In Close Elections, Small-State Voters Have Most Power, Columbia Statistician Tells Presidential Candidates

March 16, 1998

In close presidential elections, voters in small, politically moderate states such as Vermont and New Mexico are more likely to determine the outcome than voters in large states such as California, Texas or New York, according to a study by a Columbia University statistics professor and his colleagues.

Because the electoral college magnifies the influence of smaller states, a voter in those states has a higher probability of affecting the outcome of presidential races. But the state must be politically balanced, the study's authors said, because when vote tallies are close in politically extreme states, like Utah or Minnesota, national elections are unlikely to be cliffhangers.

"The states that are more extreme are where your vote is less likely to make a difference, because it's unlikely a national election would split such an electorate very closely," said Andrew Gelman, associate professor of statistics. "Any presidential vote that split Utah would probably be a Democratic landslide on the national scale, in which case the votes of Utah would be irrelevant anyway."

Even in a small, politically moderate state such as Vermont, the research shows that the probability that a single vote will be decisive in a close national election is less than one in a million. This is not trivial, however, since if a presidential candidate can convince 10,000 voters in the state to switch their votes to him, he will increase his probability of winning the election by one percent.

In addition to Professor Gelman, the authors of the new work are Gary King, professor of government at Harvard, and W. John Boscardin, a postdoctoral researcher at the University of California, Los Angeles, and a former student of Professor Gelman's. The study appears in the March issue of the Journal of the American Statistical Association.

The research shows that statistical analysis can be applied to situations that have never occurred and are extremely unlikely; for example, when one vote changes the outcome of a presidential election. The approach is also useful for estimating unlikely events that have happened, such as a shuttle explosion, or unlikely events that may yet occur, such as a large asteroid collision with Earth.

A commonly-used, but flawed, method to estimate probabilities is to multiply together the estimated probability of each event in a series, even though each step might not be independent of the others. Another approach, which is strictly empirical, bases the probability of a future event -- such as a shuttle launch failing -- on the past frequency of the event. But that won't work if the event has never happened.

The authors of the current study adapted aspects of both approaches for their study: they break each event into steps, or precursors, of the event being studied, but try to find empirical evidence that allows them to calculate the probability of each step taking place.

In the election example, for a single vote to decide the presidency, the vote in one state must be tied or within one vote, since the result could be changed either by a voter switching parties or by a nonvoter deciding to vote. Then, that state must be needed in an electoral college coalition to decide the election. By multiplying these probabilities, the authors determined that the chance that one vote will determine the presidency in a close election is in the range of about one in 10 million to one in 20 million, depending on the closeness of the election and the size of the state in which the voter resides.

The finding shouldn't deter people in large states, or anywhere, from voting in national elections, Professor Gelman said. No state has gone for the same party in every postwar presidential election, so there is still considerable volatility in the electoral college, he said. This document is available at Working press may receive science and technology press releases via e-mail by sending a message to

Columbia University

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