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Granite Geek: One man, one vote – but why for only one candidate?


Tuesday, November 01, 2016

As a newspaper reporter in politics-ridden New Hampshire, I am contractually obligated to write something election-ish or lose my privileges with the office coffee machine. Since I’m running out of time, here is my topic of choice: Arrow’s impossibility theorem, the groundbreaking discovery by a Nobel Prize winner that shook up social choice theory.

Honest, it’s related to the election. Plus there’s a news hook: Some people in Maine have cried “Fie on you, Kenneth Arrow!” and think they can do better.

The issue at question is what voting system does the best job reflecting the will of the people when there are more than two candidates seeking a single office, such as in party primaries.

Our “first past the post” system means that whoever gets the most votes wins, even if they don’t have a majority. Some people argue that this system encourages success by extreme candidates – or, as Slate put it in a headline Monday, “Don’t blame voters for the rise of (a candidate the writer hates). Blame the stupid way we vote.”

Why? Imagine that one crackpot and several reasonable people are running for their party nomination. The latter group will split the reasonable vote but the crackpot contingent will coalesce around its candidate and win, even though a large majority of voters strongly oppose him or her.

The proposed solution is to change ballots so that we aren’t stuck with a single yea-or-nay preference. Give us a chance to provide more nuanced opinions, they argue, and the result will be better politicians.

In Maine, a ballot initiative wants to do just that. It seeks to allow ranked-choice voting, also known as instant runoff, for all state and federal offices. (I guess local offices would still be decided by fistfights during town meeting.)

Under that system, voters rank candidates on the ballot, listing them from first choice to last. Those preferences would be used on election night to winnow people out via repeated recalculation, with the least-popular candidate dropped each round, until one person has a majority and is declared the winner.

If adopted, which I’m guessing is unlikely, Maine would be the first state to use such a system for its state races, although some cities (including Cambridge, Mass.) use variants for their elections, as does the Australian parliament and a number of professional groups. North Carolina once tried the system in a statewide judicial race, but didn’t keep it.

Advocates say ranked-choice voting lets you support a person you like (e.g., a minor-party candidate) without indirectly helping a major-party candidate you hate, because you can nail that bum with a last-place ranking. They say it would eliminate extreme candidates because they alienate too many voters, resulting in more reasonable politicians.

Instant-runoff is far from the only method that tries to improve election results by giving more voting options. There is the Borda count, the Condorcet method, various approval voting methods and positional voting methods. I own several books on the topic with titles like Gaming the Vote and Chaotic Elections, and analysis of their pros and cons involves matrix algebra.

Which is, I think, their fatal flaw.

Whether or not these systems are better at expressing the will of the electorate – we’ll get to that in a moment – the complexity turns off voters. It seems to hide some sort of trickery.

Burlington, Vt., offers the perfect example. It adopted instant-runoff voting for mayoral elections in 2006 and all went swimmingly until 2009, when the candidate with the most first-place votes, who would have won under ordinary voting, came in second because he also received a lot of very low rankings.

That is exactly how instant-runoff voting is supposed to work, but people freaked out, alleging some sort of arithmetic ballot-rigging. The next year the city returned to traditional voting and has stayed there since. In Maine itself, Portland uses instant-runoff for city elections since 2011. (EDITOR’S NOTE: The column initiatially said, incorrectly, that the city had dropped the system.)

There’s another problem, and it’s a deep one. It comes from Kenneth Arrow, a Stanford University professor who won the 1972 Nobel Prize in economics for Arrow’s impossibility theorem and related discoveries.

Arrow’s impossibility theorem showed mathematically that with three or more candidates, any possible system of balloting faces problems, although some are as non-intuitive as failing to meet Pareto efficiency involving the allocation of resources. This is part of a field called social choice theory which, as you might suspect from the name, analyzes ways that society makes choices.

In other words, Arrow found, it’s impossible to develop a perfect voting system. If you’re going to drop one system and adopt another system, you’ll be trading one set of drawbacks for another. The tradeoff might seem reasonable – would you rather have crackpot politicians or a violation of Pareto efficiency? – but it’s still a tradeoff, making it much harder to choose what to do.

Arrow’s theorem was a bucket of cold water tossed on more than a century of efforts to develop the best voting system. In that role of intellectual wet blanket, it has many scientific parallels, such as Heisenberg’s uncertainty principle in physics and Godel’s incompleteness theorem in mathematics. These show that absolute assurance is always outside our grasp, which is either depressing or exhilarating.

As a side note, may I note that alternative voting is catnip to geeks. It appeals to a deep, deep belief that the proper algorithm can overcome any obstacle, even to the point of cutting the Gordian knot that is human nature.

All we need to do is implement the right system and everything will finally make sense!

Darn you, Kenneth Arrow.

(David Brooks can be reached at 369-3313, dbrooks@cmonitor.com or on Twitter @GraniteGeek.)