Ten Miles Square


July 30, 2012 12:45 PM The Electoral College Favors Voters in Small States (On Average), Not Large States

By Andrew Gelman

Jonathan Bernstein writes:

The big, urban states traditionally did very well in the electoral college… . New York used to be a major swing state; California also was very contested once it became large, and even Texas had a run as a competitive state with big cities for a while. For whatever reason, all of that has slipped some over the last twenty or thirty years … Still, all else equal, a presidential candidate would rather pander to a large state with lots of winner-take-all electoral votes than a small one, which should tend, over time, to balance out the small-state advantage in the Senate.

I think this is wrong and I suspect Bernstein’s claims are based on casual reflections rather than a systematic study of the data. My colleagues and I have published three papers on the electoral college:

[2009] What is the probability your vote will make a difference? {em Economic Inquiry}. (Andrew Gelman, Nate Silver, and Aaron Edlin)

[2004] Empirically evaluating the electoral college. In {em Rethinking the Vote: The Politics and Prospects of American Election Reform}, ed. A. N. Crigler, M. R. Just, and E. J. McCaffery, 75—88. Oxford University Press. (Andrew Gelman, Jonathan N. Katz, and Gary King)

[1998] Estimating the probability of events that have never occurred: When is your vote decisive? {em Journal of the American Statistical Association} {bf 93}, 1—9. (Andrew Gelman, Gary King, and John Boscardin)

We have consistently found three things:

1. In the ultimate election outcome, the electoral college generally matches the popular vote winner pretty closely: if a candidate wins 51% of the popular vote, he typically has about a 95% chance of winning the electoral college.

2. The electoral college benefits voters in certain swing states, which vary from election to election (for example, Vermont was a swing state in 1992 but is not a swing state now).

3. On average, the electoral college benefits voters in small states, in the sense that an individual voter in a randomly-selected small state is more likely to have a decisive vote, compared to an individual voter in a randomly-selected large state. With a national popular vote, of course, all votes are equally likely to be decisive.

Thus, compared to a national popular vote, under the electoral college a presidential candidate would rather pander to a small state, not a large state as Bernstein claims. But, again, this is on average. New Mexico and Utah are both small states but only one of them is going to be competitive in 2012.

P.S. Here are some graphs from the above papers (click for larger versions). Here’s 2008:

Here’s another look at the 50 states:

Here’s 1952-1988 (excluding 1968), averaging across states to get a look at how Pr(decisive) varies by state size:

The above are all showing Pr(decisive), which is from the voter’s perspective, but it’s the exact same story from the campaign’s perspective, it just gets directly translated into the probability that a campaign will change the election outcome by persuading one person to change his or her vote (or by persuading two supporters to turn out to vote), or 1/1000 the probability that a campaign will swing the election by persuading 1000 people to change their votes, etc.

[Cross-posted at The Monkey Cage]

Back to Home page

Andrew Gelman is a professor of statistics and political science and director of the Applied Statistics Center at Columbia University.


  • oldgulph on July 31, 2012 3:25 PM:

    The current state-by-state winner-take-all method of awarding electoral votes (not mentioned in the U.S. Constitution, but since enacted by 48 states), ensures that the candidates, after the primaries, will not reach out to about 76% of the states and their voters. Candidates have no reason to poll, visit, advertise, organize, campaign, or care about the voter concerns in the dozens of states where they are safely ahead or hopelessly behind.

    Presidential candidates concentrate their attention on only a handful of closely divided "battleground" states and their voters. There is no incentive for them to bother to care about the majority of states where they are hopelessly behind or safely ahead to win. 9 of the original 13 states are considered “fly-over” now. In the 2012 election, pundits and campaign operatives agree, that, at most, only 12 states and their voters will matter. They will decide the election. None of the 10 most rural states will matter, as usual. About 76% of the country will be ignored --including 19 of the 22 lowest population and medium-small states, and 17 medium and big states like CA, GA, NY, and TX. This will be more obscene than the 2008 campaign, when candidates concentrated over 2/3rds of their campaign events and ad money in just 6 states, and 98% in just 15 states (CO, FL, IN, IA, MI, MN, MO, NV, NH, NM, NC, OH, PA, VA, and WI). Over half (57%) of the events were in just 4 states (OH, FL, PA, and VA). In 2004, candidates concentrated over 2/3rds of their money and campaign visits in 5 states; over 80% in 9 states; and over 99% of their money in 16 states.

    More than 2/3rds of the states and people have been merely spectators to presidential elections. They have no influence. That's more than 85 million voters, 200 million Americans, ignored. When and where voters are ignored, then so are the issues they care about most.

