The Tyranny of the Majority Weak Preferences

Suppose you and a pair of friends are looking to order a pizza. You, and one friend, really like mushrooms, and prefer them over all other vegetable options, but you both also really, really like pepperoni. Your other friend also really likes mushrooms, and prefers them over all other options, but they're also vegetarian. What one topping should you get?

Clearly the answer is mushrooms, and there is no group of friends worth calling themselves such who would conclude otherwise. It's so obvious that it hardly seems worth calling attention to. So why is it, that if we put this decision up to a vote, do so many election methods, which are otherwise seen as perfectly reasonable methods, fail? Plurality, top-two runoffs, instant runoff voting, all variations of Condorcet's method, even Bucklin voting; all of them, incorrectly, choose pepperoni.

The Tyranny of the Majority

The answer is simple: All of these methods obey the majority criterion. This criterion seems so reasonable: If a majority of voters prefer one choice over all others, then that choice should be elected. And that's the case here. A majority, 2 out of 3, prefer pepperoni to all other options. Therefore, pepperoni must win. It's completely reasonable. And it means you're willing to send your friend home hungry.

If we examine the ballots these three friends would submit to the pizza-topping election, we can see the problem. Even though you and your one friend both really like mushrooms, the ballots don't show that. They only show that you like them less than pepperoni. There's no way for you to indicate the importance of that preference, and no way to mitigate it. You can't say, as you would if you and two friend were actually face-to-face and making such a decision "I like pepperoni better, but, dude, since you couldn't eat it, I'd totally be alright with eating mushrooms." Well, almost no way: You could choose to rank mushrooms above pepperoni, making a deliberate action to, after considering the thoughtful dialogue of the other voters, submerge your own narrow self-interest by voting for the choice you have determine is the one that would deliver the best result for society at-large, despite your own personal preference....

Or we could use a voting method that already knows how to do that, and lets you express your personal preferences in the same natural way that you would among your friends.

The Tyranny of Weak Preferences

The problem here is that these majoritarian methods have no way to indicate strength of preferences. Your weak preference between pepperoni and mushrooms is given as much importance as a your friend's overwhelming preference between pepperoni and mushrooms. And yet, the ability of approval voting and score voting to cleverly subvert the majority criterion in this way has been used as an argument against it. The detractors argue that it is horrible, absolutely horrible, that a candidate could be preferred by the majority of voters but that the election method would pick someone else. But is it really so horrible? After all, didn't you say you really liked mushrooms?

The truth is, under the voting methods for which I argue, voters have the power to express a willingness to compromise, and if they choose to express that desire, then these voting methods have the ability to honor it. And conversely, if the voters do not have an interest in compromising, then they can express that too.

Now, I know that, in the voting booth, we're not all friends. But that only makes it more important that we use election methods which strive for consensus, instead of divisiveness. You don't have to vote on pizza toppings with your friends, because it's a mostly unimportant decision with only a few people affected, none of which are especially invested in the outcome. You trust each other, and can quickly talk out all possible outcomes and come to a mutually-acceptable agreement. That's harder to do with 100 million angry people deciding on their government. But you still want—no, you still need—a consensus result. The majority criterion is detrimental to that goal.

Arguing Both Sides

What I find especially funny is that the other common argument used against approval and score voting is that they will degenerate to plurality voting, because voters will only vote for their single favorite choice. We know that's not true, but it's also contradicted by their arguments favoring the majority criterion. Because, for an approval or score voting election to actually exhibit majority failure, a substantial number of the voters would have to vote for multiple candidates; while, for accusations of bullet-voting to carry any weight, nearly all voters would have to vote for just one candidate. And yet, detractors argue that both of these things will happen, which is logically inconsistent.

The truth is, sometimes voters will bullet-vote, but only when it suits them to do so. And sometimes (rarely) a majority candidate won't win, but only when the voters who prefer that candidate have made the decision to express that preference as a weak preference, and defer to the whims of the minority. In other words, only when they have said "I like this other candidate better, but dude, if you really hate him, I'd totally be alright with one of these other guys."

It's called a compromise. It's how friends stay friendly, and how civilization stays civilized.

Better at the State Level?

