Heads or tails?

By Stephen Jay Gould, 11/30/2000

HE TIME HAS COME, I think, to advocate the unspeakable in a forthright and unapologetic manner, and not in the facetious or peripheral way that tradition and circumstance have heretofore demanded. By our rules of procedure, and by any scientific method of counting or reckoning under these rules, the race for the presidency has ended in a flat tie and should be decided by the toss of the coin.

I speak solely as a student of probability and measurement. I do not address any of the entirely legitimate and deeply felt issues of general fairness raised with equal justice and fervor by both sides: Gore's tiny majority in the national popular vote; Bush's advantages in uncounted military votes; Gore's probable, but undeterminable, Florida majority in voters' intentions (as opposed to their actions, sometimes in nervewracking circumstances with unclear ballots); or Bush's complaints about varying standards in counting among Florida counties.

All these problems must be settled - and undoubtedly will, for we cannot do this again - by future reforms in voting procedures. For now, we work by the constitutional system of the Electoral College. By the fate of this system, the electors of Florida will determine the victor of this national contest. And the result in Florida is an unbreakable statistical tie by the imperfect and unstandardized procedures used for recording votes. Real and true ties are most fairly settled by a random trial with a 50 percent chance for each contestant - in other words, by a coin flip.

The officially certified vote on Sunday has Bush in the lead by 537 votes. This disparity is less than one-100th of 1 percent, or .0001, of nearly 6 million votes cast in the state or, in concrete terms more easily grasped by all, less than one penny's difference in a hundred dollars.

Unfortunately, in making a deadly serious, even prayerful, case for the fairness of coin flipping in this circumstance, we must fight both the greatest failure of education and the deepest foible of the human mind; our propensity to misunderstand probability. The human mind, as a pattern-seeking, story-telling device, rebels against decisions that cannot be made for causal reasons rooted in an achieved victory - whether for good or evil reasons in our personal judgments - by one side over another.

We cannot abide the message of Ecclesiastes (9:11) that, in many circumstances, no reason of deterministic natural law or active human will can adjudicate our outcomes, even for our most important events, for sometimes ''the race is not to the swift, nor the battle to the strong ... but time and chance happeneth to them all.''

Thus, the mind rebels against a claim that Florida should be declared a true tie. Count them again, we say. Count them more carefully. Count them by a single standard. Count them by more accurate machines. Count them by the undeniably fairest method of human scrutiny for each ballot, no matter how long it takes. Count them and recount them until we know who won, even if the true difference comes down to a single vote.

But we never will, and never can know by this false standard of determinability. We can count for every metaphor of eternity, until Kingdom Come, hell freezes over, or the cows come home, and we will never know because the vote is tied by any achievable standard of measurement. Any method, machine or human, ineluctably embodies an intrinsic margin of error.

Differences smaller than this margin cannot be resolved, and any contest with a measured difference within this range is a tie. The disparity between Bush and Gore in Florida lies well within this range - not even near an outer edge that might be tweaked by special care - using any method of machine or hand counting. To cite the excellent metaphor presented by J.A. Paulos in the New York Times, any attempt to determine whether Bush or Gore won Florida is equivalent to trying to measure a bacterium with a yardstick.

I hold little practical hope that this best and fairest solution, lacking either constitutional mandate or popular understanding, can possibly prevail.

But think of the gain, if only we could free ourselves from a host of false assumptions about causality, measurement, and factual accuracy. No angers; no recriminations. An understanding that the true will of the people, as ascertainable under accepted rules then in practice, has indeed been determined in the fairest possible way under extraordinary circumstances that must not be allowed to occur again. Football teams grasp the justice of a coin flip when each side has an equal claim.

Can't a nation do as well? Is there not something wondrously impartial - and blessedly healing - in breaking a genuine tie by a truly arbitrary action that favors no man or doctrine: So flip a quarter, Mr. Chief Justice, high in the air, with the whole world watching. The head of George for George, or the eagle of America for Al. Let the fortunate man win, and the United States triumph.

Stephen Jay Gould is a professor of zoology at Harvard University. His latest book is ''Crossing Over.''