Wednesday, December 10, 2008

Marching Two By Two

Voting is easy, at least if there are only two options. When congress is deciding on what form a bill should take, they don't ask the congresmen to vote for their favorite of 3 (or 4 or more) options; they break it into pieces, and vote yes/no on incorporating each one as an ammendment. How would this procedure work if we tried to apply it to elections?

Presume, as before, that there are three candidates, and that the 9 congressmembers opinions break down as in our previous examples:

4 prefer A > B > C
3 prefer C > B > A
2 prefer B > C > A

Three "bills" are introduced, one naming each of the candidates, A B and C, as the ultimate winner of the election. At first, each member only votes "yes" for the bill naming their first-choice candidate. Since no candidate has a majority of first-preference, none of them pass. Not picking a winner is clearly sub-optimal, so we'll have to try something else.

Let's suppose B's supporters get a clever idea: they resubmit the "C wins" bill... but vote in favor of it, along with all of C's supporters. By a one-vote margin the bill passes. This is almost analogous to what would happen in a plurality election or in a run-off; B's supporters compromised and got their second-choice candidate.

Now suppose that B's supporters, feeling a bit cheeky, get even more clever: they submit a motion to change the winner from C to B. Obviously, their allies in the "C wins" vote are against them this time, but A's supporters more than make up for it, and the motion passes. A and C's supporters can try similar tricks, but neither such bill will pass; each opposes the other's motion, and B's supporters oppose both. A temporary compromise (like the B voters voting for C) can shift the field, but if the voters always eventually fall back to their honest opinions, B always comes out on top. I contend that this means that B is, overall, the more prefered candidate, the best compromise among all the options, and that the best vote-counting method would choose them as the winner.

Multiple votes are probably out of the question as a method to replace our current election process; this is why the "instant" in instant runoff is appealing. But IRV would give C the win, and that's only half-way to the solution. But there is a voting method that, like IRV, can determine the winner in one round of ballots, and those ballots are not any more complicated than the ones used in IRV, and it's called Condorcet's Method.

Condorcet's method works by breaking the election down into a group of smaller, simpler, one-on-one elections. With only two choices, voting is easy! So, in a three way race, rather than look at it as a free-for-all of A vs. B vs. C, Condorcet looks at it as three seperate contests: A vs. B, B vs. C, and A vs. C. In our example, we see that B wins against A (since both B and C's supporters prefer B in that case), that B also wins against C (since both B and A's supporters prefer B in that case), and that C wins against A (since both B and C's supporters prefer C in that case). So who wins? Put simply (and somewhat tautologically-sounding), the winner is the candidate who doesn't ever lose. This means that there is no single opponent who a majority of voters would prefer over them. In our case, this is candidate B.

Condorcet's method is a powerfull tool for teasing a compromise out of a vote. It's not perfect (no voting method is, and I'll cover so-called "circular ambiguities" soon), but I think it gives a better result in a greater number of situations than plurality or IRV.

Wednesday, November 19, 2008

Shooting Down IRV

I hope that, by now, I've convinced you that preferential voting is a good idea. Now, onto phase II: convincing you that preferential voting is a bad idea. Or rather, that it's most popular form, Instant Runoff Voting (IRV) isn't such a good one.

Consider the following election. There are three candidates--A, B, and C--and 9 voters. Candidate A leans strongly to one side (left, right, or whatever you prefer), while B and C lean the other way, although B is a bit more centrist. Let's suppose then that four voters would prefer A the most, and prefer the more moderate B over candidate C; three would go in the precise opposite direction, prefering C over B with A in a distant third; finally two prefer candidate B, followed by C, followed by A. Like this:

4: A > B > C
3: C > B > A
2: B > C > A

Who wins? By plurality, A does; but the supporters of B and C will point out that A only won because their candidates split the vote; clearly their camp should have held a primary! But IRV would proceed by eliminating the candidate with the fewest first-ranked votes, in this case B, and passing those votes to the voters' next-higest ranked candidate, in this case C, making C the winner. This is the same result that would have occured had the "BC" camp held a primary to decide on who their candidate should be. Which is some progress; perhaps we could eliminate the need for primaries by moving to IRV, and allow supporters of minor-party candidates to speak their honest opinion instead of being forced to choose between the lesser of two evils.

