examined instant runoff voting as well, but got the same result as the plurality election, supporting that theory as well.

The second study looked at score voting. Again, Bayrou and Hollande led (and were the only candidates with net-positive scores!) while Sarkozy slipped back to fourth place. Their head-to-head challenges also found Bayrou to be a beats-all winner. They also found very little bullet voting.

These studies build on previous, smaller ones from the 2002 and 2007 elections, which found similar results. All told, this is some excellent real-world data adding further evidence to our theoretical expectations of approval and score voting.

Declaration of Independence (of Irrelvant Alternatives)

You're finishing up a nice dinner, when the waiter lets you know about their dessert options. They have apple pie (A), and blueberry pie (B). You order a nice hot slice of all-American apple pie. A minute or two goes by, and the waiter returns. "I forgot," he says, "to mention that we also have cherry pie" (C). You consider it a moment and decide, "In that case, I'll have the blueberry."

Just Dessert

Ridiculous, isn't it? If you think A is the best out of A and B, then there's no logical reason you would think that B is the best out of A, B, and C. But what if pies are parties, and you are the American voting public? Official results don't collect voter's full preferences on candidates, but (please, hold off on your Gore/Nader (or Bush/Perot) comments for a bit, thank you!) there's no shortage of people claiming that this new third option, even though they didn't win, changed the outcome. (Keep holding it.) What we're talking about is usually called the spoiler effect, or more broadly and academically, a failure of the independence of irrelevant alternatives (IIA).

In the absence of 100%-completely-non-controversial data, it's easy enough to construct a plausible example to showcase the theory:

• 30%: A > (all others)
• 45%: B > (all others)
• 25%: C > A > B

If only A and B run, A wins 55% to 45%. But if A, B, and C run, then by plurality voting rules, the winner changes to B. We can vary the percentages pretty widely (we can even throw in in some C > B > A voters) but it doesn't vary the results: C doesn't win, but they do change the winner.

This isn't C's fault. Maybe C was making a statement. Maybe A should have dropped out of the race. Maybe C's voters valued their honest vote over the practicality of supporting a "lesser evil." (Okay, now you may comment.) All of these could be true, or none of them could be true, but the fault lies not in our candidates or our voters, but in the way we have agreed to count our elections. We have decided to use a voting system which fails the independence of irrelevant alternatives. And IIA means spoilers, which means "the lesser of two evils" is an effective voter strategy, which means we will have a two-party system. In other word, not only will C lose, but C will always be feared by voters of potentially causing the election of the worst candidate.

Declare Your Independence

This is not a new revelation; this is a problem we've been aware of, and trying to fix, for at least a few hundred years. But, in 1951, Kenneth Arrow proved--on his way to a Nobel prize--that no (single-winner) voting system can pass IIA if it is both deterministic and based on ranked-order ballots. That leaves us with precisely three options.

• One, accept failure of IIA (which means we accept our two-party system.)
• Two, allow a random component in our elections (not a popular plan.)
• Three, don't use ranked-order ballots.

I chose option three. And if you're the sort who likes 3rd options when you go to vote, then option three is the most important political stance you can take. Because we cannot even fairly consider more than two options--we cannot even rationally think about cherry pie--without it.

Declare your independence from irrelevant alternatives! Support approval voting and other third-party supporting voting systems.

New Hampshire Approval Voting Bill Shot Down

HB240, the bill in the New Hampshire state house to enact approval voting, has failed to pass, having been deemed "Inexpedient to Legislate."

Apparently, some of the same state representatives who shot down Dr. Steven Brams' original push for approval voting in the state back in the 70s are still in the house, and did not find any of the research performed since 2000 persuasive.

I can only hope that this does not deter the approval voting advocates. Perhaps, given more time, they can persuade more of their colleagues of the system's benefits.

