Americans do not elect a president. They elect representatives of their state to an electoral college totalling 538 of them distributed to each state according to the size of states’ congressional delegation, reflecting the population of each state. California has 54, New York has 33, the seven least populated states have 3 each. The District of Columbia also has 3. It is a uniquely American institution which then elects the vice president and president.
Isn’t this undemocratic? Why not have a direct election? The political controversy surrounding the Electoral College is as old as the republic. In 1969, Congress started to think so. Nixon had defeated Hubert Humphrey with a popular margin of less than 1 percent. Unlike the crookery of the hanging chads of 2000, the House of Representatives was so shocked that a successful candidate could actually be denied the Presidency that it moved a constitutional amendment to abolish the electoral college. The Senate also inclined to support the amendment, and lawyers of the American Bar Association said the US electoral system was…
…archaic, undemocratic, complex, ambiguous, indirect, and dangerous.
Electing the president by direct popular vote would be simpler and fairer. But the issue lost momentum. In 1976, Jimmy Carter’s narrow victory over Gerald Ford resurrected it. The League of Women Voters and a majority of Americans, according to pollsters, thought the electoral college should be abolished. In the Senate, although the bill had majority support, it died for lack of the two thirds majority needed to pass it.
In spite of recent contentious elections that raised the controversy to new heights, the debate is unlikely to reach a resolution given the compelling political considerations on both sides. But rarely if ever does the public debate on this subject take into account objective, mathematical considerations. Nevertheless, statisticians can make an important contribution to the debate, for mathematicians have made statistical calculations on voting issues since the 18th century, when the Marquis de Condorcet, a French philosopher and mathematician, applied probability theory to voting. In the 1990s, Will Hively, reported that a physicist, Alan Natapoff, had proved the electoral college is better than a simple, direct election, and indeed the success of US democracy depends on it:
Everybody gets this wrong. Everybody. Because we were taught incorrectly.Alan Napatoff
But more recently, UC Berkeley’s Elchanan Mossel, an associate professor in the departments of Statistics and Computer Science and an expert in probability theory, begs to differ. He believes this system of electing the president is more likely to result in an erroneous election outcome compared to the simple majority voting system. Mossel’s analysis compares the Electoral College system with the simple majority voting system to test how prone to error the electoral system and whether it can change the outcome.
Originally the electoral college did not have to choose the winner of the popular vote. In 1888, Grover Cleveland got 48.6 percent of the popular vote and Benjamin Harrison 47.9 percent. Cleveland won by 100,456 votes. The college chose Harrison by 233 to 168. The representatives to the electoral college did not have to vote for Cleveland. They chose Harrison, so he was the winner. In 1824, Andrew Jackson beat his rival, John Quincy Adams, by more popular and more electoral votes—99 to 84. But 78 went to other candidates, so the House of Representatives picked the winner. They did not select Jackson.
In 1876, Samuel J Tilden lost to Rutherford B Hayes by one electoral vote, though he received 50.9 percent of the popular vote to Hayes’s 47.9 percent. An extraordinary commission awarded 20 disputed electoral votes to Hayes. In 1960, John F. Kennedy narrowly beat Richard Nixon in the popular voting, 49.7 percent to 49.5 percent, but Nixon won 26 more states to 24 for Kennedy and others. But Kennedy had won big states, and won the electoral ballot, 303 to 219. A close popular majority had turned into a big electoral college majority.
James Madison, chief architect of the US’s electoral college, wanted to protect the people against the tyranny of the majority—a built in majority for some bloc destroying tolerance so that minorities were no longer free. Madison explained in The Federalist Papers X that a well constructed union must break and control the violence of factionalism especially the force of an overbearing majority. J S Mill explicitly warned of the same thing in his later essay On Liberty.
In any democracy, a majority’s power threatens minorities. It threatens their rights, their property, and sometimes their lives. Madison and his colleagues, having won the war of independence, wanted an electoral college to avoid internal revolutions, so built a system which made representatives of each state intermediary voters. The representatives, they expected, would be responsible middle class people, like themselves, who would vote for a president like themselves, and so stability would be guaranteed. They were aiming to stifle the “popular will”—they distrusted the mob.