But consider this: what if A's supporters had decided to disingenuously rank them at the bottom of their ballot? Then we get this:

6: B > C > A
3: C > B > A

Now, B wins. Which, for A's supporters, who unanimously prefered B over C, is an improvement! We've traded minor-party supporters lying about their preferences for major-party supporters lying about their preferences (in both cases, in order to avoid what they see as an even worse outcome.) And while some might bitterly remark "Good, let them see how it feels!", upon calm reflection I can't say that this is a good thing. If we're going to change our voting methods, we should do so with an eye towards eliminating these sorts of insincerity-encouraging effects as completely as possible, rather then push them off to some other segment of the electorate.

Unfortunately (and this will be covered in more detail in a future post), it has been mathematically proven that no reasonable voting method is entirely immune to these incentives. While plurality performs quite poorly--allowing two major groups to gain a stranglehold on all political discourse across a nation--IRV doesn't do that much better. In a highly-polarized election, it can (and mark my words, it will!) tend to eliminate moderate choices, and if it doesn't, the decision of which moderate candidate (when there is more than one) ultimately wins, becomes very sensitive to the order they are eliminated, which can hinge on an incredibly thin sliver of voters. If you thought re-counts were bitter fiascos now, just wait to see the chaos of a close 4-or-more way IRV race. In the most pathological case, consider an "ultimate compromise" candidate, one who is everyone's second choice. Under IRV, such a candidate has no chance of victory, as he has no first-place votes. But I can't help but think that such a compromise candidate would be a very good choice as an election winner.

Next up, an alternative preferential system.

Monday, November 10, 2008

But Don't Forget the Primaries

Some critics try to attack preferential voting via the argument that it's too complicated. They say that it's too hard to explain how instant runoff voting or Condorcet's method work; and because of the complexity, voters will never like it.

I would ask these people to explain--in plain language and as few words as possible--how our current system work. But don't forget the primaries. Because the primaries are as decisive, if not more decisive, in determining our pressident and other elected officials, then anything that happens in early November. And if you read my state-by-state description in the comments of the first post, you'll notice that every state's primaries are also a little different.

Why do we even have primaries? Because the parties know that running multiple similar candidates is the best way to ensure that none of them win. This is identical to how a third-party candidate can pull support away from their most-similar major-party candidate and give the election away to the (mutually hated) opposition. The primaries exist solely as a way for the like-minded party members to agree to restrict the choices of the general electorate in order to avoid this vote-spliting effect, by compromising on a candidate which the whole group will agree to support. (Actually, you could argue that's the only reason political parties exist.) In other words, primaries and preferential voting try to solve the same problem. One through a complex, fractionalized labyrinth that actively prevents many voters from participating while giving disproportionate power to the leadership of the two major political parties, and the other by giving every voter a better (if slightly more complicated) way to express their choice. I think you can guess which option I would choose.

This may imply that, for instance, Hillary Clinton could have stayed in the race without increasing the chance that John McCain would have won, if we used a preferential system. Is that true? I would love to give you an unequivocal "yes", but I'll have to hedge a bit and say "almost certainly yes, but maybe not". For a full answer, we'll have to get into the nitty-gritty of voting systems and voting criteria; stay tuned! (I already made one assumption about criteria in this blog, on Friday. Can you find it?)

Sunday, November 9, 2008

Minnesota's Recount

You may have heard about what's going on in Minnesota, where Al Franken (D) and Norm Coleman (R) are just a few hundred votes apart out nearly three million cast. What's interesting is that the two candidates each have around 42% of the vote; over 15% of voters chose independent candidate Dean Barkley (and a few picked Libertarian Charles Aldrich). I wonder what those minor-party voters are thinking now. I wonder who their second choice would have been, or how many of them are going to regret their mostly symbolic gesture.

Friday, November 7, 2008

The Two-Party System is Like the Weather...

