WE'RE MEASURING BACTERIA WITH A YARDSTICK by John Allen Paulos appeared in
the NEW YORK TIMES on November 22, 2000 (copyright 2000)
PHILADELPHIA - No mountaineer would climb Mount Everest, scratch a quarter inch of ice off its summit and then claim that it was now only 29,027 feet, 11 3/4 inches high. After all, everyone realizes that its height is just an estimate - and that the margin of error is much greater than a quarter of an inch. Likewise, no one suggests that to lose weight we should go up to the attic, since gravity is minutely weaker up there than it is downstairs.
Some feeling for relative and relevant magnitudes is essential in the most diverse realms, even when it comes to counting votes.
Not to be too cryptic, let me simply state that the vote in Florida is essentially a tie. The totals for Al Gore and George W. Bush, out of nearly six million votes, are so close that the results are statistically indistinguishable from what one would get by flipping a coin six million times.
The electoral process has too many variables, too many inevitable flaws, for anyone to assume na´vely that all we need do in this dead heat is tote up the votes and be done with it. Measuring the relatively tiny gap in votes between the two candidates is a bit like measuring the lengths of two bacteria with a yardstick. The Florida electoral system, in particular, is incapable of making such fine determinations.
Its flaws were neither new nor specific to the state, but they became apparent - at least on the national level - only when the system was stressed by an electorate that was astonishingly evenly divided.
From the perspective of the Gore camp, consider that 3,000 to 4,000 butterfly ballots were cast for Mr. Buchanan when they were intended for Mr. Gore. Consider that more than 20,000 ballots in Duval County were discounted, the vast majority for double voting. Consider the approximately 19,000 ballots that were thrown out in Palm Beach County. Consider the apparent undercounts in Broward, Miami-Dade and other Democratic counties. (These latter numbers might partially explain the Voter News Service's early call of Florida for Mr. Gore. The exit polls reflected people's sometimes incorrect beliefs about whom they had voted for.)
Consider also the 15,000 absentee ballots in Republican Seminole County that so far have been allowed despite the fact that local officials, rather than the voters, filled in the required details.
From the Republican side, consider that Mr. Bush lost an indeterminate number of voters in the Florida Panhandle because the networks called the election 15 minutes before the polls had closed there. Consider that mistakes and unconscious biases can affect the manual recounting of ballots. Consider that there haven't been recounts in Republican counties where they would probably yield net votes for Mr. Bush. Consider, too, that many overseas military ballots were discarded because of the lack of postmarks.
Consider finally the problems associated with counting six million of anything. All these figures swamp the present vote difference between the candidates.
There may be too much noise - in a political as well as an engineering sense - for there to be a clear winner.
Each candidate argues for his way of counting ballots. Fetishizing the "accuracy" of incomplete machine counts, the Republicans try to de- emphasize the "Bush standard" signed into Texas election law a couple of years ago, which allowed dimpled chads to be counted as votes. The Gore camp is insufficiently sensitive to the need for closure. People on both sides are reckless in their allegations.
The Florida Supreme Court will make a decision about whether there can be a recount, and it or another court will surely examine the dimpled chad and other electoral squabbles. But no court of law can determine, with sufficient accuracy, what the true count actually was. It's virtually impossible to know.
So if the vote count is inevitably fuzzy - and no method of counting will make the tally truly accurate - what should the country do?
I have a modest proposal. Flip a commemorative Gore-Bush coin in the Capitol Building in Tallahassee. To avoid another tie, we'd better make sure it has rounded edges.
John Allen Paulos, a math professor at Temple University, is the author of "Innumeracy" and "A Mathematician Reads the Newspaper."
P.S. (not in NY Times) The dependence of the outcome on
the interpretation of everything from statutes to dimples
suggests that we should replace (or supplement) the term
"margin of error" with the term "margin of interpretation."
Without interpretation and litigation, there simply is no fact of the
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