The Electoral College May Not Actually Help Smaller States

(Bloomberg Opinion) -- On Sept. 9, 1970, Oklahoma Republican Henry Bellmon stood on the U.S. Senate floor and complained that the Electoral College worked to the disadvantage of less-populous states. His reasoning:

. As long as a voter in California is a means by which a candidate for President may hope to win 40 electoral votes and when a voter in the State of New York is a means whereby a candidate can win 43 electoral votes, those votes are going to be more important to the candidate than the votes of citizens in a State like Oklahoma where the candidate can hope to gain only eight electoral votes or, perhaps under the new census, only seven votes.

. Nowadays California has 55 electoral votes and New York 29 (which adds up to one more than they together wielded in 1970), while Oklahoma has seven. The Electoral College seems to have become a lot more popular with Oklahoma Republicans, though! Getting rid of it, or circumventing it via a National Popular Vote Interstate Compact , would reduce Americans outside of large metropolitan areas to “serfdom,” Trent England, executive vice president of the right-leaning Oklahoma Council of Public Affairs, wrote in USA Today a couple of weeks ago. “The Electoral College requires more than just the most raw votes to win — it requires geographic balance,” England continued. “This helps to protect rural and small-town Americans.”

. England’s argument that having your vote count the same as everybody else’s amounts to serfdom is of course a tad contentious. But his belief that voters in less-populous states — and by extension in rural and small-town America — are given more clout by the Electoral College than they would have in a nationwide direct vote is shared these days by Americans across the political spectrum. Understandably so: States are apportioned electoral votes equal to their representation in the House of Representatives and Senate, which means that smaller states get more electoral votes relative to their populations than bigger states do. Low-population states are also overrepresented in the ranks of the states with high percentages of rural residents , as classified by the Census Bureau. And in 2000 and 2016, presidential candidates who led in most rural areas and smaller states and trailed in urban areas lost the popular vote but won the presidency thanks to the Electoral College.

. Yet, as I learned while working on a column earlier this year about the nearly successful late-1960s/early-1970s campaign to replace the Electoral College with a direct vote, the consensus then was that the Electoral College favored large states and cities. Why did everybody change their minds? Political circumstances and political expediency explain a lot of the shift, but in 1970, Bellmon and other politicians were also under the influence of a then-new academic theory of voting power that offered strong backing for the view that big-state votes count for more. That theory has since been subjected to repeated critiques and tweaks, and I think it’s fair to say that expert opinion no longer holds that voters from big states get a big advantage in the Electoral College. But it doesn’t really support the notion of a reliable small-state advantage, either, and it certainly does not imply that Oklahomans’ clout is amplified by the Electoral College: One estimate just before the 2016 presidential election put an Oklahoma voter’s likelihood of affecting the outcome at a lowest-in-the-nation 1 in 30 billion.

. This likelihood of affecting the outcome is at the heart of the voting-power theory that appears to have first been expounded in 1946 by British geneticist L.S. Penrose, but it didn’t get much attention until the 1960s. That’s when John Banzhaf, a young American lawyer and engineer who subsequently became a professor at George Washington University Law School, came up with it independently, described it in a law review article with the title “One Man, 3.312 Votes: A Mathematical Analysis of the Electoral College,” and testified about his findings before the House and Senate committees that were then considering a constitutional amendment to ditch the Electoral College.

. In a one-person, one-vote election, everyone’s voting power is equal. But when individuals or blocs control differing numbers of votes, as with corporate shareholders, the Council of the European Union or the Electoral College, what matters is a bloc’s likelihood of casting the deciding vote. Penrose showed that the bigger blocs’ voting power, measured this way, is usually a bit higher than their share of the overall votes. A simple way to think about this is a body with nine total votes in which Bloc A has five votes, Bloc B three and Bloc C one. Bloc A has 55% of the votes but 100% of the voting power, since no winning combination can be assembled without it. Real-world voting-power calculations tend to be a lot more complicated than that, but they also deliver results in which voting power is not equal to percentage of total votes and the biggest blocs usually (although not always; if several big blocs have the same number of votes, for example, their clout may be diminished) get an outsized share of the power.

. In 1968, Banzhaf calculated that the voting-power effects created by the winner-take-all nature of how most Electoral College votes are awarded by the states gave big-state voters a huge advantage. The “One Man, 3.312 Votes” of his title was the estimated edge in voting power that a resident of New York held over a resident of the District of Columbia. The District is limited by the Constitution to only as many electoral votes as the least-populous state, which shortchanged it relative to its population in the 1960s, so a better measure might be New York’s advantage over Maine, the state where residents had the least per-person voting power, which was a still-substantial 2.79.

. These calculations were based on a model in which state vote margins fluctuated randomly and narrowly around a mean of zero. A side effect, thanks to the statistical law of large numbers, was that high-population states would tend to have closer elections than small-population ones, which further boosted the likelihood that a resident of a large state would cast the deciding vote. At the time, this may have seemed like a reasonable assumption. The five states with the most electoral votes in the 1960s — New York, California, Pennsylvania, Illinois and Ohio — were all seen as battlegrounds that both Democratic and Republican candidates had a shot at winning, and some thought this competitiveness was an inevitable result of their size and diversity. “Given vigorous party competition, which is the prevailing condition in the big states, cohesive groups, voting substantially en bloc, are capable of determining the result,” constitutional scholar Alexander M. Bickel wrote in 1971 . “A portion of the popular vote in smaller, more homogeneous states is, very often, simply wasted.”