Many pro-third-party and pro-independent voters resign themselves to the difficulty of winning a federal congressional seat. There are, after all, just two, assuming you count Connecticut senator Joe Lieberman, who lost a reelection primary after three successful bids as a member of the Democratic party before deciding to go it alone. A strict count might only include Vermont senator Bernie Sanders, who never once ran for office as a member of either of the major parties. Counting both men, out of the 535 House and Senate members that's only about 0.37%. Meanwhile, there are 7,442 state legislators currently serving in the 50 state legislatures. Some believe that at the state level, since it's a smaller and less rancorous market, third-party and independent candidates can have more success.

So, out of those 7,442 seats, how many do you think are not currently filled by Republicans or Democrats? Write your guess down before reading on.

Did You Write it Down?

Good. Now, if state legislatures had about the same percentage as the US congress, we could expect about 27 or 28 independent and third-party members. The truth? It's actually a little bit lower than that. There are, according to Wikipedia, just 24 such legislators. And about half of them are independent more in the Lieberman sense than in the Sanders sense.

Consider members like Harri Smith of the Alabama Senate, who lost a Republican primary and endorsed the Democrat. She was expelled from the Republican party for doing so, and ran as an independent in the subsequent election, in which the Democratic party did not field a candidate; Smith won. Or New York Assembly member Fred Thiele, who was originally elected to his seat as a Republican in 1995. After a decade and a half of reelections, Thiele joined the Independence Party of New York in 2009, and held on to his seat. Or you can find a hybrid version of those two stories in what Kent Williams did. Elected to the Tennessee House in 2006 and 2008 as a Republican, in his second term he was elected speaker—via the unanimous votes of the Democratic members of the body, and a lone Republican vote from himself. Promptly expelled from the Republicans, he decided to make his own party.

These politicians, like Lieberman, seem more opportunistic than truly independent. But there are some independent state legislators about whom, like Sanders, there is no such doubt. And like Sanders, most of them are in the state of Vermont. In fact, of the 24 legislators, ten of them are from that one small state. That's over 40% of the non-Democrat non-Republican state legislators in the country, from a state with just 0.2% of the nation's population. Of the ten, three list themselves as independents, while the other seven are members of the Vermont Progressive Party, making it the only third party with a substantial (>2%) presence in any state legislature.

Progressive Success

Why has Vermont's Progressive party been so successful? Not because of an advanced voting method; despite the party's support for instant runoff voting (which doesn't even help third parties) the Vermont legislature is elected by plurality, just like the other 49 states. We get an interesting piece of information by looking at the state wide voter totals. Despite taking 3.89% of the legislative seats, the party only received 2.96% of the votes. It's very unusual for a third party's seat-percentage to over-perform its vote-percentage like that, and it happens because, as they say on their website, "We pick the races we enter strategically." Sometimes this means a fusion ticket with the Democrats, or sometimes it means that there's enough political space to the left of the Democrats for the party to succeed on its own. This is possible because parts of the state have a significantly-more than 2:1 voter preference imbalance between the Democrats and the Republicans, leading to the unlikely situation where two left-wing candidates can run without concern of splitting the vote, effectively making the Republican party the "third party" in those elections.

But other states have pockets with similar imbalances, and other states allow fusion tickets, so make no mistake: the Vermont Progressive party's success isn't based strictly on those elements of their voting environment. They're doing something right.

Answer:

Third party and independent legislators are no more common, overall, in state legislatures than in the national legislature. But an astounding number can be found in Vermont. Third party supporters may want to take a close look at what the Progressive party is doing there, and try to emulate it.

IRV a Uniquely Poor Choice for Centrists

The other day, I noticed that the number-one referrer to this site recently has been Rise of the Center. So, first of all, thanks to them and everyone who's found their way here through them. Second, I have an important observation to share with you: instant runoff voting is a uniquely poor voting reform option for centrist. I was reminded of this fact while playing with Ka-Ping Yee's Voteline simulator, in order to respond to points made in the comments of my previous post on the Independence of Irrelevant Alternatives. And while it's something I've alluded too before, I don't think I've ever stated it this bluntly.

Model On Line

The Voteline simulator uses a very simple model. Voters are smoothly distributed along a left-to-right spectrum. Candidates occupy one point on that spectrum. Voter preferences are based on the linear distance from themselves to the candidates; closer candidates are preferred. The meanings of the colors may not be obvious though. The represent who the winner of the vote would be if the entire electorate were shifted, together, so that the median voter was at that point on the line. The relative distances between the candidates don't change, nor does the distribution of voters.