More on New Hampshire Approval Voting Bill

The story has made it all the way around my corner of the internet and found its way to Slashdot (which links back to how I ended up writing about this topic in the first place), so now would be a good time to summarize some of the arguments and counter arguments I've been having with people about this:

First, look over to the right and take note of the pink-highlighted link, What Do You Mean By Best?. There I talk about Arrow's Theorem, the debate over voting systems and voting system criteria, and how computer simulations can help us resolve it. Approval voting and range voting stand head-and-shoulders above other alternatives. This is especially important to the Slashdot crowd, because many Linux distributions, as well as Wikimedia, all perform their elections using a Condorcet method, and so many have come to accept that Condorcet methods are the way forward (although the Fedora project uses range voting). Regular readers will of course recall that Condorcet's ideal is better-met by approval voting than by any actual rank-based "Condorcet method".

The bill is having committee hearings next week; I'll continue to keep you posted.

Approval Voting Bill Introduced in New Hampshire

Longer pieces are in the works, but I have a quick link to share. A bill has been introduced in the state of New Hampshire to move all state-level elections to approval voting. But potentially even more interesting, the bill would move the chronologically-important New Hampshire presidential primary to approval voting as well. I'll be keeping an eye on this as it continues throughout the legislative session.

"I'm the Greatest!"

Sports metaphors are always popular when discussing politics. But is an election more like a boxing match, or a foot race? To answer that question, let me ask some more questions: Who do you think is the fastest runner in the world, and who do you think is the best boxer in the world? And how would you know?

In a foot race, the number of contestants is limited only by the width of the track; actually, since everyone runs against the same clock, even that isn't necessarily a restriction. And so there's no question who the fastest runner in the world is.

But boxing is different. If you put Muhammad Ali, George Foreman, and Joe Frasier together in the same ring at the height of their careers, which one would have won? And could you even be sure that the last man standing was the best boxer, and not, for instance, that #2 and #3 didn't just gang up on the "real" world heavyweight champion?

Sadly, elections seem more like boxing matches. Any third challenger either is forced out and not allowed into the ring (via ballot access laws), or drags down a better winner (by being a spoiler). But a little over 200 years ago (or perhaps quite a bit earlier) an improvement was discovered by the Marquis de Condorcet: if there are more than two candidates, have each of them compete, in effect, one-on-one; the truly best one will always beat any other challenger.

(This is done be examining every ballot for its expressed opinion on each pair of candidates; every ballot that list A above B, is a point for A over B. Rankings for any other candidates are inconsequential in the A versus B determination. Then we compare A versus C, and then B versus C, and so on, until we've examined every ballot while considering every pair of candidates.)

There's only one little problem: such a "beats all" or "Condorcet winner" doesn't always exist. Just like Foreman beat Frasier, and Frasier beat Ali, but Ali beat Foreman, so it can go when counting votes. This may not seem obvious, but it's true! Consider:

• 40%: A > B > C
• 35%: B > C > A
• 25%: C > A > B

65% of these voters prefer A over B, and 75% prefer B over C... but 60% prefer C over A! (For this to happen, there would have to be more than a single topic over which voters consider the options. It couldn't just be "right versus left," for instance, but left versus right on "social issues" and "fiscal issues" would be enough to trigger this problem.) When a Condorcet voting method is used then, it's important to have a method to break these "Condorcet cycles," a sort of circular-tie-breaker. Over the years, different tie-breakers have been proposed and used, but they all run into one problem or another, especially when voters begin to act tactically; potentially even electing the worst possible candidate.

How can we improve on this? We can make elections more like a foot race. The problems that other election methods have, they have because they ask the voters to explicitly rank the candidates relative to each other; they ask "who would win in a fight?" But if we instead make the seemingly-minor change of rating every candidate against an independent scale--in other words, have them all race against the clock, so that they are ranked against each other only implicitly--then we discover some surprising things.

For one, we'd find that we can allow many more contestants to run simultaneously, without "spoiling" the election; any supporter of third-party or independent candidates should be excited by that. Of course, there would still be some interaction among candidates; I might rate a candidate lower not because I think they are worse, but because I think it will help my favored candidate win. That's tactical voting. So rather than a 100 meter dash, perhaps a marathon, where all the runners bunch together and pace each other (i.e., run faster or slower because of the presence of the other runners), is a better analogy. (Although we should point out that not even the 100 meter dash is immune to pacing effects.)

