Who really "won" in Iowa?

Update, February 3: The New Times reports today that Iowans, and others, are questioning the reliability of caucus results. They should.

Update, Feb. 1: The NY Times reports today that the Iowa GOP chairman has resigned.

News reports over the past few days have told us that, after a recount, Mitt Romney did not win the Iowa Republican caucuses by 8 votes, Rick Santorum won them by 23. Or maybe by 34.

The early reports were a tipoff, confirmed by subsequent events, that neither man "won." I think they probably tied. As I reported a year ago in a post about Charles Seife's book "Proofiness," numbers of that exactitude - a win by so few votes out of more than 120,000 cast - suggest a certainty that may not exist. According to the results certified by the Iowa Republican party, the exact number is 121,503. The Iowa Republicans worked very hard to develop this data. You can download the spreadsheet, with its 1767 lines of data yourself, and see it all (along with the potential for error). Eight precincts did not report certified vote totals. For a good discussion of the outcome see, as usual, Nate Silver's analysis. (He thinks it is fair to say that Santorum won.)

The issue of who won isn't all that important any more, though the question of whether those Iowa voters are in any way representative of the general electorate remains. So let's consider the outcome a tie, and move on. The Republican primary season is turning into an interesting time.

Critical thinking and mathematical literacy

Mathematics, and statistics in particular, offer us powerful tools to understand and explain the world. Unfortunately, they also offer us equally powerful ways to conflate information, confuse us, and confound us as well.

In Proofiness, a book geared to non-mathematicians, journalism professor Charles Seife offers some simple measures to make sure we keep our critical facilities intact:

• Pay attention to the context -- a number alone can suggest a certainty that might not exist. (Even counting can be prone to errors.)
• Remember that correlation and causation are not the same thing, and that a correlation may not have meaning. We are wired to look for patterns, and sometimes our brains fool us into finding a pattern that is not there.
• We don't know how to calculate risk so we often base decisions on the information in front of us and how it's presented.
• Polling is not a perfect science, and knowing the margin of error does not correct all the possible errors.

And so on. He calls succumbing to these errors and others "proofiness." Along with that term, he uses additional, equally memorable coinages: randumbness, causuistry, and regression to the moon. But it's in the examples that this book is most useful. Drawing from recent events--the 2000 Presidential election, the 2008 Minnesota senatorial election, the OJ Simpson trial, various death penalty trials--he shows us all too many places where numbers have been used to trump logic, common sense, and, well truth. And Seife shows us how lawyers, journalists, and we ourselves as consumers, are party to continuing these errors. Proofiness,  (Viking, 2010, 260 pages) is well worth reading and even more worth absorbing.