The two-party system is like the weather; everyone complains about it, but no one ever does anything to fix it. Not a presidential election goes by anymore without disaffected voters complaining about their choices. Fed up with the "Republicratic" (or Dempublican?) party, you don't have to go far before you find someone advocating for another option: Green, Libertarian, Constitution, Independent, or something even more obscure. But if the Democrats and Republicans are so universally reviled, why don't any of the alternatives do better?

Two-sided elections are easy. Everyone picks their favorite, and whichever side gets the most votes wins. But adding a third side complicates issues. Lets assume for starters that every voter is rock-solid in support of their current two-party pick, or at least--and this is more likely--rock-solid in their opposition to the other party's candidate. When a third option is added, every voter has a choice to make: stick with their current candidate, or change to the new one. Changing is dangerous because, even though they may like the third party a little better, they run the risk of a catastrophic outcome, throwing the election to that evil, horrible, opposition candidate!

Let's consider this three party election, or rather, all possible third-party elections. Imagine a triangle. Every point inside the triangle represents a different outcome in an election, each corner representing the outcome where 100% of voters chose the same party. Democrat on the left, Republican on the right, and Green off to the top somewhere. The further from that point, the less voters chose it.

When you put it all together you can see at a glance the result of any three-party election:

It all looks very nice and symmetrical. But let's remember, we're always starting at, or very near to, the bottom edge of the triangle, with almost no votes for the Green party. Now, let's assume that we're in a blue-leaning district. And we know that, predominantly, potential Green party voters are going to come from the Democratic party, and not from the Republican party. This change would be represented as a movement from a point on the bottom edge, up and to the right, parallel with the left side. Do you see what happens?

In trying to move to a more-preferred choice, these Republican-hating voters have accidentally given the election away to the party they hate! Now, you might say that these Democrats should just wait until there's enough of them to avoid clipping the Republican corner of the triangle. But for that to be safe, they would have to have more than two-thirds of the electorate on their side. Taking a quick look at Tuesdays highly-polarized election results, there are only two "states" where the leading party (plus all third-party votes) had a 2:1 or better margin over the losing party; Vermont and Washington D.C.. Among Senate races, only five had such lop-sided outcomes (one, Arkansas, had no Republican running). The point being that, if 3rd parties waited for such "safe" situations, they would have to wait for a very long time. The alternative is to try to gain so much support so quickly that they can "jump" over the offending party. But such fast changes are difficult to pull off on a local scale, never mind nationally.

But I promised you a solution. The problem is this: if the winning candidate gets less than 50% of the vote, then the system fails.

Okay, that's not much of an answer. But there's not much else we can do; you and I know that most Green party voters would have otherwise picked Democrats, but are we sure they all would? We just can't know. Not for sure. And what if we also add a Libertarian candidate?

This is why these two reviled opponents will always have a stranglehold on American politics. Because a vote for a third party is a vote against their closest allies. Because a vote for something new also implies a vote for the greater of two evils. It's impossible to give them (by which I mean, us) what we really want, because by the point that it really matters, what we really want is no longer clear.


...we ask.

This is the essence of preferential voting. Asking for a voter's first choice is fine and dandy... but only as long as there are only two options. But with three options, asking you to pick one isn't enough for me to really know what you prefer. Imagine if I asked you "Would you prefer wine, beer, or some warm urine?" and when you said "Wine", I came back and told you "We're out of wine; I wasn't sure what you'd prefer otherwise, so I brought you the piss." By asking for voters to specify their alternate choices, we remove the element of fear and give third-parties the chance to grow and really compete in the market of political ideas, to offer us real options for change.

Wednesday, November 5, 2008

First Mistake

Welcome to the kick-off entry of Least of All Evils! Here, I intend to advocate in favor of preferrential voting in general (and Condocet ranked pairs in particular), with the hope of increasing its use in the United States at large, but especially in my home district and state.

I don't think today I'll get much attention from Democrats or third-party voters; the first is too busy celebrating, the second is perhaps too accustomed to their position at electoral whipping-boy. So we start with the Republicans, as I think they're the ones looking for answers today. So:

My condolences, Republicans; you lost.  Now is a time for reflection, a time to look back, a time to analyze, a time to determine what went wrong, and what you can do differently next time to fix it.  Please, allow me to offer an possible answer to these questions.  Your first mistake, was in selecting John McCain.