Although tactical voting is still present, what we find is that it is a much less significant factor in determining the outcome. The truly surprising thing though is that, when we allow our models to account for tactical voting, we discover that these rating-based methods--such as approval voting and score voting--are more likely to elect the honest Condorcet winner than any actual, rankings-based, Condorcet voting method! (Scroll down to the first chart; Condorcet methods are highlighted in blue; score voting is equivalent to range voting.)

Condorcet's insight is a powerful tool for evaluating election methods. And even though he only considered it in the context of ranked ballots, in practice, the most reliable way to achieve it is through rated ballots; through approval voting and score voting.

Strategy-Free Elections, And The True Measure of a Voting System

If you get involved in the debate on voting system reform, it's never long before someone brings up the concept of "strategic voting." The idea is simple enough: we all want to be as honest as possible on our ballots, but because the voting system is imperfect, we vote otherwise. This is easy to see in plurality; lots of people who claim to really want a third-party candidate end up voting for one of the two major-party candidates on election day. But it happens, to a lesser or greater extent, under all voting methods.

Actually, that's a cleverly-constructed lie of omission.

It turns out that there are a number of voting systems which are 100% strategy-free, so your honest vote will always also be your best vote. But you're not going to like them. Here's an example: voting is performed like plurality, i.e., each voter picks a single candidate. The winner is whichever candidate is named on a ballot chosen at random. Clearly, you should always vote the one candidate you think is best for the job, because there's no reason to fear that you're "throwing your vote away" or making it easier for a candidate you dislike to win. The clever part in the constructing of the lie was omitting the word deterministic, which means "no random components". There are no strategy-free deterministic voting systems.

Constructing other (and better) strategy-free methods is easy enough. So if strategy is so vitally important that it invariably comes up in every voting-system discussion, why don't we use one of them? The answer is: average performance. Random ballot voting, as your intuition probably tells you, is an absolutely terrible system. But intuition is sometimes wrong, so it's important that we can back it up with data by running computer simulations to calculate Bayesian regret. And the data shows that, based on the number of candidates competing, random ballot is two- to four-times worse than plurality voting; which we all know from experience to be a pretty bad system.

Strategy, and a voting system's susceptibility to it, are an important thing to be aware of. But immunity to strategy, even though it sounds like a great thing to strive for, isn't the goal of a voting system; if it were, we'd have an easy answer to the problem, in the form of non-deterministic voting methods. And there are a host of other reasonable-sounding things for a voting system to accomplish, many of which have been codified as voting system criterion. But, besides many of them being mutually-exclusive (i.e., you can't meet them all), using any of them as a litmus test obscures the true objective, in the same way that focusing exclusively on being strategy-free obscures the true objective. The only true measure of a voting system is it's expected performance: how well it delivers a desirable candidate to the electorate. Average performance, as measured by Bayesian regret, smooths over all the coarse edges of criterion, implicitly assessing all of them for frequency as well as impact.

Why should it matter that, for instance, approval voting fails the majority criteria, if the failure rate is vanishingly-infrequent and has minimal impact? When it performs significantly better than a host of other systems that do meet this criteria, but fail some other, equally-reasonable criteria? It shouldn't. Holding the percentage of strategic voters constant, approval voting has significantly better performance than just about any other voting method. Range voting (AKA score voting) can be even better. Which criteria are passed are secondary to that fact.

How it Might Have Been Different

Sorry for the lack of posting, but my political energy has all gone towards volunteering my time to my favorite candidates. One of those candidates was Scott McAdams, who ran in the race I am about to discuss. I have tried to keep my partisan views out of this piece as best as I can and to refer only to polls and election results in the most dispassionate way possible, but I feel it would be deceptive of me to not acknowledge my connection to the campaign.

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Sometimes it's hard to articulate how approval voting or score voting would serve to create better electoral results. The typical election quickly boils down to just two good choices, and despite the rare holdout, most voters begrudgingly accept that they have a binary choice to make. But when there are only two options, every voting system produces the same result; the improvements only come by making more choices viable. Yet, for whatever reason, people have a hard time imagining how a better system encourages more choices, preferring instead to just complain about the lack of options or to simply demand more options, without supplying any mechanism that could encourage such a thing.