If you believe the winner of an election should be the candidate closest to the center of the political distribution, you would want an election method that always has a nice broad swath of matching color around each candidates' place in line, and 3 of the 5 methods used in Voteline do precisely that. The two that don't are plurality and "Hare (IRV)", AKA instant runoff voting. Instead, a candidate's place in line can easily be taken up with other colors, meaning that even if they are the most-centrist candidate, a different candidate would win the election.

It's not even that hard to squeeze a centrist candidate completely out of the running.

I've talked before about why we use models in these arguments. All models have their shortcomings though, and the one used here certainly contains some exaggerations; not all voters fall neatly on a single axis for instance (but see Yee's two-axis simulations) and we only have symmetrical voter distributions to play with here and so on. And there are other models in which IRV doesn't look quite as bad. But those models don't have any way of defining a center, so if you're buying into the idea of centrism, you don't have many other places to turn to for data.

It is certainly the case that voting method reform could help centrist. But, what these models suggest is that IRV is probably the least helpful voting method reform for that.

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.

Other Good Ideas: Proportional Representation

(Note: This post was going to go up sooner, but with Wikipedia going down to protest SOPA, I put it off for a bit.)

Before disappearing for a third of a year, I was asked a simple question in the comments: Would I support an effort in favor of proportional representation (PR), even if it were for single transferable vote (STV), the PR method on which instant runoff voting (IRV) is based. And yes, I would. I often refer to Duverger's Law, the observation that single-winner plurality elections tend toward two-party dominated government, and PR effectively attacks one of the two legs of that problem.

What is Proportional Representation?

The familiar method for electing a legislature is to divide the region into districts, and elect a single representative from each one, the idea being that someone from where you're from, will want what you want. In practice, this isn't always true. There tend to be factions in each district that split along similar lines, and these ideological splits may be completely independent from the geographic split of the districts. It's possible (by accident or by design) for the narrowest of political majorities to win every single seat in a legislature, or for a group that is a minority in the electorate to have a majority of legislative seats. If the legislature is intended to represent the viewpoints of the whole electorate, only with a smaller number of participants, then these single-winner districts often fail.

The goal of PR is to fix this deficiency. Rather than each district electing a single winner, they elect multiples, and in proportion to the number of votes they have received. In this way, the diversity and popularity of viewpoints among the people will more-closely match the diversity and popularity of viewpoints among the representatives.

Variations and Usage

There are many different variations of PR. The most basic is changing the number of winners elected from each district. This number may be as small as 3 or 5 (usually, but not always, the number is odd) or as large as the 120 used for the Israeli Knesset, which is elected from a single, nation-wide "district". The other major point of variation is whether the system is candidate-based, like our current single-winner elections are, or whether it is explicitly party-based, so that voters do not vote for individual candidates but rather for a party or a list of candidates they have supplied; there are also mixed systems, like the one used in Germany, which provide for both simultaneously. There are also different ways of dividing the votes--basically, which way to round fractions--which can favor having fewer, larger parties or more, smaller parties. Depending on the precise method used, a PR ballot may look just like a plurality ballot, like a pair of plurality ballots (one listing candidates and one listing parties), or it may ask you to rank several choices (candidates or parties), or it may even look like an approval voting or score voting ballot

Most of the worlds democracies use proportional representation, which may come as a surprise to those of us in the United States, but that's because some of the largest exceptions--the United Kingdom and Canada--also happen to be some of the countries we Americans are most familiar with.

Criticisms and Difficulties

Since multiple winners are elected in each district, some critics have said that PR severs the connection between a voter and "their" representative. However, since each district elects multiple representatives, it is more-likely that you'll be in political agreement with at least one of "your" representatives. I also have commonly heard complaints about the party-centric aspects of party-based PR, but usually this is from people who don't realize that there are PR methods that are not party-based. Candidate-based PR tends to become somewhat unwieldy as the number of winners increases, as it becomes more difficult for voters to determine and remember which candidates they prefer. The counting procedures, regardless of the specific form of PR used, are also more complex than plurality voting is. Finally, there are people who legitimately believe that it is best to have as few large political parties as possible, in order to best guarantee the existence of a cohesive majority government, although this is less-significant in the US since we have less expectation of party-line voting, as well as extra veto-points in the President and in one chamber of congress acting more-and-more often under super-majority rules via the filibuster.

