Statistics Give Gore a Longshot to Win With a Recount

Even if the Florida Supreme Court gives Al Gore everything he is seeking, he might not pick up enough votes from recounted ballots to overtake George W. Bush and become the next president, according to statistical analyses by The Times and independent scholars.

Despite claims from some Democrats that a hand recount in Miami-Dade County would put Vice President Gore over the top, projections by statisticians and The Times suggest that might not be the case.

And while Gore says that he considers his chances of winning the White House to be “50-50,” statisticians poring over voting data calculate that his prospects of winning the votes he needs actually may be no higher than 40%. Even then, that’s only if the Florida Supreme Court awards Gore a recount in Miami-Dade County plus several hundred disputed votes in Palm Beach and Nassau counties, they said.

That’s still a significant chance, perhaps even enough to make a recount worthwhile in the eyes of the state Supreme Court, but it’s no sure thing.

“In plain English, I’d say 40% is a reasonable possibility,” said H. Peyton Young, an economist at Johns Hopkins University in Baltimore who co-wrote a forecast of Gore’s chances. “It’s less than 50% but not by much.”

Here’s how the numbers stack up:

The official Florida results, as certified by Secretary of State Katherine Harris last month, gave Republican Texas Gov. Bush a lead of 537 votes statewide.

In his contest of those results, Democrat Gore asked the state Supreme Court to award him 215 votes from a manual recount in Palm Beach County, 51 votes from a disputed machine recount in Nassau County, and 168 votes from a hand recount in Miami-Dade County that was never completed, for a total of 434 votes.

If the court agreed on all those points, Gore would still trail Bush by 103 votes.

Thus the importance of the recount in Miami-Dade County. Miami-Dade’s canvassing board started a hand recount on Nov. 18 and got about one-fifth of the way through before abruptly stopping on Nov. 22 as Republican demonstrators clamored outside its meeting room.

Gore has asked the courts to order the county to finish its hand recount. If the court agrees, what would the likely outcome be?

A simple arithmetic projection by The Times computer reporting staff estimated that, based on the precinct-by-precinct distribution of “undercount” ballots--those that did not register a vote for president when they were counted by machine--Gore would pick up about 115 more votes from a hand recount--enough to eke out an improbable winning margin of 12 votes.

The Times study was relatively simple. Using figures supplied by the Miami-Dade Elections Department, it located the 8,720 “undercount” ballots that have not yet been recounted by hand, precinct by precinct. Those uncounted votes were distributed among the candidates according to the results already reported in their precincts. Then, because the Miami-Dade County canvassing board found valid votes on only 20.5% of the ballots it examined in its partial hand count, the study added 20.5% of its results to the candidates’ existing totals.

The Miami-Dade hand recount covered about one-fifth of the county’s precincts. The Times study looked at the remaining four-fifths.

The statisticians, however, applied more sophisticated techniques and derived ranges of probability.

At Johns Hopkins, Young and Chris Carroll estimate that Gore’s chances of gaining more than 103 votes in Miami-Dade County is about 40%. At the University of Wisconsin, economist Bruce E. Hansen estimates Gore’s chances of going over the top as “somewhere between 5% and 30%, depending on how you do the calculations.”

A recount expert for the Gore campaign, Chris Sautter, said that all those estimates sounded credible to him--as far as statistical estimates go, that is.

“They’re a guide, but you never know until you get there what’s going to happen,” said Sautter, one of Gore’s chief recount watchers in Florida. “You can’t project votes with any kind of certainty. And the bottom line is, when you count ‘em all up, it’s pretty darn close.”

“There’s a range of estimates, and they leave you right in the middle,” agreed John Hardin Young, one of Gore’s recount lawyers. “It’s clearly in doubt--and that’s why there should be a hand count.”

Many Democrats, pointing to the 8,720 ballots that Miami-Dade County did not subject to a hand recount, argue that Gore would fare much better than the estimates suggest.

But statisticians point to two reasons Gore’s yield from those ballots might be lower than expected.

One reason is that Miami-Dade County’s initial hand recount started with 135 predominantly Democratic precincts. The remaining 655 precincts are much less favorable to Gore. Some went solidly for Bush. The unrecounted ballots also include 1,358 absentee ballots, most of which are expected to go for Bush. Gore likely would lose a little ground there.

The projections all look at the uncounted ballots on a precinct-by-precinct basis and assume that the uncounted ballots will split between Bush and Gore the same way the counted ballots in each precinct did.

A second reason for Gore’s potentially low yield is that most of the uncounted ballots will not produce any additional votes at all. Miami-Dade County’s recount focused on the undercount ballots.

But not every “undercount” ballot yields a readable vote. Indeed, some are “undercounts” because the voter deliberately did not vote for any presidential candidate. In Miami-Dade County’s initial recount, only about 20% of the “undercount” ballots yielded actual votes. (That is similar to neighboring Broward County, where a manual recount produced a 26% yield rate.) So a recount of the remaining ballots in Miami-Dade County might produce an additional 1,788 votes--if the yield rate (actually 20.5%) held steady.

Different projections handle the yield rate in different ways--from assuming that the rate of 20.5% is constant across the county (unlikely) to estimating rates based on similar precincts (chancy).

“You’ve got two sources of uncertainty there,” Young noted.

The challenge of estimating the outcome of an undecided presidential election has galvanized dozens of statisticians across the country. Papers have been exchanged, calculations swapped. Some of the academic researchers have even been consulted by the two warring campaigns in Florida.

“A very well-developed Internet network has popped up in a very short period of time,” said Hansen, an expert in economic forecasting theory. “As to whose work is more accurate, we don’t know yet.”