Approval voting and score voting are the mechanisms. And this election has actually provided an example to illustrate it: the three-way Alaska Senate race. Thanks to Public Policy Polling, we have some excellent information [PDF] pertaining to the candidate's favorability ratings. Favorability is a pretty good proxy for three-point score voting (where the scores are -1/0/+1). The first thing that jumps out when we look at these numbers, is that Miller and Murkowski had some of the worst favorability scores out of all Senate candidates across the entire country. Miller had 36% favorable versus an astounding 59% disfavorable, for a -23 net, and Murkowski had a 37/53, for a -16 net. But McAdams had one of the best favorability scores in the country, with a 50/30 for a +20 net.

This means that, under this simple score voting system, McAdams would likely have won this race, and it wouldn't have even been close. Under plurality though, he got only 24% of the vote, while Miller got 34% and Murkowski got up to 41% (41% is the total for all write-ins, but polling suggest that about 95% of those (so about 39% of the total) are for Murkowski). Looking at just these numbers it's clear that not only did a large number of Murkowski-and-McAdams approving voters chose to go with Murkowski, but that at least some Alaskans voted for Murkowski in spite of the fact that they did not approve of her.

Clearly, this is an example of tactical voting. No (deterministic) system is completely immune to tactical voting, and we can't be fully certain that voters would have voted precisely how the poll suggest they would have if they knew their favorability opinions would decide the outcome (indeed, some PPP favorability polls would have called narrow two-way races backwards). But, assuming the poll represents honest opinions, we can be certain that a majority of Alaskans (i.e., over 50%) would be disappointed with either a Miller win or a Murkowski win, while about half would have been satisfied with a McAdams win. And yet, the winner will be either Miller or Murkowski, and certainly not McAdams, depending on how many write-ins survive the auditing process.

Plurality voting breaks down when there are more than two good choices. That's why most elections see just two "viable" candidates. But simply adding more candidates (or even more parties) accomplishes nothing, because we don't have a system that can deal with more than two options. We have a two-party political system because we have a two-party voting system. But if we change to a better system, one where we can get better results by adding more candidates, only then can we find success by doing so.

Clowns to the Left of Me, Jokers to the Right

I have a game for you. Get one hundred things--pennies, toothpicks, whatever--and set them up in a line, from left to right. This is our voting populace in simplified, one-dimensional form. Each "voter" has just one simple rule to decide how to vote: vote for whichever one candidate stands closest to them (yes, we're using plurality voting; and if there's a tie for closest, each gets a half vote). Now, grab another thing--a pencil, a button, it doesn't matter--and place it on the line, between two voters, so that 17 voters are to the left of it. This new thing is one of our "candidates", Libram McLeftyson. Nearly five out of six voters think he's too liberal. Grab another candidate, and place it, mirror-like, so that 17 voters are to the right of it, and in equal measure to her competitor, nearly five out of six voters think Constance O'Righterly is too conservative.

Now, here's how you win the game: place a third candidate between any two voters (except right on top of one of the existing candidates) such that they win the election. Go on, try it; I'll wait while you count your things.

Give up yet? You should, because the challenge is impossible. No matter where you put your third candidate, it is impossible to make it so they win; even putting them right in the center won't do it. As an added bonus, you'll find that whichever of the other two candidates you put them closer to, also loses. And if I move them from inside the 17 marks to precisely the 25 marks, you can't even come in second. I can even put them at the 49 marks, practically next to each other, and there's still nowhere you can go where you can win.

More and more Americans are agitating for a "third party", most without even realizing that there are already dozens of active third parties to choose from. But they don't win. They can't win. And this is without even acknowledging the effects of tactical voting, this is with honest voters! In this simulation, the only ones voting for the big-two are the ones who honestly believe them to be the uniquely best option available.

The existence of a multitude of third parties hasn't change this. Screaming that we need even more third parties won't change this. You cannot win this game. The only way you can win, is if you change the rules.

