Charles Seife raises an important point that I've been batting around in my mind, oh, since Florida 2000. But the nail-biter between Al Franken and Norm Coleman in Minnesota's Senate election has raised this issue back to the front of my brain.
Elections that come down to a couple of hundred ballots out of millions cast are in fact statistical ties. Florida's was a tie (until you get to the overvotes that were never counted). Minnesota's is a tie.
How can we know this? Before the recount began, the state ran a post-election review to gauge the accuracy of the voting process. The review involved auditors going into select precincts and, like the recounters, counting by hand, doing the most careful job humanly possible. So in some precincts, we have not just a recount but a re-recount. Both auditors and recounters were hypervigilant to possible sources of error, and yet they disagree on their tallies by about 20 thousandths of a percent.Given the error-prone measurement systems we have - and Minnesota's is relatively good, especially compared to Florida's - no scientist or engineer would ever claim that even the count we get out of a careful, conscientious recount is accurate enough to measure a real difference in voter preference from vote totals that only differ by 0.008%.
In an ordinary race, errors this tiny wouldn’t be a problem. But the Coleman-Franken race is so close that this error rate is more than double the margin between the two camps.