    The number and population of battleground states is shrinking as the U.S. population grows.

    Policies important to the citizens of ‘flyover’ states are not as highly prioritized as policies important to ‘battleground’ states when it comes to governing.

  • oldgulph on July 31, 2012 3:26 PM:

    Anyone concerned about the relative power of big states and small states should realize that the current system shifts power from voters in the small and medium-small states to voters in the current handful of big states.

    With National Popular Vote, when every vote counts equally, successful candidates will find a middle ground of policies appealing to the wide mainstream of America. Instead of playing mostly to local concerns in Ohio and Florida, candidates finally would have to form broader platforms for broad national support. Elections wouldn't be about winning a handful of battleground states.

    Now political clout comes from being among the handful of battleground states. More than 2/3rds of states and voters are ignored.

    Now with state-by-state winner-take-all laws (not mentioned in the U.S. Constitution, but since enacted by 48 states), presidential elections ignore 12 of the 13 lowest population states (3-4 electoral votes), that are non-competitive in presidential elections. 6 regularly vote Republican (AK, ID, MT, WY, ND, and SD), and 6 regularly vote Democratic (RI, DE, HI, VT, ME, and DC) in presidential elections. Voters in states that are reliably red or blue don't matter. Candidates ignore those states and the issues they care about most.

    Support for a national popular vote is strong in every smallest state surveyed in recent polls among Republicans, Democrats, and Independent voters, as well as every demographic group. Support in smaller states (3 to 5 electoral votes): AK -70%, DC -76%, DE --75%, ID -77%, ME - 77%, MT- 72%, NE - 74%, NH--69%, NE - 72%, NM - 76%, RI - 74%, SD- 71%, UT- 70%, VT - 75%, WV- 81%, and WY- 69%.

    In the lowest population states, the National Popular Vote bill has passed in nine state legislative chambers, and been enacted by 3 jurisdictions.

    Of the 25 smallest states (with a total of 155 electoral votes) 18 received no attention at all from presidential campaigns after the conventions. Of the seven smallest states with any post-convention visits, Only 4 of the smallest states - NH (12 events), NM (8), NV (12), and IA (7) - got the outsized attention of 39 of the 43 total events in the 25 smallest states. In contrast, Ohio (with only 20 electoral votes) was lavishly wooed with 62 of the total 300 post-convention campaign events in the whole country.

  • oldgulph on July 31, 2012 3:27 PM:

    With the current state-by-state winner-take-all system of awarding electoral votes, it could only take winning a bare plurality of popular votes in the 11 most populous states, containing 56% of the population of the United States, for a candidate to win the Presidency with a mere 26% of the nation's votes!

    But the political reality is that the 11 largest states rarely agree on any political question. In terms of recent presidential elections, the 11 largest states include five "red states (Texas, Florida, Ohio, North Carolina, and Georgia) and six "blue" states (California, New York, Illinois, Pennsylvania, Michigan, and New Jersey). The fact is that the big states are just about as closely divided as the rest of the country. For example, among the four largest states, the two largest Republican states (Texas and Florida) generated a total margin of 2.1 million votes for Bush, while the two largest Democratic states generated a total margin of 2.1 million votes for Kerry.

    Among the 11 most populous states in 2004, the highest levels of popular support, hardly overwhelming, were found in the following seven non-battleground states:
    * Texas (62% Republican),
    * New York (59% Democratic),
    * Georgia (58% Republican),
    * North Carolina (56% Republican),
    * Illinois (55% Democratic),
    * California (55% Democratic), and
    * New Jersey (53% Democratic).

    In addition, the margins generated by the nation's largest states are hardly overwhelming in relation to the 122,000,000 votes cast nationally. Among the 11 most populous states, the highest margins were the following seven non-battleground states:
    * Texas -- 1,691,267 Republican
    * New York -- 1,192,436 Democratic
    * Georgia -- 544,634 Republican
    * North Carolina -- 426,778 Republican
    * Illinois -- 513,342 Democratic
    * California -- 1,023,560 Democratic
    * New Jersey -- 211,826 Democratic

    To put these numbers in perspective, Oklahoma (7 electoral votes) alone generated a margin of 455,000 "wasted" votes for Bush in 2004 -- larger than the margin generated by the 9th and 10th largest states, namely New Jersey and North Carolina (each with 15 electoral votes). Utah (5 electoral votes) alone generated a margin of 385,000 "wasted" votes for Bush in 2004. 8 small western states, with less than a third of California’s population, provided Bush with a bigger margin (1,283,076) than California provided Kerry (1,235,659).