Nowadays, whoever wins the popular vote in any state (except in Maine) wins all the electoral votes in that state automatically, so whole states become blue or red ones, and the large states carry more weight. The representatives to the electoral college have no independence. They must vote according to their state’s popular vote. It means that the popular vote in a few states can overwhelm many others who might dissent. Actual representatives are superfluous. Each state gets a weighted vote for the presidency based on its weighting and the popular vote in it. If the Madisonian system had any original merit by requiring candidates to win states on the way to winning the nation, it has now been neutralized into a series of popular votes, many of which matter only when the large states balance themselves out. So, the votes in small states and states which go against the trend can only matter on the odd occasions when by chance the large states neutralize each other’s votes.
Natapoff looked into the math, and convinced himself, the US electoral system increases voters’ power. The same logic that governs our electoral system, he saw, also applies to many sports—which Americans intuitively understand. In baseball’s World Series, the team that scores the most runs overall does not get to be champion. To do that, a team has to win the most games. In 1960, the New York Yankees scored more than twice as many total runs as the Pittsburgh Pirates, 55 to 27. Yet the Yankees lost the series, four games to three. The Yankees won three massively (16-3, 10-0, 12-0), but lost four close games. Napatoff says:
Nobody walked away saying it was unfair.
Runs must be grouped in a way that wins games, just as popular votes must be grouped in a way that wins states. In sports, we accept that a true champion should be more consistent than the 1960 Yankees. A presidential candidate worthy of office, by the same logic, should have broad appeal across the whole nation, and not just play strongly on a single issue to isolated blocs of voters.
Napatoff argued that under a tyranny, everyone’s voting power is equal to zero. Equality of the vote is not enough. Mossel agrees:
Statistically, the most robust system in the world is a dictatorship. Under such a system, the results never depend on how people vote.
But since most people would prefer an alternative to dictatorship, the question is which democratic voting system will produce accurate results. To that end, Mossel compared different voting systems, including simple majority voting and the Electoral College system, both of which offer voters two alternatives to pick from.
A well designed electoral system might include obstacles to thwart an overbearing majority. But direct, national voting has none. In a democracy, as a nation gets larger, everyone’s voting power shrinks. So, the immense size of the US electorate means everyone’s individual vote is of negligible weight, and only counts a little more when the voting in the big states turns out to be tight. In large democracies, with massive electorates, each person’s voting power in direct elections is virtually zero!
Napatoff says people are less vulnerable to tyranny when their voting power increases, and individual voting power is higher when funneled through districts—such as states—than when pooled in one large, national, direct election. Anyone's vote has more chance to determine the outcome locally, in one's state, and thereby anyone has more chance to change the outcome of the electoral college, than when one's your vote is among the many more of a direct federal election. He concludes a voter has more power under the current US electoral system.
Under raw voting in a divided society, a candidate wants to woo a bloc large enough to be the majority. In a two person or two party situation, where each party represents blocs on the right and left respectively, given that neither can expect an overall majority only from its core supporters, then both have to woo the floating voter caught between the two, usually those in the center. Some think this makes for constancy and stability, but it makes for a lot of frustration on both wings., and that is being felt today as the US polarises.
The probability that anyone’s vote will turn the election is the probability that all the other votes balance out. In a small town with 135 citizens, the probability any vote will be decisive because the others are in balance can be calculated as 6.9 percent. The 1960 presidential race between Kennedy and Nixon was one of the closest ever. A deadlock would have been 34,167,371 votes for Kennedy and for Nixon. Kennedy got 34,227,096 to Nixon’s 34,107,646. The chance of one vote being decisive is minuscule.
Unfortunately, in such a case, the electoral college system has little or no advantage. Districting never boosts voting power in close elections, the time when you hope it might. It does not help any electorate of any size when the contest is perfectly even. Doing the math shows it slightly reduces individual power. Abolition of the electoral college as it now operates would improve democracy when the votes are close.
