November 21, 2000
Analyze This: A Physicist on Applied Politics
By LAWRENCE M. KRAUSS
Who would have guessed that the election of the president of the United States would come down to a question of measurement error?
On Nov. 7, roughly six million people in Florida cast their votes for president. Such a vote normally produces a signal so clear that television networks can discern its nature even before the votes are counted. Not this time. A machine count and recount of the votes (along with a sprinkling of manual recounting) produced at the initial deadline for certifying the vote last Tuesday a mere 300-vote margin between the candidates.
In many areas of science we are used to analyzing the significance of tantalizingly small signals, like the margin in this election. In such analyses, three questions normally come to mind:
Is the size of the signal significant in comparison to random noise? If not, can the resolution of the detector be improved to increase the significance of the signal? And finally, are there sophisticated statistical methods that might resolve features of the signal that would otherwise be buried in the noise?
It may be illuminating to consider how these considerations might apply to the Florida election.
All measuring systems have uncertainties. With six million votes, even a small relative uncertainty can involve a significant number of votes. If measurement errors are random and if we measure on an event-by-event basis, a mathematical theorem called the law of large numbers suggests that roughly 68 percent of the time, if one performed precisely the same experiment on precisely the same system over and over again, the total number of events counted would be expected to vary by at least 2,000 events.
This suggests that in any one experiment, for example one statewide vote, a 300-vote margin in either direction is not statistically significant. Send the same voters back to vote for the same candidates again and one would not be surprised if the final vote count were to change by up to 10 times this amount.
This is not much help, however. Our electoral system requires us to choose a winner. So we should attempt to choose the most accurate measuring system possible.
In this regard, are "machines" more accurate than humans?
Some have argued that ballots should not be manually counted because there is no objective criterion for determining the effects of human error. This depends on what the meaning of "is" is. The contention that a machine count is more objective is based on the presumption that the rules by which machines decide on the outcome are more rigorous than those that can be applied by humans. But human beings program and design the machines, and the decision the machine makes is only as good as the human manufactured software and hardware.
The chief issue here is whether the punched out paper, known as a chad, is fully attached or not. A Florida election standard adopted in 1990 implies that a vote is cast if either zero, one, two or three corners out of four is attached. If this is the definition of a vote, there is no ambiguity. The question of whether a chad is completely attached or not is a question of physics, not politics.
Whether or not a machine can accommodate the straightforward algorithm necessary to separate properly executed ballots simply depends upon the adequacy of the machine. High-resolution laser scanning of ballots, for example, would unambiguously allow a determination of whether any part of the chad was not attached to the rest of the ballot.
Such laser scanning would be prohibitively expensive. We do not, however, have to require such machines. The human eye, combined with appropriate use of the human brain, provides a level of discrimination, which certainly exceeds the ability of the existing vote counting machines to evaluate detached chads.
As long as there is a well-defined algorithm for what constitutes a properly executed ballot, the more sophisticated the machine that can execute this algorithm, the more accurate the result. To suggest that a mechanical vote-counting device is more accurate than a human vote- counting device (consisting of at least two humans with competing motives) demonstrates a misplaced faith in automation.
As Bill Joy, chief scientist at Sun Microsystems Inc., put it in a recent television interview, "If your life depended on the measurement of a single ballot, would you prefer it be read by a machine, or examined carefully by three different human beings?"
Finally, I come to the question of the use of statistical methods to try to untangle the uncertainties. Because such methods cannot be applied on an event-by-event basis, they naturally offend our notions that every single vote counts. It may be, however, that they can convincingly unmask anomalies that are far larger than the signals we are trying to unearth.
Everyone has by now heard of the anomalously large vote for Patrick J. Buchanan in Palm Beach County. But is there a statistical way to verify that it is indeed anomalous, and not just large? One way to do this is not to simply count votes for Mr. Buchanan, but to search for trends present everywhere else not present in Palm Beach. For example, if one plots votes for Mr. Buchanan against votes for Gov. George W. Bush on a county-by-county basis, one can search for a possible correlation between support for one candidate and support for the other across the state. With good regularity, counties with a larger number of Bush votes also produced a larger number of Buchanan votes. If one does a statistical test of the Buchanan-Bush correlation, one finds that one can predict the number of Buchanan votes, given the number of Bush votes, with an accuracy of within about 500 votes at least 99 percent of the time.
There is one glaring anomaly, however, and one does not have to be an expert in statistics to spot it. In Palm Beach County, this correlation is violated by over 2,500 votes! It is so large that we can argue with great numerical confidence that such a violation would occur at random less than one time in 100,000 measurements. And the level of the effect is eight times as large as the difference in claimed vote totals between the Democratic and Republican candidates in the entire state. If a physics experiment produced such a result, it would be clear that something of significance, warranting further investigation, was at work here.
Of course, the vote in Florida is not a laboratory event, and we cannot expect the courts or political parties to treat the result as we would those of a physics experiment. Nevertheless, we can learn from our experience in science about ways to make the final measurement as sound and as significant as possible. Of course, in the end, whether or not this is the goal of either side in this election is a question of politics, not physics.
Copyright 2000 The New York Times Company