Dragging the Electoral College into the 21st century
a.k.a.  Introducing the Proportional Electoral College

Introduction

The American Electoral College is controversial, and not without reason. It is arguably undemocratic, and results in a peculiar situation where a few swing states receive intense focus, while undisputed states are all but ignored, and the minority party in them has no voice.

However, the College has its defenders. Its argued benefits include preventing low-population states from being disregarded, localizing electoral idiosyncracies and voting irregularities to the state they occur in, and maintaining America’s federal character.

There are frequent calls to replace it with a popular vote. Support for this is (perhaps sadly) often partisan: e.g., the current National Popular Vote initiative has won support of Democrat-heavy states, likely due to the perception it would benefit Democrats; some might withdraw if it turns out to help Republicans.¹ In any case, change is difficult.

Feasibility aside, the arguments for the College strike me as having merit but not enough to balance the problems noted above.

But perhaps we can salvage the Electoral College as specified in the Constitution and adapt it to be more democratic, equitable, and modern.

The proposal

Our understanding of voting theory and the mathematics of elections has advanced considerably in the last 240 years. The notion that whoever gets the most votes is the people’s choice can be seen as simplistic and, well, wrong. There are well-understood phenomena such as vote-splitting, spoiler effects, and compromise voting. Thus, throwing all of a state’s weight behind the candidate with the plurality of its votes is logically suspect.

Maine and Nebraska have implemented a scheme along the right lines, called the “congressional district method”. Two “at-large” electors are assigned to the candidate who has won the state by a plurality, and then one elector each is assigned to the plurality winner of each congressional district. (For those that don’t know, the number of electors a state has is equal to its number of senators (always two) plus its number of representatives (roughly proportional to population). Also, the Constitution does not require any particular method for a state to choose its electors.)

However, districting itself is (or deserves to be) somewhat archaic. Districts are not natural cultural boundaries, but drawn after each census to divide the population evenly, and sometimes shaped (“gerrymandered”) to favor the party in power. The Constitution mandates their use for the House of Representatives, but they needn’t be used for allocating electors.

ELECTORS

 

allocated proportional to votes

“at-large”

to winner of state

A more logical and modern system is proportional representation, where representatives are allocated in proportion to the votes received. Thus, a candidate with twice as many votes will get roughly twice as many electors. No longer can a candidate’s support be stuffed into one district.

My proposal is therefore this: Two at-large electors are assigned to the plurality winner of each state, and the remainder of that state’s electors are allocated in proportion to the candidate’s votes received. This will be called the Proportional Electoral College, or PEC, and is diagrammed on the right.

Apportionment

You can skip this section if you don’t care about the math.

There are a few algorithms in use for apportioning representatives, often designed to meet certain criteria.² The method I find most suitable was first developed by Thomas Jefferson³ and is also known as the d’Hondt method or the method of greatest divisors, and is used for elections in many countries.

For each state one chooses a quota, which is the number of votes a candidate needs to receive one elector. That is, for each candidate

The partial bracket means one should always round down.

A first guess would be that the quota should be the total number of votes divided by the number of electors to be assigned. However, this will usually under-assign electors because of the remainders. We thus reduce the quota till we get the required total. Any number of a range of quotas might suffice; all will give the same result.

The quota does not even need to be a whole number⁴, although in a large election it usually can be. There is the theoretical but unlikely possiblity of a tie, where no value for the quota will work, and a tie-breaker will have to be used.⁵

I will illustrate with the 1980 election in Ohio. Incumbent Carter ran as a Democrat; Reagan ran as the Republican, while Anderson, who lost the primary to him, launched an independent run; Ed Clark was the Libertarian. All other candidates combined got only about 21,000 votes. Ohio had 4,283,603 votes cast and 25 electoral votes. We proceed as follows:

Thus the final elector counts will be Reagan 14, Carter 10, Anderson 1.

Note that the quota could be as high as 175,214 (above which Carter’s allocation drops to 9) and as low as 169,735 (below which Reagan’s increases).

If you want to try your hand at this, New York had 41 electoral votes, with Reagan receiving 2,893,831 votes, Carter 2,728,372, Anderson 467,801, and Clark 52,648. How many electors would each win under PEC? What would a suitable quota be?

Another algorithm for getting the same result does not require successive guessing, but may be less self-explanatory: Start with each candidate’s vote count; this will be their starting “score”. At each step assign one elector to the candidate with the highest score, then replace their score with the vote count divided by the next higher number (first 2, then 3, etc.). Here is this algorithm applied to the above election, with the order of the steps numbered (and the scores rounded to whole numbers):

We stop at the underlined score, when all 23 non-at-large electors are assigned.

One can read off the allowable quotas from this tableau: The highest score from the last column is the cutoff where the quota is too low, while the lowest score from the second-last column is the highest possible quota.

An example election

Here is how the 2012 election would be tabulated under PEC:

The electoral difference is smaller, as often happens when moving away from winner-takes-all. But the gap is harder to close. For instance, even if Romney had swung Florida, Ohio, and Virginia to narrow victory (and the latter two were not that close), that would only be 8 electoral votes, not enough.

A minimum win path for Romney would be multifaceted. If he could convert⁶ only 1,060 Obama voters in New York, he’ll pick up one more electoral vote there (so it’s only 19–10 for Obama); another 1,555 conversions in Idaho get one more. Next would be 5,691 in Pennsylvania, and from there it gets harder. 19,822 votes in New Hampshire will net him two electoral votes, and 37,155 in Florida will gain three. And so on.⁷

Meanwhile, there are places for Obama to pad his lead; for example, taking 1,411 votes in Oklahoma would net him one more elector, and the next easiest would be 8,507 votes in Tennessee.