When one party or candidate has a landslide, the electoral college, Natapoff says, strengthens the individual vote a little. For a town of 135, the notional crossover point for voting power is about a 55-45 percent split in voter preference between two candidates. In any contest closer than this, voters would have more power in a simple, direct election. In any contest more lopsided than this, district voting will give individual voters more power—but it matters less, because the result is so lopsided it cannot be affected by one vote anyway! In that town of 135 citizens, when voter preference for one candidate is 55 percent, the probability of deadlock, and of anyone's vote turning the election, falls below 0.4 percent. The probability that one vote will matter keeps on falling, as a candidate pulls further ahead. For all that math, there is less chance of changing the outcome. Natapoff says:
If candidate A has a 1 percent edge on every vote, in 100,000 votes he’s almost sure to win. And that’s bad for the individual voter, whose vote then doesn’t make any difference in the outcome.
One can imagine an extreme case of district voting where every voter is in a district of their own. Plainly the district voting model becomes the same as a direct election. So extreme districting is no different from direct election, whether the voting is lopsided or close—districting cannot help when the election is heavily skewed, and, as we saw, it is no advantage when the election is close.
So, when one candidate gains an edge over another, a 1 or 2 percent change in the electoral college system hugely reduces anyone’s chance of changing an election with their solitary vote, and candidates have less incentive to keep the losers happy. We have what Madison wanted to avoid. The larger the electorate, the more telling a candidate’s lead becomes, so the best idea is not to allow large elections. That is an advantage of dividing the national election into smaller, state contests, but today the states themselves are mainly far too big for this to matter.
The United States is not a perfectly districted nation. States vary enormously in size. The more lopsided the contest, the smaller each district, or state, needs to be to give individual voters the best chance of a local deadlock. So in close elections, voters in larger states would have more power, in lopsided elections, voters in smaller states would.
Either the national electorate has to be divided into smaller sizes, preferably all nearer the same size, meaning large and intermediate states themselves have to be split into national voting districts about as big or smaller than the smallest states today, or the electorate must have a greater choice of responses. With a lot of small voting districts, the candidates have a lot more chance of losing and the voting pattern comes more into balance, and, of course, the votes count for more.
But a similar effect can be had in a single national vote by allowing voters to vote for more people, the list of candidates being opened up from just two, to several. By having an alternative vote or, better still, a single transferable vote, everyone can still vote for their preferred candidate, but they can also vote for the others in order of preference, their second and third choices, all the way down the list…or not, just as they wish. When no one has an absolute majority, the least popular candidate drops out and his second choices are redistributed, successively until there is an overall winner. The modern automatic telling machines now used in the USA makes transferable voting (STV) practicable, when once it would not have been.
Natapoff says, the point of districting is to reduce the death grip of blocs on the outcome. But small districts which the math says give a notionally better chance of a tie, so that the individual vote counts, also make it easier for a bloc of big enough size to form and dominate the election.
Mossel’s assumption is that any voting model is subject to error, meaning that the vote cast by a small number of voters in each election will end up being recorded differently from what those voters intended. This may be due to human error, hanging chads, or voting machines that flip some vote randomly.
In 1899, W F Sheppard found that majority voting has an error on a given vote of its square root. So, if the error—say a faulty voting machine—is 1 in 10,000, the chance that the result of the election will be changed is roughly the square root, or 1 in 100. In a landslide election such unfortunate occurrences make no statistical difference. But in a close election, such errors may wreak havoc, even without our knowledge. Mossel uses advanced mehtods like Gaussian analysis, and isoperimetric theory, but he finds that the answer is unequivocal:
We don’t have the best system. Isoperimetric theory tells us majority voting method is optimal. It is the most robust.
With Electoral College voting, in essence you’re doing majority twice. First you do majority in each state and then you do the majority of the majority, so you take the square root of the square root. So you take square root of 1/10,000 once and get 1/100, and then you take square root again and get 1/10.
The Electoral College appears to fail miserably based on the robustness to error criteria, and in comparison with direct elections. If the democratic ideal is for the outcome to reflect the intent of the voter as much as humanly possible, then the analysis suggests a change is needed. If Americans want the best electoral system, they should change the electoral college method to a direct election for president, and to try to achieve Madison's aims, should have multi candidate elections by alternative vote or preferably single transferable vote.