Also particular to the US, it is currently federal law that the states elect their representatives from single-winner districts (the law was enacted because some states had chosen to elect all their representatives at-large, guaranteeing that 51% of the voters would choose 100% of the representatives, eliminating representation for minorities) and that law would have to modified in order for any form of PR to be usable for House elections. Furthermore, the constitution requires that House seats be apportioned to the states, so no cross-state proportionality would be possible without a constitutional amendment, making the system rather moot for the 7 states who have a single representative.

This hasn't stopped PR from being used in several US cities, even, at one point, New York City; although most of these later returned to single-winner elections, so that, as of today, Cambridge, Massachusetts has the only governing body in the nation that is still elected via proportional representation.

Conclusions

For those who favor a diversity of opinions, proportional representation can be an effective way to achieve it. It has shortcomings and legal hurdles standing in the way of its use, and obviously can't be used for single-seat offices like a governor or the president. I won't stop pressing for approval or score voting, but there's no reason these advances can't be pursued in parallel. Although, anyone who sought to do so should familiarized themselves with how and why PR elections were rolled-back in recent US history, in order to avoid running into the same mistakes again. But that's a blog for another day...

Now, why would I support STV, but not IRV? It's a known property of STV that, the fewer winners it elects per district, the less proportional it is (and the balancing act becomes ballot complexity versus proportionality.) Since IRV is precisely equivalent to STV with one winner, we know that it loses all proportionality (in other words, IRV is not a PR election method.) This, combined with the other deficiencies of IRV make it an unacceptable alternative to my mind.

The Coming Year

Just want to let everyone know, we're not dead. It's just that in September I bought a house, in October I got married, in November I was standing with the local Occupation group, and in December it gets really, really dark and depressing in Alaska so I just didn't feel like writing anything. But now the solstice is behind us, the new year is in front of us, and we'll be back with a vengeance starting in January. My apologies for the unexpected absence (and my further apologies for making a "my apologies for not posting" post.) I left a couple of important comments un-answered in my haste to the bank/altar/park/dark, and we'll (if all goes to plan) be starting off with a response to those early next year. See you then!

The Franchise

I've been waffling about discussing today's issue for the last month, for two reasons. One, while it's about voting, it's not about voting systems, so it's a bit off-topic. And two, it's become something of a partisan issue. On the other hand, I've made no posts since last month. So here we go!

The essential component of democracy is elections; to let the people who will be affected by the law decide the law (or at least, representatives who will do so.) Give people a choice over the government, and they will be more satisfied with that government's choices. That's why we have only, and always, expanded the franchise; to African Americans, to women, to 18 year-olds. Even if you disagree with the choices another voter makes, it is essential to democracy to allow them to make that choice. Which is why I am disgusted at the numerous efforts around the country to blatantly disenfranchise groups of voters because of their expected partisan voting habits.

I am, of course, speaking about the attempts, almost exclusively^* in Republican-controlled state houses, to enact legislation that would impose stringent requirements, or strengthen the existing requirements, for government-issued photo identification before a voter is allowed to exercise their right to vote. These bills are nominally being introduced to combat voter fraud, and yes, voter fraud is something any democracy should be worried about. But in modern America, it is not a grave problem (a rough estimate finds that there is one alleged case of voter fraud for every 100,000 eligible voters, and only approximately one in 40 of those leads to a conviction. That's one in 4 million, and there are only slightly over 210 million eligible voters in the United States; do the math.) But worse, the laws being proposed do very-little to absolutely-nothing to prevent the majority of fraud cases (most fraudulent votes are cast by election insiders, and outsiders who vote fraudulently typically do so via absentee ballots or through multiple registrations at different polling places, neither of which can be caught by checking ID.)

Rather, the effect of these laws will primarily be to prevent innocent poor, minority, and youth voters from voting; all groups which tend to vote for Democrats. A generous estimate would be that 3,000 legitimate voters will be turned away at the polls for each case of fraud that these laws would stop, and the true number is possibly orders of magnitude higher.

In any functioning democracy, we will disagree. But attempting to win by reducing the electorate cuts at the very essence of democracy.

(Numbers based off various articles from The Voting News's "voter fraud" topic.)

*Rhode Island's law, although passed through a Democratically-controlled house, is much milder than the other laws pushed forward this year. It does not go into effect until 2014 (i.e., will not affect the next presidential election), it allows a much broader class of documents to count as valid identification, and rather than turn voters away it allows them to cast a provisional ballot.