. The states with the most electoral votes are now California, Texas, Florida, New York, Illinois and Pennsylvania (those last two are tied for fifth). Texas has voted Republican in every presidential election starting with 1980, while New York has voted Democratic since 1988 and California and Illinois since 1992, leaving only two of the six biggest states as presidential battlegrounds in recent elections. Meanwhile, Banzhaf’s assumptions about state vote margins have come under fire on both theoretical and practical grounds. The most persistent critic has probably been Andrew Gelman, the prominent and prolific Columbia University professor of statistics and political science. Together with Jonathan N. Katz and Francis Tuerlinckx, Gelman showed in a 2002 journal article that percentage vote margins in large and small states had been similar from 1960 to 2000. The trio also calculated voting power using state vote margins derived from pre-election forecasts and actual election results for every election from 1952 to 1992, finding a slight advantage for voters in the very smallest states (because each state, no matter how small, gets at least three electoral votes), but with by far the largest differences depending not on state size but on how close state vote margins are to the national average.

. That is, when an election is close nationally, the states where people have the most chance of affecting the election outcome are the states where the election is close. You probably did not need a statistical analysis to tell you that, but it is lots of fun to look through the numbers that Gelman’s models churn out. Using data available before the 2008 election, he, Nate Silver and Aaron Edlin estimated that voters in New Mexico, Virginia, New Hampshire and Colorado had the highest probability of determining that year’s outcome, at approximately 1 in 10 million, while in California, New York and Texas, the odds were closer to 1 in a billion, and in several smaller states with strong partisan leans, they were “nearly zero.” Just before the 2016 election, Gelman estimated that voters in New Hampshire and Colorado had the highest probability of determining the outcome, at 1 in a million, while those in Oklahoma had the lowest, as I have detailed above, and Wyoming (the least-populous state) the second-lowest.

. When I ran those numbers by Trent England, the Oklahoma think tanker whose op-ed I cited above, his email response was, in part:

. I think the stats on the odds of being the one decisive voter are a bit silly. If elections are just about that, then really nobody should vote in any big country. The more important questions are about how campaigns are shaped and party coalitions constructed. Those are harder to quantify, more interesting, and matter much more.

. When I pressed England on how exactly he thought the Electoral College shaped campaigns, he responded that “the 2000 and 2016 elections show that if one of our parties has an urban base, the EC makes it harder to win with just that base.” As noted above, this is perhaps a reasonable reading of the evidence from those two elections. It is also perhaps a reasonable description of the workings of the rest of the U.S. political system: In his new book “Why Cities Lose: The Deep Roots of the Urban-Rural Politics Divide,” Stanford University political scientist Jonathan A. Rodden argues that the deck is stacked against cities by not only the U.S. Senate’s explicit small-state bias but also a de facto bias produced by first-past-the-post U.S. House and state legislative races and geographically concentrated urban voters.

. Thanks to the countervailing power advantage of big blocs of votes and other complications, though, the Electoral College’s tilt isn’t quite as straightforward as all that. Nicholas Miller, an emeritus professor of political science at the University of Maryland, Baltimore County who has written extensively on these matters , estimated that the Electoral College was actually aligned in the Democrats’ favor in 2008 — that is, Barack Obama would have won even if he had trailed John McCain slightly in the popular vote. Weeks before the election in 2012, polls pointed in the direction of just such an electoral-popular split between Obama and Mitt Romney. Which, if it had happened, would surely have generated endless op-eds from Republicans decrying the Electoral College as a subversion of democracy and (fewer, but definitely some) from Democrats extolling it as evidence of the genius of the Founders.

. It’s easy enough to look back at a presidential election and determine how the Electoral College hurt or helped your side. It’s a little harder, but far from impossible, to come up with reasonable suppositions about which states will play a more or less decisive role in an impending election. Determining who the Electoral College helps or hurts over the long run, though, may be too tough a puzzle for anyone to solve. As Josiah Neeley, a Texas-based senior fellow at the R Street Institute, a conservative/libertarian Washington think tank, tweeted in March:

. The Founding Fathers were suspicious of vulgar democracy. That's why they designed a system where 95% of the time the candidate with the most votes wins, while in 5% of elections the 2nd highest vote getter randomly wins instead.

. That sounds about right. The best way to think of the Electoral College may be as a wrench that occasionally gets thrown into the works of American presidential elections, delivering a result that is at odds with the popular vote. I would beware of becoming too confident that said wrench is on your side.

. It begins on page 75 of this PDF edition of that day's Congressional Record.

. The Census Bureau defines as rural as everybody who doesn't live in a densely settled community of 2,500 or more. It's worth noting that the rural population of the five smallest states in 2010 was still smaller than the rural population of the largest state, California, while the rural population of the 10 smallest states fell short of that of the second-largest, Texas.

. Game theorists Lloyd Shapley and Leonard Shubik constructed a voting-power index in 1954 that delivers similar results by different means and was for a time more popular with political scientists than the Penrose method, but political scientist Dan Felsenthal and mathematican Moshé Machover seem to have won most everybody over to the latter with a 1998 book and 2004 journal article on voting power.

. Simply because Democrats seem on the whole less prone to make genius-of-the-Founders arguments.

. Neeley's tweets delete automatically after a couple of months, but there's a cached version currently still available from Google and Neeley told me he's fine with having it preserved for posterity.

. To contact the editor responsible for this story: Brooke Sample at bsample1@bloomberg.net

. This column does not necessarily reflect the opinion of the editorial board or Bloomberg LP and its owners.

. Justin Fox is a Bloomberg Opinion columnist covering business. He was the editorial director of Harvard Business Review and wrote for Time, Fortune and American Banker. He is the author of “The Myth of the Rational Market.”

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The Electoral College May Not Actually Help Smaller States