Sunday, October 20, 2013

Voting Systems

If there's one thing I've learned from designing games, it's that if you want different outcomes in a system involving human participants, you can't just expect people to start behaving differently/better, rather you need to modify the system in which they are behaving. The way people behave tends to be fairly predictable mostly as a pursuit of self interest with some psychological quirks thrown in. This view puts me at odds with some who discuss politics by lamenting the greed and corruption of man (possibly with the implied undercurrent that "things never change"). In my view, the 2008 housing crisis was not cause by "a bunch of greedy bankers" but rather a bunch of rational actors sensibly taking advantage of a system which heavily rewarded dealing in highly questionable mortgages while offering minimal risk of punishment (unless a 700 trillion dollar bailout can be considered punishment). Relatedly I don't blame someone for exploiting a dominant move in a poorly balanced fighting game. Don't hate the player, fix the game.

In most cases I feel the best fixes would involve simplifying law, language and procedure since a highly complex and arcane system ends up being understood only by those who can profit by exploiting it. It's hard enough to balance a system with five players and ten pages of rules, let alone one with millions of players and enough rules that one can earn several degrees simply by trying to learn them. However there's one area of policy for which I believe the beautifully simple and elegant way of doing things is in fact horribly misguided, and that's the First Past the Post voting system. I delivered a speech at Toastmasters a while back on this subject, and since I made some cute slides I figured I'd throw it up here as well. (A shout-out to CGPGrey's excellent YouTube videos on the subject for inspiration.)

 Since most concepts are better explained with anthropomorphized letters, we imagine a fictitious election involving three horrifically mutated animals: Alligator, Bear, and Cat. How shall we elect a leader from this sorry bunch? (And we're disregarding any system that results in a coalition government; two carnivores aren't going to be able to share an office. Single winner required.)

At initial glance the ubiquitous First Past the Post system seems simple and obvious: have everyone vote for the person/thing/outcome they want, and the one that gets the most votes wins. If there are only two candidates, this method is wonderful. More people like Bear, Bear wins, no problem (until Bear inevitably goes drunk with power and delicious honey).

Problems arise as soon as with introduce a third candidate. Even though voters #4 and #5 hate Alligator and everything he stands for, Alligator ends up winning the election because the majority, who prefer warm and cuddly rulers, found their vote split by the "spoiler effect."

The spoiler effect is a very real thing that happens. There was a quiet little town in Ontario that decided it would let its citizens vote on what it should be named. The ballot included three options: "Lakehead," "The Lakehead," or "Thunder Bay." Of course they used First Past the Post and the final result looked like this:

The Lakehead - 8,377 votes
Lakehead - 15,302 votes
Thunder Bay - 15,870 votes!!!

If this vote were held semi-annually, it can be assumed that the people who liked "The Lakehead" would quickly jump on the "Lakehead" bandwagon. This spoiler effect, and the reactionary bandwagoning, is why nobody bothers voting for Ralph Nader (or the Green Party), and why all political system that use First Past the Post are doomed to devolve into a two-party system where everybody votes for the side they hate the least.

Enter my personal favorite solution, Instant Runoff Voting (aka "Alternative Vote"). In this system, voters order their candidates in order of preference, and then when the votes are being tabulated, candidates are "eliminated" if they have the fewest ballots rating them highest until only one candidate remains. In the above example, only two voters rated Cat highest, so he is scrubbed off everyone's ballots as though he never existed. Voters #5 and #6 are left with Bear as their highest rated candidate. Five people now rate Bear highest with only four preferring Alligator, and so now Alligator is eliminated and the fur-lovers have it. (Note that this system does not require voters to cast multiple ballots. All the elimination and recalculation is done during tabulation.)

As much as I am a fan of Instant Runoff Voting, it's not perfect (although literally no system is. Stay tuned.) In the above example, the majority of voters have a preference for Cat. Some hate Bear, some hate Alligator, but everyone thinks Cat is a pretty cool guy. Unfortunately under this system he is immediate eliminated because not enough voters listed him as their highest candidate (though it's worth noting that First Past the Post has exactly the same problem).

A way to alleviate this issue is the Borda Count Method. With the same set of ballots, candidates are assigned points based on their ranking on each ballot, the points are added up, and the highest total wins.

Alas this system is also imperfect. In the above example, a majority want to elect Bear, but those slimy Alligator voters have purposefully put him at the bottom of their ranking, thereby allowing Alligator to eke out a victory.

So clearly voting systems are more problematic than one might assume. How does one construct a one that gives fair results in all situations. Short answer: you don't.

Arrow's Impossibility Theorem is a mathematical proof that all voting systems imaginable are, in some instances, horribly flawed and unfair. The criteria given for "fairness" are:
  • If every voter prefers alternative X over alternative Y, then the group prefers X over Y.
  • If every voter's preference between X and Y remains unchanged, then the group's preference between X and Y will also remain unchanged (even if voters' preferences between other pairs like X and Z, Y and Z, or Z and W change).
  • There is no "dictator": no single voter possesses the power to always determine the group's preference.
I won't try to go into the mathematical proof that a system that satisfies all three criteria is impossible (since frankly some of the math is over my head). As a briefer means of illustrating, consider the following:

How do you solve that?? You don't. All three candidates have equal claim to victory. The only reasonable solution is some sort of caged death match. No voting system can sensible deal with this result. But it's important to keep one thing in mind.

Even though no voting system is, or can ever be, perfect, that doesn't mean all voting systems are created equal. First Past the Post is strictly worse than Alternative Runoff Voting because it doesn't solve any of the latter's problems, and it is plagued with the spoiler effect. Its only real advantage is that it's easier to explain and looks more logical at first glance.

So remember, the next time someone complains that both the Democrats and the Republicans are terrible and yet no other party will become a serious force in American politics in the foreseeable future, the problem is not that politicians are corrupt and greedy scum who have created a stranglehold on the nation via their control of the media or what have you, the problem is that First Past the Post is a terrible, terrible voting system.

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