• By
  • Carl Bialik

A graduate student in statistics has gained some notice online for his analysis of just how few votes it would have taken to change past presidential election results. It’s well known that in 2000 just a few hundred Floridians who voted for President Bush could have swung the election to Al Gore by changing their votes. But that election wasn’t unique: Five other presidential-election outcomes could have been reversed by fewer than 1% of voters in a single state switching their allegiance. And six other presidential elections could have been swung by fewer than 1% of voters in a group of states.


The analysis, by Mike Sheppard of Michigan State, was picked up by ABC News and debated on Slashdot. Interest in the analysis lies chiefly in its alarming conclusion, namely that in a somewhat close race, the winner is more or less arbitrary, and a very small swing can change the outcome.

But some of the scenarios Sheppard describes are fairly implausible. For instance, the 1968 election would have required less than a 1% total swing among all voters in seven states to produce President Hubert Humphrey. Among these was Vermont, where Nixon won by nine percentage points. “Some are quite probable, while others are more mathematical, ‘what if’ scenarios,” Sheppard told me in an email.

Sheppard wrote a computer program to analyze historical election results and answer the question “What is the smallest number of total votes that need to be switched from one candidate to another, and from which states, to affect the outcome of the election?” Keep in mind that in this theoretical exercise, the votes are being switched from the winner to the loser, meaning a net gain of two votes for each vote switched. So Bush’s 537-vote victory in Florida in 2000 corresponds to a needed swing of 269 votes. Sheppard ran this analysis for results from the 43 elections since 1836, by which time most states adopted a winner-take-all format in the Electoral College.

The analysis imagined a best-case scenario for the losing candidate, in which he managed to overturn those votes that would be most valuable to him. Theoretically, Bob Dole could have beaten Bill Clinton by winning over just 575,515 Clinton voters in 1996, even though Clinton won the popular vote by 8.2 million. Realistically, there was no campaign strategy that would have picked up exactly those needed votes — while not alienating other voters in those states or in states Dole won by a narrow margin.

Still, campaign strategists may want to read Sheppard’s analysis for some sense of where they can get the biggest bang for their buck. New Mexico voters have participated in 24 presidential elections; in 17 of them, the state was among those that the loser would have needed to flip in order to win with minimal overall vote gains. Delaware and Nevada also have been influential in more than half of the elections they’ve been involved in. “Larger states tend to have wider margins between the two candidates and it usually would take a larger effort to encourage undecided voters in that one state,” Sheppard said, “while fewer total votes in multiple smaller states could have more electoral influence than the one big state alone.”

Sheppard’s program was also able to help answer a question that’s been of particular interest to me lately: How close prior elections have been to a tie. In 2004, just 18,771 votes would have had to switch to produce an Electoral College tie, and in 2000 it would have taken just 5,375 votes (assuming in both years that a lone elector who deviated from his or her state’s vote hadn’t). In 1960, fewer than 10,000 votes would have had to switch.