Odds That One Vote Can Make a Difference in an Election

"I Voted! Did You?" sign in front of crowds of voters

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The odds that one vote can make a difference in an election are almost nil, worse than the odds of winning Powerball. But that doesn't mean it's impossible that one vote can make a difference. It's actually happened. There have been cases in which one vote decided the election.

Odds That One Vote Can Make a Difference

Economists Casey B. Mulligan and Charles G. Hunter found in a 2001 study that only one of every 100,000 votes cast in federal elections, and one of every 15,000 votes cast in state legislative elections “mattered in the sense that they were cast for a candidate that officially tied or won by one vote.”

Their study of 16,577 national elections from 1898 through 1992 found that one vote had only influenced the outcome of one election. It was the 1910 election in New York’s 36th Congressional District, won by a Democrat who claimed 20,685 votes to the Republican candidate’s 20,684.

Of those elections, the median margin of victory was 22 percentage points and 18,021 actual votes.

Mulligan and Hunter also analyzed 40,036 state legislative elections from 1968 through 1989 and found only seven that had been decided by a single vote. Of those elections, the median margin of victory was 25 percentage points and 3,256.5 actual votes.

In other words, based on this research, the chance that your vote will be the decisive or pivotal one in a national election is almost zilch. The same goes for state legislative elections.

Chances That One Vote Can Make a Difference in a Presidential Race 

Researchers Andrew Gelman, Gary King, and John Boscardin estimated the chances that a single vote would decide a U.S. presidential election to be 1 in 10 million at best and less than 1 in 100 million at worst.

Their work, titled Estimating the Probability of Events That Have Never Occurred: When Is Your Vote Decisive? appeared in 1998 in the Journal of the American Statistical Association. “Given the size of the electorate, an election where one vote is decisive (equivalent to a tie in your state and in the electoral college) will almost certainly never occur,” Gelman, King and Boscardin wrote.

Still, the odds of your one vote deciding a presidential election are still better than your odds of matching all six numbers of Powerball, which were smaller than 1 in 292 million.

What Really Happens in Close Elections

So what happens if an election really is decided by a single vote, or is at least pretty close? It’s taken out of the electorate’s hands.

Stephen J. Dubner and Steven D. Levitt, who wrote Freakonomics: A Rogue Economist Explores the Hidden Side of Everything, pointed out in a 2005 column in The New York Times that extremely close elections are often settled not at the ballot box but in courtrooms.

Consider President George W. Bush’s narrow victory in 2000 over Democrat Al Gore, which ended up being decided by the U.S. Supreme Court.

“It is true that the outcome of that election came down to a handful of voters; but their names were Kennedy, O'Connor, Rehnquist, Scalia, and Thomas. And it was only the votes they cast while wearing their robes that mattered, not the ones they may have cast in their home precincts,” Dubner and Levitt wrote.

When One Vote Really Did Make a Difference

The races won by a single vote, in addition to the new 1910 Congressional election in New York, according to Mulligan and Hunter, were:

  • A 1978 race for Rhode Island state Senate was tied at 4,110 votes and decided by a second runoff election. So was a 1980 race for New Mexico state House, at 2,327 votes for each candidate.
  • A 1982 state House election in Maine in which the victor won 1,387 votes to the loser’s 1,386 votes.
  • A 1982 state Senate race in Massachusetts in which the victor won 5,352 votes to the loser’s 5,351; a subsequent recount later found a wider margin.
  • A 1980 state House race in Utah in which the victor won 1,931 votes to the loser’s 1,930 votes.
  • A 1978 state Senate race in North Dakota in which the victor won 2,459 votes to the loser’s 2,458 votes; a subsequent recount found the margin to be six votes.
  • A 1970 state House race in Rhode Island in which the victor won 1,760 votes to the loser’s 1,759.
  • A 1970 state House race in Missouri in which the victor won 4,819 votes to the loser’s 4,818 votes.
  • And a 1968 state House race in Wisconsin in which the victor won 6,522 votes to the loser’s 6,521 votes; a subsequent recount found the margin to be two votes, not one.
View Article Sources
  1. Mulligan, Casey B., and Charles G. Hunter. "The Empirical Frequency of a Pivotal Vote." National Bureau of Economic Research, Nov. 2001.

  2. Gelman, Andrew, et al. “Estimating the Probability of Events That Have Never Occurred: When Is Your Vote Decisive?” Journal of the American Statistical Association, vol. 93, no. 441, Mar. 1988, pp. 1–9.

  3. "Prizes and Odds." Powerball.

  4. Dubner, Stephen J., and Steven D. Levitt. "Why Vote?" The New York Times, 6 Nov. 2005.