There’s a 25% chance Santorum won Iowa

By Nick Rizzo
January 5, 2012

Lost in all the press coverage of Mitt Romney’s victory in Iowa is that election results as close as these — indeed sometimes less close — are often overturned in a recount. For the Iowa Caucus, however, there will be no recount.

A recount is considered unnecessary because it wouldn’t change delegate counts. But Iowa’s importance lies in the campaign momentum that comes from winning or beating expectations there.

And while Santorum is being recognized for exceeding the conventional wisdom estimates of a few weeks ago, that doesn’t change the fact that Romney emerged as Iowa’s winner.

But here’s the thing: there’s roughly a one-in-four chance that Santorum actually received the most votes.

Romney’s margin of victory was 8 votes out of 122,255 cast, or 0.0065%. If you look at a number of recent recounts — Florida Presidential 2000, Ohio Presidential 2004, Washington Gubernatorial 2004, and four recounted Minnesota races in 2008 — the initial error margin in all but Ohio and one of the Minnesota races was greater than that. The Washington race underwent two different recounts, checking for different errors; one of them, and the sum of the two together, exceeded Romney’s victory percentage. The difference between the Florida election night vote count and just the 537 vote certified Bush margin is more than three-and-a-half times Romney’s winning percentage.

As you’d expect, the biggest percentage errors tend to come in the elections with the smallest number of total votes: Gail Kulick Jackson’s victory over Sondra Erickson in Minnesota House District 16A was reduced from 99 votes to 89 votes, out of 21,999 votes cast. That’s a 10-vote change from an electorate less than one fifth the size of the number of people who voted in Iowa, and it corresponds to an error of 0.0455%. And if you look at the relationship between the size of the error and the number of votes cast, you’d expect the error in Iowa to be 0.0183% — or about 19 votes.

None of this is highly scientific, of course. But assume that you can model the number of votes that Santorum got by taking his vote count of 30,007, and replacing it with a normal distribution where 95% of the area is within 0.0183% of that number. And you do the same thing for Romney, with a normal distribution centered on his vote count of 30,015. Then what is the probability that Santorum ends up with more votes than Romney? It turns out to be 24.2%.

That probably understates the true figure. The 95% confidence interval should probably be higher than 0.0183%, since that number represents the results of real-world recounts, rather than an indication of how big recount errors can be if you just ignore 5% of the outliers. And the recount figures are for machine-counted election night totals, which I suspect are more accurate than the Iowa Caucus’s haphazard hand-counting. We need to remember that election night totals are measuring bacteria with a yardstick. But to a first approximation, it’s fair to say that there’s actually a one-in-four chance that Santorum got more votes in Iowa than Romney did.

Santorum didn’t win in Iowa: he came second. That’s the official result, even if to all intents and purposes the result was a tie. And the official result matters: it’s Romney, not Santorum, who can head to New Hampshire claiming the win. But if you just counted the exact same votes all over again, there’s a good chance the result would be different, and Santorum would end up being declared the winner instead.

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