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The Semantics and Statistics of Santorum’s Win in Iowa

Amid the swirl of developments on Thursday came word from the Iowa Republican Party that it had certified the results from the state’s Jan. 3 caucuses — and that Rick Santorum, not Mitt Romney, had gotten more votes. Mr. Santorum received 29,839 votes in the state’s certified tally, 34 more than Mr. Romney, who had 29,805.

Iowa Republicans were hesitant to deem Mr. Santorum the winner, however. Early Thursday morning, the state party chairman, Matt Strawn, instead described the result as having been “too close to call.” Later, Mr. Strawn was somewhat clearer. “One thing that is irrefutable is that in these 1,776 certified precincts, the Republican Party was able to certify and report Rick Santorum was the winner of the certified precinct vote total by 34 votes,” he told reporters. He cautioned, however, that there was ambiguity in the outcome because the results from eight other precincts were unaccounted for and had never been certified.

How safe is it to assume that Mr. Santorum in fact won? And does any of this matter, other than to historians and data geeks?

There is a series of roughly six questions that are pertinent to the vote count. Some of them cannot be answered definitively, but we will give it our best shot.

Just how much doubt is there about the real winner of the caucuses? Here is one way to think about the outcome: although the certified vote totals showed an extremely close result, it was not quite as close in percentage terms as some other famous elections, including one that determined the winner of a presidential election.

According to the state’s certified results, Mr. Santorum won by 34 votes out of 121,503 ballots that were tallied — a margin of victory of 0.028 percent.

By contrast, George W. Bush’s victory margin in Florida in 2000 is officially listed at 537 votes — but this was out of nearly 6 million votes cast. In percentage terms, Mr. Bush won by 0.009 percent, making it about three times as small.

Al Franken’s victory in the 2008 Senate race in Minnesota, meanwhile, came by 312 votes out of about 3 million ballots cast, for a  margin of 0.007 percent.

That said, both the Florida and Minnesota votes were subject to recounts, albeit exceptionally controversial ones. There was no such recount in Iowa: the results changed as individual precincts double-checked their accounting of the results, but there was no process of physically counting the ballots a second time. Nor, for that matter, would this have been possible, since the votes are cast by a show of hands in some precincts rather than by paper ballots.

It’s certainly well within the realm of possibility that more people left their caucus sites on Jan. 3 thinking they had voted for Mr. Romney.

What about the “missing” precincts? On the other hand, Iowa’s stated reason for being reluctant to declare a winner — the ballot counts from eight precincts could not be certified — is somewhat dubious. Had those ballots been counted, Mr. Santorum would probably have won by a larger margin.

Although the results from those precincts were not certified, they were included in a spreadsheet that the state party produced and continually updated on caucus night. And based on the unofficial results from these precincts, they were generally strong ones for Mr. Santorum.

Based on the unofficial results, a total of 269 votes were cast in these precincts. Mr. Santorum won 81 of these votes to Mr. Romney’s 46. If they were included in the total, Mr. Santorum’s margin of victory would roughly double to 69 votes from the 34-vote lead that he officially holds.

The 69-vote lead is noteworthy because it exceeds the magnitude in any identified vote-counting error. (In a precinct in the town of Oelwein, Mr. Romney was originally listed as having 54 votes when he actually had 4 — a discrepancy of 50 votes.)

Thus, while the winner might have changed if a thorough recount had been conducted, and although there are inherent ambiguities when the margin of victory is so small, the outcome is extremely unlikely to have changed based on the missing precincts alone. Instead, Mr. Santorum would almost certainly have had a larger lead had they been included in the total.

How cautious was the news media in describing the initial results? Although the news media, following Mr. Strawn, have been cautious about declaring Mr. Santorum the winner now, they were less so after caucus night, when Mr. Romney unofficially held an eight-vote advantage.

According to a count of Lexis-Nexis citations in press accounts from Jan. 4 through Jan. 18, there were 1,739 instances in which Mr. Romney’s name was used within five words of the term “Iowa” as well as one of the following five terms: “win,” “wins,” “won,” “winner” or “victor.”

By contrast, there were 387 cases — less than a quarter as many — in which Mr. Romney’s name was used in conjunction with the terms “tie,” “tied” or “draw.”

A search through databases like Lexis-Nexis will not always place citations in their full context, but there are hundreds of unambiguous cases. The phrase “Romney won Iowa,” for instance, was used more than 250 times in mainstream press accounts. Meanwhile, many news organizations, including The New York Times, ran headlines that touted Mr. Romney’s apparent victory after the state published its unofficial totals.

Did the news media’s initial depiction of the caucus results have any substantive effects? One way to address this is to evaluate whether the winner of the Iowa caucuses gets an additional bonus in the next state to vote, New Hampshire.

