Election: Human and machine imperfections in the vote-counting process make a small degree of uncertainty inevitable.

As the Florida presidential ballots are counted and recounted, a disquieting possibility looms: Though either George W. Bush or Al Gore will undoubtedly become the 43rd president of the United States, we probably will never know which candidate actually got the most votes in that crucial state.

The gap between the two candidates in Florida is apparently smaller than the margin of machine and human error inherent in the vote-counting system, experts say. In other words, the presidential election was - and will always be - literally too close to call.

As of yesterday, according to an unofficial count by the Associated Press, Bush led in Florida by 388 votes, out of nearly 6 million votes cast. That is a vanishingly small difference of 1/153rd of 1 percent, a gap far smaller than the votes lost or miscounted in routine glitches.

"Election officials are being asked to deliver a perfect result with an imperfect system," says Iain Murray, senior analyst with the Statistical Assessment Service, a Washington organization that tracks media use and misuse of numbers.

"I don't think there is a single county in the country - except maybe one with 22 voters in New Hampshire - where the count does not contain at least some errors."

Joseph Waksberg, a prominent statistician and chairman of Westat Corp., a Rockville research company, suggests that determining precisely the outcome in Florida would require careful, unhurried review of every ballot, possibly including repeated machine and hand recounts.

"Given enough time and enough will, you could get pretty close to an accurate count," Waksberg says. "As a practical matter, it may be impossible."

Like a dam that stands for years and then collapses under the pressure of a 100-year flood, the U.S. voting system has suddenly been placed under intense scrutiny because of the uncannily close vote. And it turns out that, by comparison with other large-scale measurement systems in science and industry, elections are inconsistent and unscientific.

Often, ballots are designed and voting machines overseen by relative amateurs, with little of the expertise, consistency and quality control that characterize, say, SAT examinations, HIV testing or even cereal manufacturing.

"American elections are a giant black box," says Michael Traugott, a political scientist at the University of Michigan. "There were thousands of different ballots used on Tuesday. People don't understand the huge variation from place to place."

A telling comparison is with the 2000 U.S. Census, which this year collected about 100 million forms, close to the number of votes cast in the 2000 election. But the census used just two forms (short and long), both of which had been pre-tested and pored over by statisticians, psychologists and marketing experts for years. The questionnaires were processed in four centers, all operating under the same rules.

"The government has spent billions of dollars to try to get better counts," says Waksberg, a former top Census statistician.

Contrast that care with the handling of the ballot design used in Palm Beach County. When Democrats complained that 19,000 punch-card ballots had been rejected because confused voters selected two presidential candidates, Republicans pointed out that 14,000 Palm Beach ballots were rejected for the same reason four years earlier. But because the election outcome was not affected, officials didn't bother to redesign the ballot to reduce voter confusion.

In most complex systems - from air traffic control to stock trading - "human factors" are constantly analyzed and procedures improved, says Michael E. Wiklund of the American Institutes for Research, a nonprofit research firm. But voting procedures rarely benefit from the "usability testing" routine in industry.

"A mock voting exercise with some of these ballots might have avoided this whole electoral mess," Wiklund says.

One person who has long tried to call public attention to voting system inconsistencies is Rebecca Mercuri, a computer scientist at Bryn Mawr College who has studied voting machines for a decade and defended her doctoral dissertation on "Electronic Vote Tabulation" at the University of Pennsylvania two weeks ago.

"I couldn't get anyone to listen to me," she said yesterday. "Now my phone is ringing off the hook."

Mercuri says that in test runs, new voting machines using perfectly filled-out sample ballots generally perform with almost no errors. But in actual use, the machines have error rates of 2 percent to 5 percent because of wear and tear and voter mistakes, she said.

Old lever-style machines miscount when gear teeth break. Punch cards - as in Florida - are misread when the tiny piece of punched-out paper, called a chad, is not completely removed. Ballots imperfectly marked by pen are often misread by optical scanners.

"If voters don't follow instructions, they may not blacken in the whole bubble," says Doug Lewis, executive director of the Election Center, a Houston nonprofit organization that advises local election officials on voting procedures. "There can be a mark that if you read it 50 times, 20 times it's a 'yes' and 30 times it's a 'no.'"

A classic voter error, Lewis says, is to circle the bubble rather than blackening it. Such a ballot would show no presidential choice when read by machine but could be easily interpreted by election officials in a hand count.

Lewis was part of a team of experts who recounted ballots and analyzed errors last year in Hawaii after complaints about the 1998 election, the results of which had already been certified.

The experts found malfunctions in seven voting machines, mostly caused by glue that melted off ballots and occluded the lenses on optical scanners, Lewis says. But when ballots were recounted on working machines, vote totals changed by less than 1 percent, not enough to change any outcome.

He said the kind of deliberate recount he helped conduct in Hawaii was possible only because the election was long over and its result not at issue. In Florida, he says, "You can't say, 'Let's take 30 days and do three machine counts and three hand counts.'"

They need for a quick, clear conclusion distinguishes the election from most scientific work, says Joseph F. Dolan, an astrophysicist at the National Aeronautics and Space Administration's Goddard Space Flight Center who studies the end-stage of stars. If the results of an observation are as ambiguous as the Florida vote count, scientists don't have to hurry to a conclusion. They can repeat a measurement dozens or hundreds of times, or they can discard the results and start over.

"We can always go back and measure again when it's a close call," Dolan says.

That might not be possible in this election. But even this disputed vote might be far fairer than many U.S. races of decades past.

Dolan remembers, for example, his grandfather's experience working for the city of Boston during the famously corrupt mayoralty of James Michael Curley, when errors were not so random.

Curley's operatives, he said, "used to go to their opponent's districts and put paper matches under the lever so that votes would not be registered."

"So democracy depended," he said, "on scoundrels stealing the same number of votes from both parties."