The Mathematics of Voting

 Posted by on 26 December 2012 at 10:00 am  Election, Mathematics, Politics
Dec 262012

Undoubtedly, the award for “The Funniest Story of the 2012 Election” goes to “Candidate’s Wife Sleeps In, Misses Tie-Breaking Vote“:

Katie MacDonald was joking the night before Tuesday’s election when she told her husband – a candidate for city council in the small town of Walton, Kentucky – that if he didn’t wake her up to vote the next day, the race would end up as a tie. He should have taken her more seriously.

Katie, who works night shifts at a hospital as a nurse assistant while finishing up training as a nurse, didn’t wake up in time to vote. Now her husband, Robert, is involved in a 669 to 669 vote tie with his opponent Olivia Ballou.

“Well, obviously she was upset about it,” Robert MacDonald told ABC News. “She feels bad, but it was me who was in charge of waking her up and making sure she got out to vote. I’ve tried to be nice to her today. It’s her birthday.”

Robert MacDonald, 27, intends to request a re-canvassing, a simple re-tally of the vote, which will take place next Thursday. If the result is the same, the winner will be determined by coin toss.

Even with in such small races with just a few hundred voters on each side, such an outcome is highly, highly unlikely. As Katherine Mangu-Ward explains in this article in Reason:

In all of American history, a single vote has never determined the outcome of a presidential election. And there are precious few examples of any other elections decided by a single vote. A 2001 National Bureau of Economic Research paper by economists Casey Mulligan and Charles Hunter looked at 56,613 contested congressional and state legislative races dating back to 1898. Of the 40,000 state legislative elections they examined, encompassing about 1 billion votes cast, only seven were decided by a single vote (two were tied). A 1910 Buffalo contest was the lone single-vote victory in a century’s worth of congressional races. In four of the 10 ultra-close campaigns flagged in the paper, further research by the authors turned up evidence that subsequent recounts unearthed margins larger than the official record initially suggested.

The numbers just get more ridiculous from there. In a 2012 Economic Inquiry article, Columbia University political scientist Andrew Gelman, statistician Nate Silver, and University of California, Berkeley, economist Aaron Edlin use poll results from the 2008 election cycle to calculate that the chance of a randomly selected vote determining the outcome of a presidential election is about one in 60 million. In a couple of key states, the chance that a random vote will be decisive creeps closer to one in 10 million, which drags voters into the dubious company of people gunning for the Mega-Lotto jackpot. The authors optimistically suggest that even with those terrible odds, you may still choose to vote because “the payoff is the chance to change national policy and improve (one hopes) the lives of hundreds of millions, compared to the alternative if the other candidate were to win.” But how big does that payoff have to be to make voting worthwhile?

If you’re interested more on this topic, I interviewed historian Dr. Eric Daniels on “Why Voting Doesn’t Matter” in this October 2012 episode of Philosophy in Action Radio:

  • Anthony

    People play lotteries. People watch football games. People go to New Year’s celebrations in Times Square. The mere “chance to change national policy” is almost never sufficient reason in itself to vote. But that doesn’t mean it’s not worth it to vote (or play the lottery, or watch a football game, or celebrate New Year’s in Times Square) in order to have an enjoyable experience.

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