On voting, elections, and game theory

(Reposted from a previous iteration of my blog)

Let’s say there’s three candidates running for President:

  • Candidate A is a liberal, and gets 30% of the vote.
  • Candidate B is a liberal, and gets 30% of the vote.
  • Candidate C is a conservative, and gets 40% of the vote.

60% of the vote went to liberals, but under our winner-by-plurality electoral system, where each person gets one vote to cast, the election went to a conservative. This is essentially what happened in 2000. Liberal candidates (Gore and Nader) clearly beat the conservative candidate (Bush), but Bush won the election (though some dispute this). Had Nader’s votes gone to Gore, Gore would have been the undisputed winner in 2000. A similar thing happened in 1992, Ross Perot took votes that otherwise would have gone to Bush the first, thus handing Clinton the victory.

Third parties in the US serve little purpose other than to act as spoilers. Whenever a third party gets enough interest to actually matter, they (or their platforms) are typically absorbed into one of the two big parties – if the vote splinters, then the plurality candidate wins despite representing a minority view. One may argue that this serves is a good thing as it serves to alter the course of the main parties, which I believe is true. However, this also has the very negative effect of greatly limiting the diversity of viewpoints in this country. Only two viewpoints are possible at any given time, rather than being able to choose from the full matrix of ideas that represents political thought.

One vote one person has other negative consequences as well, beyond dampening third party politics. The modern Republican party typifies this; they rely heavily on an army of single issue religious voters to win elections; they’d never win on their economic policies alone. Similarly, those religious voters would never gain power solely on those issues. The coalition between these two groups gives them disproportionately more influence than they should have on their merits and level of support alone, in this case allowing the religious right (a mere 20-30% of the country) to set policy for 100% of the country. It’s impossible for a voter to make the distinction between being an economic Republican or a religious one (though in this case they may not want to, however bad it may be for the rest of us).

To further explain this dilemma, take myself: I view the Republicans as being actively evil whereas the Democrats are merely passively evil. I’m often stuck voting for the lesser evil rather than the greatest good, simply because failing to do so is a de facto vote for the greater evil. One can argue the merits of whether one should vote their conscience or vote pragmatically, and indeed this is a recurring debate in political discussion. But such debates usually miss the more basic issue, the source of the conflict, which is one person one vote. Voting your conscience and voting pragmatically isn’t a choice anyone should have to make; it is possible to have an electoral system where we can have our cake and eat it to.

Mathematically, from a game theory perspective, our elections are bogus. Our elections are a zero sum game, known as a plurality vote. A vote that goes to one candidate must necessarily be taken from another candidate. By design, they make it nearly impossible for a third party to gain a real foothold, or often even for the real preferences of the voters to be shown. One vote one person throws away an awful lot of information about voter intentions, making complex statements at the voting booth impossible. Under our system, we can’t even tell if a voter is really voting FOR a candidate or AGAINST the other guy, since it looks the same either way.

There are better voting systems, ones that allow for voters to make more complex statements at the voting booth and thus have election outcomes that more accurately reflect the desires of the electorate. At the heart of any democratic system is the act of voting, and at the heart of voting is game theory. The two party system, and everything we think about as elections, such as swing voters, core constituents, bases, swing states, these are a natural consequence of one vote one person. Elections are a zero sum game for the politicians with very few game path choices for the voters. The game as it’s played now is essentially fixed; why not look at ways to improve the outcome?

Instant runoff voting would be the simplest solution to implement. Simply, it allows voters to rank candidates in order of most preferred to least preferred. It would give people the option to vote for third parties and still weigh in on which of the two “main” candidates they’d rather see win, the electorate could vote their conscience and vote pragmatically at the same time.  If we had this, it’s unlikely Bush would be President today (though obviously its impossible to say for certain). I will say for certain that Nader would have gotten a much larger percentage of the vote than he did with runoff voting in place. This move alone would be be enough for third parties to become viable and would go a great way towards decreasing voter apathy, perhaps getting those who currently feel alienated out to the voter booths.

Alternatively, one could move to an approval vote – simply put a check on the ballot next to every candidate you find acceptable, eliminating the zero sum aspect of the game. This would have a profound effect on political campaigns, as there would cease to be bases as we think of them today; just because a person will vote for one candidate does not preclude them from voting for anyone else, candidates will have no reason to “write off” enter regions or parts of the electorate as unwinnable – every voter would effectively be a “swing voter”. Candidates would have to be individually appealing rather than simply being “better than the other guy”, and appeal to the large middle rather than the the fringes. The candidate who wins would be the one who’s the most appealing to the most people, rather than the one would can win the largest market share.

Further, there’s no reason to stick with one vote per person at all. Why not give each person ten votes, to spread around as they see fit? It would allow for people to weight candidates relative to one another, and let people throw a few votes at third parties with a clean conscience.

Which leads us to my ideally designed system, a form of range voting. Hand a voter a ballot. Ask them to rank each candidate listed on a scale from 0 to 10. This lets them express how strongly they feel for each candidate separately, and weight each candidate relative to each other. Every candidate would try to appeal to every American – gone would be the bases, swing states, and a lot of the other nasty artifacts of the way the game is played now.

Of course, no system of voting is perfect (see Arrow’s Impossibility Theorem). And none of these are new ideas – if you follow the wikipedia links provided, you’ll see some of them have been around for centuries. But, if I could make one change to the country it would be the above. The best system is a matter of debate, but clearly plurality is the worst of the bunch. Politics is controlled by the rules of the game – this is a simple change that would have profound effects on the political landscape. Change the rules, change the game, and get a better system.

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One Response to “On voting, elections, and game theory”

  1. Why winner takes all democracy isn’t democracy at all « Musings of the Great Eric Says:

    […] I’ve proposed a solution to this before, a reform to our voting system based upon game theory that would select the most centrist candidates rather than the most polarizing (reposted below this post). However, such a drastic overhaul is unlikely to happen anytime soon (if ever), and reform is needed now. So I’ll propose two modest solutions here, designed to distribute power in a more proportionate way to the way to the will of the electorate. […]

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