November 6, 2006, The New York Times
Op-Ed Contributor
The Deciding Vote
By DALTON CONLEY
THE Democrats may or may not capture the House or Senate tomorrow. But one thing appears
certain: There will be a lot of close races where the results are uncertain late into the night (and
perhaps even the next morning) and where the outcome may hinge on legal rulings about which
ballots count and which don’t.
After all, in the last few years, several statistical dead-heat elections have ended up in court. The
mayoralty of San Diego and the governorship of Washington are just two of the more high-
profile examples since Bush v. Gore in 2000 in which elections were decided by a few votes and
controversy followed the winner into office.
The rub in these cases is that we could count and recount, we could examine every ballot four
times over and we’d get — you guessed it — four different results. That’s the nature of large
numbers — there is inherent measurement error. We’d like to think that there is a “true” answer
out there, even if that answer is decided by a single vote. We so desire the certainty of thinking
that there is an objective truth in elections and that a fair process will reveal it.
But even in an absolutely clean recount, there is not always a sure answer. Ever count out a large
jar of pennies? And then do it again? And then have a friend do it? Do you always converge on a
single number? Or do you usually just average the various results you come to? If you are like
me, you probably settle on an average. The underlying notion is that each election, like those
recounts of the penny jar, is more like a poll of some underlying voting population.
In an era of small town halls and direct democracy it might have made sense to rely on a literalist
interpretation of “majority rule.” After all, every vote could really be accounted for. But in
situations where millions of votes are cast, and especially where some may be suspect, what we
need is a more robust sense of winning. So from the world of statistics, I am here to offer one: To
win, candidates must exceed their rivals with more than 99 percent statistical certainty — a
typical standard in scientific research. What does this mean in actuality? In terms of a two-
candidate race in which each has attained around 50 percent of the vote, a 1 percent margin of
error would be represented by 1.29 divided by the square root of the number of votes cast.
Let’s take the Washington gubernatorial race in 2004 as an example. After a manual recount,
Christine Gregoire was said to have 1,373,361 votes, 48.8730 percent, while her Republican
rival, Dino Rossi, garnered 1,373,232, or 48.8685 percent (a third-party candidate got 63,465
votes). That’s a difference of only 129 votes, or .0045 percent. The standard error for a 99
percent certainty level was 0.078 percentage points. Since Ms. Gregoire’s margin of victory
didn’t exceed this figure, under this system she wouldn’t be certified as the victor.
If we apply the same methodology to Bush v. Gore in 2000, the results are equally ambiguous.
The final (if still controversial) vote difference for Florida was 537 (or .009 percent). Given
Florida’s vote count of 5,825,043, (excluding third party votes) this margin fails to exceed the 99