The best predictor of the “bounce” that a candidate gets after the Iowa caucuses is not his absolute performance, but his performance relative to his polls (or less literally, his performance relative to expectations). My colleague John Sides has shown that candidates who beat their polls in Iowa tend to get more news media coverage in advance of New Hampshire. Some examples of this are obvious: Gary Hart surged dramatically to win the New Hampshire Democratic primary in 1984, even though he lost Iowa to Walter Mondale by more than 30 percentage points, because his results were better than forecast by polls and consensus expectations and he was deemed to have favorable momentum.

However, actually winning the caucuses probably provides a candidate with some additional boost.

I ran a regression analysis that seeks to describe a candidate’s vote share in New Hampshire based on four variables: his New Hampshire polls in the two weeks before the Iowa caucuses, the share of the vote he received in Iowa, the Iowa polls in the two weeks before the caucuses, and a flag indicating whether the candidate won Iowa outright. The goal is to see which candidates beat their polling in New Hampshire as a result of having favorable momentum from Iowa. The analysis covers 68 candidates since 1984, when polling data in Iowa and New Hampshire became robust.

The analysis estimates that actually winning Iowa provides a candidate with a four-point bonus, above and beyond these other factors. In other words, the rank order of the candidates probably matters some, in addition to their actual vote total.

However, the estimate is tenuous. Some Iowa winners, like John Kerry in 2004, have received extremely large bounces in New Hampshire, while others, like Mr. Mondale, won Iowa but had disappointing results in the Granite State.

Moreover, even if you assume that Mr. Santorum had won an additional 4 percent of the vote in New Hampshire, and that Mr. Romney had won 4 percent less, it would not have changed the outcome there in a meaningful way. Mr. Santorum would have taken about 13 percent of the vote in New Hampshire, putting him in fourth place, while Mr. Romney would still have had a solid victory, with 35 percent of the vote. Thus, in practice, this probably made relatively little difference.

Is the news liable to change anything now? It is unlikely that the news of the reversal in the Iowa result will provide much help to Mr. Santorum now. He is no longer within striking distance in South Carolina, which has turned into a two-way race between Mr. Romney and Newt Gingrich.

That the news is unlikely to help Mr. Santorum would not preclude the possibility that it could harm Mr. Romney at the margin. My view is that there are too many competing news stories for the Iowa news to actually affect the South Carolina results much. If Mr. Romney were to lose South Carolina, however, perhaps you’ll hear the talking point that he has won just one of the first three states, when he had previously appeared to go two for two.

But this talking point might not get much traction. As Jonathan Bernstein, a political scientist, notes, the “spin” that emerges after a candidate wins or loses a state depends on large part on the whims of party elites, who will interpret news in a more favorable light for candidates whom they hope to see win the nomination. Because Mr. Romney has the strong backing of the Republican Party establishment — and because he has highly capable and alert spokesmen — the news is unlikely to affect him as much as it might a candidate who relied more exclusively on media-driven momentum.

What, if anything, was done wrong? Iowa Republicans, although they do not provide for recounts in their caucuses, have a strong process for certifying their results. Observers from each of the campaigns are invited to each precinct to verify that the vote has been recorded correctly. Disorganized campaigns sometimes do not take advantage of this provision, but well-run ones like Mr. Romney’s and Mr. Santorum’s usually do.

Moreover, Iowa’s vote-counting process has been open and transparent. That the state party posted a Google spreadsheet that was updated in real time throughout caucus night is exemplary, and goes beyond what most states do.

And although Iowa officials played somewhat coy when reports of vote-counting discrepancies first emerged, they ultimately looked into them carefully. There are minor vote-counting mistakes in every election, and there is no reason to think that there were a higher-than-normal amount of problems in Iowa.

With that said, I think you can fault the Iowa Republicans for rushing to declare a winner on caucus night. The wording Mr. Strawn originally used in the wee hours of the morning on Jan. 4 was relatively unambiguous: “Congratulations to Governor Mitt Romney, the winner of the 2012 Iowa caucuses,” Mr. Strawn told reporters.

Mr. Strawn also told reporters, however, that the results had yet to be certified — an important detail that was rarely relayed in news accounts. I don’t mean to play the role of media critic, but my view is that it is the job of the news media to pay attention to the fine print rather than rush to judgment.

Whether a news outlet now describes Mr. Santorum as having won Iowa, or instead says that it was too close to call, is a matter of editorial discretion; either choice is probably defensible.

However, in my view, there is little justification for having described Mr. Romney as the winner previously but not using that language for Mr. Santorum now. Although the outcome remains in some doubt, the statistical likelihood that Mr. Santorum in fact won Iowa is considerably higher now than it was for Mr. Romney on caucus night. And the results are certified now, which they had not been before.

This post has been revised to reflect the following correction:

Correction: January 25, 2012

A previous version of this post incorrectly stated the number of votes by which Senator Al Franken won. It was 312 not 215.

Nate Silver founded and was the editor in chief of FiveThirtyEight.