A Mathematical Look at the Election
Nov. 13, 2000 -- Is there anything left to say about the torrent of vote numbers and exit polls that have washed over us the last couple of days? A few random observations come to mind.
The Electoral College should probably be abolished, but the chaos of the recount in Florida suggests one defense for it. If the popular vote determined the victor, any comparably close national election would call for a national recount. Imagine going through the returns precinct by precinct, county by county, state by state. At least now the tempest is confined to Florida alone.
The results in other states are close and the Bush campaign has hinted that it might demand recounts in Wisconsin, Iowa, and Oregon. A recount in these states, however, is much less likely to change the outcome since the differences in vote totals are bigger there and the states are much smaller.
Get a Grip on the Numbers
With nearly 6,000,000 votes cast in Florida and roughly 300 votes (as of this writing) separating the candidates, the difference between them is less than one part per 20,000. Both Bush and Gore like to jog, so to get a grip on how small a margin this is, let’s imagine them competing in a mile-long race. Dividing the mile into 20,000 parts, we find that each part would be about 3 inches long, the margin of victory. Talk about a photo finish!
Another way to look at it is to realize that the difference between the Florida vote totals of Gore and Bush (if we ignore Nader and Buchanan) is what we would expect if the approximately 6 million voters flipped a coin to determine their votes.
The spike in the number of Buchanan voters in Palm Beach County is extremely unlikely. A non-statistical measure of this unlikelihood is that Buchanan said on NBC’s Today show that he believed most of the 3,407 votes he got in Palm Beach County belonged to Gore and that many people voted for him by mistake.
The networks’ calling Florida prematurely was likely the result of the uncertain, ever-changing demographics of the state. Unlike Pennsylvania’s population, for example, which is quite stable, Florida’s is bolstered every year by a large number of new residents — hordes of retirees, people moving from other states, immigrants from South America and elsewhere. Computer models of electorates work better on stable populations that stay put and vote the same way from election to election.
Nothing Is Fool-Proof
The desire to be first also motivated the early awarding of Florida to Gore. Which network gets the scoop is determined by which one is willing to take the biggest risks. Despite the appearance of independence, all the networks use the same numbers, those provided them by VNS, the Voter News Service. Switching to another network to get confirmation is a little like buying another copy of the newspaper to see if something in it is a misprint or not.
There’s a mathematical result known as Arrow’s theorem which says very roughly that there is never a fool-proof way to derive group preferences from individual preferences that can be absolutely guaranteed. This election certainly bears this out.
Watching the parties maneuver and stress those aspects of the situation favoring them reminds me of the advice the old lawyer gave to his protege. “When the law’s on your side, pound the law. When the facts are on your side, pound the facts. And when neither is on your side, pound the table.”
Professor of mathematics at Temple University, John Allen Paulos is the author of several best-selling books, including Innumeracy and A Mathematician Reads the Newspaper. His Who’s Counting? column on ABCNEWS.com appears on the first day of every month.
This column was originally written for the Philadelphia Daily News.