Wait, hold on; don't go!  I don't mean it like that! Give me the chance to explain. Selecting John McCain was a mistake, but not in the sense of "It was a mistake for you to pick him."  It was a mistake because you didn't pick him, and yet he was your nominee anyway.  You see, it's not your fault.  You didn't do anything wrong.  You went to your caucus or your primary (or in some cases, both), and you voted.  You voted based on a careful analysis of the candidates positions; you voted what you knew in your heart was right; you voted for who you thought was the best man for the job.  The fault was not in how you voted, but in how you voted.

John McCain, by and large, was not the candidate most members of the Republican party had as their first pick for the nomination.  And yet, he still got the job.  How?  There are a lot of details that build up to arrive at the answer, but the short version comes in two parts: you used a bad system, and Mike Huckabee.

Going in to the Iowa caucus, way back on January 3rd, all the talk was about Mitt Romney and  Mike Huckabee and which of them was going to win the kick-off of the primary season.  John McCain didn't even make it into the top three there, losing not only to Huckabee and Romney, but even to Fred "I'll do it if you make me" Thompson.  McCain of course turned it around five days later and won New Hampshire.  But what do we mean when we say that, "won"?  Let's take a closer look.

John McCain "won" New Hampshire with 37% of the vote.  Compare that to yesterday's returns in Alabama, where no one is surprised Barack Obama lost by a huge margin, but he still took 39% of the vote. Now, I know what you're saying: You're saying that the New Hampshire primary was different because there were a lot more than two contenders.  But that is precisely the point, and in  fact, is the point of this entire blog.  That point being, the methods we use to choose our elected officials do a surprisingly poor job when we use them to pick between more than two options, but there are ways to fix that short coming.

Let me offer you a hypothetical.  Suppose Mitt Romney and Mike Huckabee hadn't run in the primaries, but instead there was another candidate, let's call him Mital Rockabee.  Rockabee, had he been running instead of these two, would have gotten all the votes that either of them would have otherwise gotten.  How would the primaries have gone differently?  Due to the vagaries of election laws, Rockabee would not have gotten only the sum of Huckabee and Romney's delegates, but would have also received a large chunk of McCain's delegates; enough to make all the difference.

I've written a torturous state-by-state analysis (which you'll find in the comments) if you're a detail-oriented type of person, but feel free to skip it if you're comfortable taking my word for it.

Following the results of Super Tuesday, Romney suspended his campaign, at which point he had 270 delegates, and Huckabee had 176, versus McCain's 680.  With the 259 (or more) votes that would have shifted away from McCain due to vote-tallying minutia, Rockabee would have had 705 delegates, versus a McCain total of 421.  At that point, Rockabee would certainly stay in the race (like Huckabee did).  It's hard to do any kind of what-if analysis from this point on. Did more voters figure that, since McCain had it in the bag, they'd vote for their #2 favorite and try to get him a VP slot?  Or did more of them decide to jump on the party bandwagon, an show their support by adding it to the presumptive winner?  It's difficult to say.  But with that kind of lead, it's certainly possible that Rockabee would have gone on to assume the nomination.

But what does that mean, since there obviously is no Mital Rockabee? Rockabee represents a rough estimate of how a prefferential voting system would have adjudicated the election, given the assumption that every Huckabee and Romney voter preffered either of those two options over John McCain. (Is this a fair assumption?  Hard to say without data. Hit up the comments with your thoughts!) Had the primaries used such a system, instead of Huckabee spoiling the election for Romney by spliting the vote, Romney likely would have defeated Huckabee and McCain and become the Republican nominee. This is suggesting that, in essence, the Republican party as a body, didn't want John McCain; it wanted Mitt Romney.  But due to the use of these poor methods for measuring the will of the voters (which, I should mention, are the same poor methods used for virtually ever election in this country) a candidate you didn't want was put forward as your selection.

Now, I'm not going to guarantee that Romney would have defeated Obama yesterday.  But you wanted him, and picking someone you didn't want, that was your first mistake.

Tomorrow, we'll start talking about how to fix it.