And the rules that would give third parties a chance to win are approval voting and score voting.

Irony: Aspen To Use Approval Voting... Once

In 2009, Aspen, Colorado voters chose to begin using instant runoff voting in some elections. They were, apparently, less than satisfied with it, and are now working out their options for replacing it. Aspen Daily News describes how the choice will be made:

Aspen voters will be asked if they support the winner-take-all system that was used through 1999, and one that requires a majority for council members and the mayor, which was used through 2007.

Both options will have their own “yes” or “no” question on the ballot. Whatever receives the most support will become the new voting method...

Does this sound familiar to you at all? It should, because this is approval voting! Each option can be approved or disapproved of independently, and the most-approved option is the winner.

There is one hitch though:

If neither method gets a majority, IRV will remain.

For this to be a proper approval voting election, the un-stated third option in favor of the status-quo ought to also be on the ballot. After all, it is possible that both replacement options will get more than 50% support but that an even greater percentage would approve of keeping IRV. (I didn't say likely, I said possible.) Or, conversely, that both alternatives could get less than 50% but that even fewer voters would want to keep IRV. Leaving one of the options unstated leaves open these possibilities. Imagine if this near-approval format were used when two challengers faced an incumbent office-holder; you wouldn't want the incumbent off-ballot and to make these sorts of assumptions about how the voters truly judge them!

Thankfully, Ward Hauenstein, a member of the city's election commission, has suggested precisely this; although his reasoning was due to the possibility of voter confusion. Either way, it's not clear if the people in charge of the ballot will take him up on the idea.

So, Aspen will be using approval voting (or at least something close to it) this one time; but they will be using it to decide which less-effective-than-approval voting method to use for future votes. Come on Aspen, you're so close!

Topsy-Turvy Instant Runoff

Instant runoff voting (IRV) is known to display a number of perverse problems when there are more than two strong candidates. As a thought experiment, and mental exercise, Professor Warren Smith--mathematician and founder of the Center for Range Voting--try to determine the simplest IRV election that can showcase the greatest number of these issues.

9 voters: A > B > C
12 voters: B > C > A
8 voters: C > A > B

The example has only three candidates, and needs just 29 voters, but still illustrates:

• Reversal Paradox: if all the ballots have their order reversed, the "winner" stays the same, so the "best" choice is also the worst choice. (It's A in both cases.)
• Less-is-More: one of two forms of non-monotonicity, where by lowering the rankings for a losing candidate on certain ballots, they become the winning candidate. (Change two B-first voters to C-first, and B wins instead of A.)
• More-is-Less: the other form of non-monotonicity, where raising the winning candidate's rank on certain ballots makes them lose. (Raise A from bottom to top on 5 of the B-first ballots, and C wins instead of A.)
• Participation Paradox: where, if certain voters had just stayed home instead of voting, the result of the election would have been better for them. (Remove 5 B-first voters (who rank A last!) and C wins instead of A.)
• Anti-Participation Paradox: where, if more of a certain group of voters had shown up and voted, the results of the election would have been worse for them. (Add 2 C-first voters (who rank B last!) and B wins instead of A.)
• Precinct Paradox: the ballots can be divided into precincts, and the winner in each precinct is the same, but is not the same as the winner of the overall election. (Break into 3 precincts such that A-first/B-first/C-first in each is 3/4/4, 3/4/4, 3/4/0; B wins in each precinct, but A wins the aggregate.)
• Tactical Opportunity: some voters could prevent their least-favorite choice from winning by ranking a different candidate above their honest favorite. (If at least 2 B-first voters instead rank C above B, then A doesn't win; either B or C wins.)

I want to emphasize the last point, tactical opportunity; because this is the number-one problem that I see IRV-proponents falsely claiming that IRV doesn't have. It is simply not true that IRV removes the incentive to vote for the "lesser of two evils". There are less-contrived examples that can show this too, but it's worth pointing out every time it comes up.

