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.

10 comments

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Nick, while your overall hypothesis that a recount may yield a different result is supportable (8 votes is miniscule), your use of a percentage as your measure of the normal distribution is probably not statistically appropriate. And your last sentence, “there’s a good chance the result would be different” is misleading because I suspect that most of us would not consider 25% (assuming your dubious calculations) a “good” chance. That’s simply bending an interesting hypothesis to a conclusion that you apparently want to see, for whatever reason. And I fail to see what this has to do with either economics or finance, which is supposed to be the subject of this blog.

Posted by Curmudgeon | Report as abusive

It is absurd to view Iowa as anything other than a dead heat. Just because the idiots on CNN call it a victory, that doesn’t mean you have to start parsing the results as though it mattered beyond the obvious fact that Santorum and Romney ran even.

Posted by maynardGkeynes | Report as abusive

getting a different number than you.
If 95% of data is within .0183% of romney’s mean then we have .000183 * 30015 = 5.493 which means for romney, the normal distribution has standard deviation of 5.493/2.

Doing similar for Santorum and then generating random variables from those two distributions gives me portion of time that santorum > romney = 1.99%.

Posted by zubin | Report as abusive

I have not checked your math, but one thing that you should consider is that the errors are correlated. That is, if a vote lost by Romney has a ~25% of going to Santorum.

Posted by InvisHand | Report as abusive

It doesn’t make a difference who actually won. The early primaries are just a winnowing process anyway, to get the race down to 2-3 candidates by the time Super Tuesday rolls around.

The big story is that Mitt Romney only got 24.5% of the vote. The MSM is falling all over themselves to say that the nomination is now Romney’s to lose, but I’d take the opposite position and wonder how the heck he’s going to win the nomination when roughly 3/4 of the GOP primary electorate doesn’t like him. He’s survived so far only because the conservative opposition to him has been fractured among several candidates (Cain, Perry, Bachmann, Gingrich, Santorum), but now that the religious right seems to be coalescing around Santorum’s candidacy, and with libertarians swarming to Ron Paul Romney is not going to be able to win too many more primaries/caucuses unless he can raise his support levels above 40%.

Posted by mfw13 | Report as abusive

Nick, you say hand-counting is less accurate than secret ballots. How likely is a miscount in a caucus, where voters literally stand in a particular area of a room to cast their vote? Paper (or machine) ballots could be lost, stolen, corrupted or improperly scanned.

Even in the event of a miscount, good luck doing a recount – there are no ballots.

Posted by Chenenko | Report as abusive

@zubin It’s entirely possible that my percentage is wrong. Can I give you my data and have you double-check? I did this based on change in margin and total votes. Is it better to use each candidate’s before and after vote totals?

Posted by Nick Rizzo | Report as abusive

@Chenenko Counting procedure varied by precinct, but the three GOP precincts I saw televised all used handwritten, hand-counted paper ballots.

Posted by Nick Rizzo | Report as abusive

A bigger factor is that, now that some candidates are dropping out, the two seemingly-tied candidates will pick up different shares of their voters. My hunch is that former Bachmann supporters will favor Santorum over Romney, giving Santorum the advantage going forward.

Posted by JayCM | Report as abusive

“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.”

Not really, it wouldn’t have made much difference if the result had been in reverse with Santorum beating Romney by a handful of votes. First of all they both received 7 delegates, as did Ron Paul. More importantly however, the fact that Romney did exceedingly well in Iowa, and again it doesn’t matter if he won or tied for 1st, builds his momentum (which is all-important in primaries) and considering his huge lead in New Hampshire and front runner status in Florida (giving him a lock on 3 of the 4 first states), he now seems to be the inevitable candidate for the GOP; at the very least in perception if not in reality.

Most critical, however, in the results of the Iowa caucus is the fact that Romney and a hitherto minor conservative candidate dominated. Now that Santorum has gained momentum the anti-Romney vote is effectively split between the former senator from Pennsylvania, the last front runner Gingrich, and to a lesser extent Rick Perry. The very fact that Gingrich – the only candidate with the poll numbers to challenge Romney – and Perry – the only candidate with the money to challenge Romney – both tanked in Iowa is in and of itself a major Romney victory. The distinction between a clear-cut Romney win and a statistical tie would only be at all meaningful if the runner up had been Gingrich. In this case all matters is that A) Romney did extremely well in a state that initially he had little support in and B) the anti-Romney vote was hopelessly divided, which essentially ensures Romney as the nominee.

Posted by Dawidh | Report as abusive