Before the election, we computed the probability that a single vote would be decisive in the presidential election, in any state. In addition to answering the perennial question, “does my vote matter?” our goal was to explore the degree to which the Electoral College gives voters in some states disproportionate power.

The probability of one person’s vote being decisive, we found, ranged from roughly one in a million for a resident of New Hampshire — a swing state with a relatively small population — to less than one in one billion in states that are reliably “red” or “blue,” such as New York, California, Kansas, and Oklahoma.

We can use a similar approach to show how the Electoral College increases not just the weight of voters in swing states but the weight of voters of certain ethnicities — based on their distribution across the states. We find that, based on the current distribution of voters of different ethnicities across states, and particularly within swing states, the Electoral College amplifies the power of white voters by a substantial amount.

Our first calculation — the probability of a single resident’s vote making the difference nationally, regardless of ethnicity — is straightforward. You multiply together two factors: 1) the probability that your state is needed for an electoral college win and 2) the probability that the vote in your state is tied, given that its electoral votes are necessary. Take California, for example. There we estimated a probability of over 50 percent that the state's 55 electoral votes would be required for a win. But there was a probability of less than 1 in 10 billion that the vote in the state would be tied, under this scenario.

In contrast, a single voter's probability of determining the election was highest in New Hampshire, where we estimated there was only a 4 percent chance that this state's electoral votes would be a necessary part of a winning coalition. However, in that circumstance there was a 1 in 40,000 chance of your vote being decisive (if the state's electoral votes were to make the key difference). Multiply these together and you get a one in a million chance of a New Hampshirite’s vote being decisive.

One in a million isn't much, but from the standpoint of a political campaign, it's not nothing. Sway 10,000 voters in a one-in-a-million state and you have a 1 percent chance of swinging the election. In a close election like the 2016 presidential race, an effective campaign in several different swing states has a good shot of making a difference, as Donald Trump, and the world, learned on election night.

White voters are overrepresented in swing states

The same approach also lets us introduce ethnicity into the picture, because we know the approximate ethnic composition of voters in each state — the proportion who are white, black, Hispanic, or “other.” We can average this across states and thus compute the average probability of decisiveness for everyone of each of these ethnic groups, across the country.

After running the numbers, we estimate that, per voter, whites have 16 percent more power than blacks once the Electoral College is taken into consideration, 28 percent more power than Latinos, and 57 percent more power than those who fall into the other category.

One can approach the issue in other ways and get similar results. For example, we might look at the ethnic composition of voters in swing states compared with the country as a whole.

Based on our calculations before the election, the five states with the highest voting power per voter were New Hampshire, Colorado, Nevada, Wisconsin, and Pennsylvania. According to exit polls, the voters in these states were 80 percent white, compared with 70 percent in the country as a whole. Or, to take a slightly different tack, after the election the five closest states in percentage vote margin were Michigan, New Hampshire, Wisconsin, Pennsylvania, and Florida. Voters in those states were 73 percent white — again, higher than the nationwide figure.

Let’s try one more approach. According to exit polls, the electorate was 70 percent white, 12 percent black, 11 percent Latino, and 7 percent other. Reweight this by voting power and you get an "effective electorate" that is 75 percent white, 11 percent black, 9 percent Latino, and 4 percent other. That's a big difference, with nonwhites declining from 30 percent of the electorate to 25 percent of the effective electorate.

Exit polls are not perfect. Indeed, our calculations showed the 2012 electorate to be much whiter than was estimated by exit pollsters. But for the purpose of estimating relative voting power, this doesn’t really matter. If we extrapolate our analysis from 2012 and assume the exit polls continue to overstate minorities' share of vote totals, we still find that the Electoral College amplifies the white vote.

For example, suppose we assess the national vote as 75 percent white, 10 percent black, 9 percent Latino, and 6 percent other. Then rescaling by voting power gives an effective electorate that is 79 percent white, 9 percent black, 7 percent Latino, and 4 percent other. Again, whites are overrepresented, and all other groups decline from 25 percent of the voters to 21 percent of the effective electorate.

Campaigns tailor their messages for swing voters, who are not demographically representative

This is important for two reasons. First is simple fairness. Residents of New York or Utah or California or Wyoming can be legitimately annoyed that our votes don't count for much. Since Asian Americans, Native Americans, Latinos, and, to a lesser extent, African Americans, mostly live in non-battleground states with large populations — as Lara Merling and Dean Baker have also noted — the unfairness falls disproportionately on them.

The second reason this is important is that campaigns are influenced by the demographics of the electorate. Candidates campaign hard for swing state voters and have very little motivation to appeal to voters outside of those few states that are going to determine the winner. This year we've been hearing a lot about appeals to white voters. Okay, that makes sense: White voters are in the majority. But swing states make them an outsized majority.

The Electoral College isn’t just a goofy way of cumulating votes that sometimes grants the presidency to the person who gets fewer votes. It also motivates candidates to aim for the segments of voters who are overrepresented in swing states. In 2016, this implied a greater focus on whites, which affected the campaign and may have far-reaching implications on politics and policy.

This is not to cast doubt upon the legitimacy of Donald Trump's Electoral College win (or, for that matter, to highlight Hillary Clinton's plurality in the popular vote). But the disproportionate power of white voters is a statistical fact that has implications for the focus and content of campaigns, and it deserves attention and scrutiny.

Andrew Gelman is a professor of statistics and political science and director of the Applied Statistics Center at Columbia University. He blogs at Statistical Modeling. Pierre-Antoine Kremp is an assistant professor of strategy and business policy at HEC Paris.