How would approval voting handle this election? That, of course, depends on exactly how many voters in each faction approve of their second choice, but the Nash equilibrium is a win for B. I believe this is also true for IRV, but it involves the majority of voters ranking their second-favorite above their true favorite. Meanwhile, under approval it never helps you to lower your vote for your true favorite. I'll explore equilibria more in a future post.

Three Is More Than Two (But Less Than Infinity)

Why are approval voting and score voting such good voting methods? This certainly wasn't the expected result when Dr. Smith's voting simulation was first run, and a lot of work has gone into trying to make sense of the result.

I've Got a Theorem...

When anyone first starts to dig into the vagaries of electoral systems, they will quickly hit upon the Nobel-winning work of Kenneth Arrow and his impossibility theorem. But there was another very important--perhaps more important--theorem that came along just a few years later. It goes by the mouthful-of-a-name of The Gibbard-Satterwaite theorem. You do have to admit "Arrow" is a much catchier, and certainly shorter, name; so we'll call this "G-S" for short.

What G-S proves is that, under any electoral system using rank-order ballots, if there are at least three candidates, there will always be situations where a voter who knew how every other voter was voting, would be better off by voting strategically. Always. Even if you allow for equal-rank preferences (which some Condorcet methods can handle) you still run into this problem. So the conjecture is that no single-winner, rank-order-based method could ever possibly support three strong parties, since any candidate would eventually run headfirst into this problem and the perfectly-informed voter will have to choose between honesty and strategy.

But approval voting and score voting don't have this problem with a third candidate. It is still always in your best interest to rate your true-favorite highest, and your true-hated lowest, and doing so will never cause the election outcome to be worse than any other outcome you could achieve. In short, there's no incentive to vote strategically.

Preemptive Counter-Counter-Arguments

Now, there are a couple counter-arguments that people will bring up at this point. One of them is that, since G-S is about a "perfectly-informed" voter, they claim that this means approval (and score) only work this well if there is perfect polling for an election. Which is clearly impossible, so we should obviously use INSERT_FAVORITE_METHOD instead. The logic here is entirely unsound. First, even if G-S doesn't guarantee the effectiveness of ratings-based methods, it certainly does guarantee the ineffectiveness of all ranking-based methods; to stump for a known-bad over an unknown-but-potentially-good, seems blindingly counter-productive. Secondly, the fact that even the best-informed voters may have to strategize to avoid a bad outcome will tend to cause less-than-perfectly-omniscient voters to hedge their bets, and strategically go with the lesser of two evils out of fear of the greater evil.

But a more bizarre (or perhaps just more brazen) argument is that, since approval and score can't pass G-S with four or more candidates, then they are clearly insufficient. Which is an absolutely mindboggling argument, since even school children know that three is still more than two, regardless of the fact that three is less than infinity. Are these methods perfect? No, they aren't. Are they able to deliver an outcome that it is impossible for any ranking-based method to deliver? Yes, they are.

Too Infinity!

The fact that these methods have no perverse incentives in three-candidate elections is probably a large contributor to their improved performance in three-candidate elections, even if they still aren't perfect. And we know that all methods do better when everyone is honest, so having nothing to gain from being dishonest probably accounts for something. And perhaps this improved performance with three candidates somehow carries over and provide better results with four-or-more candidate races too, since performance drops at a noticeably slower rate than the rank-order methods do.

Perhaps knowing why something works isn't as important as knowing that it works; but being able to explain why may help convince some people who refuse to believe that.

I Am Full of Links Today

Another one for you, this time from The New Yorker book review; but it does a mighty job of summarizing 200 years of the intersection of math and politics in that rambling, New Yorker style, with a shout-out to my favorite book on the subject, "Gaming the Vote" (Amazon link on your right). An enlightening read, even if it does unfairly complicated approval voting in the opener (selecting the voters, no matter how complicated, isn't a part of the voting system!)

Must-Read Pro-Approval/Pro-Range Piece

Frequent LoAE commenter Broken Ladder post this excellent piece at As It Ought To Be, about the superiority of score and approval voting. The piece is by Andrew Jennings, Clay Shentrup (who I believe has also commented here), and Dr. Warren Smith (whose work I regularly quote).

Note to self: write up a post on the "complexity" argument.