We see this is all over the map and not easy to predict, quite unlike focus on a few “swing states”. Voters in most states will therefore know that their vote might matter.

Some justifications

It may seem some states will still get ignored. For solid states with only 3 electors, that is true, but this can’t really be helped; and, they’re already benefiting from heavy representation. But while one might think that solid states with (for example) 4 electors will rarely be contentious because it’s hard for a candidate to have a 2:1 lead, that is not the case. For example, in 2012 Obama would have won all 4 of Hawaii’s electors, and Idaho (currently a solid state largely ignored) splits 3–1 above, but as noted Romney was 1,555 votes from 4–0.

As an extreme case, in 1932 Georgia’s 12 electoral votes could all go to Roosevelt:

One may ask why have the two at-large votes at all, rather than have all electors assigned proportionally. There are several reasons. First, there is and should be a significance to “winning a state” in a federal system, and voters will certainly feel this should count for something; otherwise, for example, a state with 4 electoral votes might always split 2–2, regardless of who wins. The scenario where no candidate gets a majority of electoral votes is less likely. It also lends the stability defenders of the Electoral College value, by raising the bar for fringe parties to make headway. Finally, it makes this a less extreme departure from the established College.

An extended discussion comparing to a popular vote is in an appendix.

Caveats about past elections

I shall be examining how past elections would have resulted under PEC. However, there are the obvious qualifications that voting and campaigning patterns could have been completely different had another election system been in use.

Three major effects: (1) Voter turnout might be different; for instance, people in swing states are more likely to vote than those who perceive their vote won’t matter. (2) Voters may be more inclined to symbolically choose a third-party candidate in an uncontested state. (3) Campaigning and issues emphasized may be wholly different depending on which states are key.

Effect (1) would matter more with a popular vote, but since this counts each state separately, we only need turnout to be representative. For (3) the effects of the candidates’ different campaigning may be guessed to approximately cancel out. And for (2) third-party runs are not usually significant, and when they are it’s not clear how much voters strategically choose them. So in summary I expect the retroactive calculations to be good approximations, but not perfect.

There are also elections where the vote was compromised by fraud or even violence. But we can do little about that now, and so I work with the available numbers. I also don’t account for occasional “faithless electors”, since that is outside the topic of counting systems.

Case study: Landslides

A landslide election is when one candidate overwhelmingly triumphs over another. Three of the biggest are those of 1936, 1972, and 1984, in each of which the opposing candidate won only two states.

Such a landslide, with a huge electoral vote margin, may give the impression the other candidate had almost no support. However, looking at it with a more proportionate scheme is perhaps illuminating:

The electoral differences are less extreme, although the results are still decisive.

Note also that some third-party candidates that got no electoral votes in real life manage to get on the board.

Case study: Multi-way races

Two modern elections had five candidates with PEC votes:

Still, the third-party candidates were clearly minor forces. For an election with multiple competitive candidates, consider 1912:

T.R. returned to run four years after turning over the reins to Taft. This may have split the vote; had Taft and Roosevelt votes been combined, they would win 279–240–12. To be a bit silly, if furthermore Eugene Debs’ votes had gone to Wilson, the latter wins with 272–259, showing the socialist’s potential relevance in the election. As it is, Wilson still wins comfortably.

Another election with four live candidates is 1948:

Progressive Henry Wallace (not to be confused with later candidate George Wallace) is barely on the board. Truman’s victory is tighter under PEC, which better reflects that the election was close.

Finally, here is a non-modern election with perhaps five live candidates:

South Carolina chose its electors by legislature, all given to the hopeless Willie P. Mangum, who was not even on the ballot anywhere else. Since there is no poll data my reconstruction does the same, although a vote would probably not give this result. Similarly, Daniel Webster was on the ballot only in Massachusetts. Hence, this is rather unlike a modern election.

Martin Van Buren still wins, but barely.

Spoilers and electoral majority

A candidate can draw votes from another with a similar audience, splitting the vote so that both have a poor showing, the so-called “spoiler effect”. With the winner-takes-all Electoral College this can be severe, as it may lose the entire state. Under PEC the effect is lessened. Splitting may lose the at-large electors, and may lose one elector between them due to splitting one quota, but this is less devastating.

I would also argue that some spoiler effect is desirable, as it provides a disincentive against a huge field of candidates.

The Constitution requires a majority of electoral votes to win—a plurality is not enough—so that splitting electoral votes alone cannot lose the election in the voting phase; a candidate must get more than all others combined. However, if no candidate has a majority, the election is decided by the House of Representatives, which will presumably vote along party lines.

Under PEC, where a majority may be less likely, we may leverage the fact that electors are human beings rather than vote aggregates. Many elections (such as for primary delegates) have multiple rounds of voting. The Electoral College could include rounds of “pre-voting”, and if no candidate receives a majority in a round, the electors are released from their candidate pledges and may choose another. This allows candidates with similar views to combine electors to build a majority.

One expects major-party electors will not change their votes. For third-party candidates, electors for the same candidate might compete in the election on who their second choice would be. We might want an electoral system similar to European party lists, where all votes for electors pledged to the same candidate are combined, and then those with the most votes (however many are won) are chosen for the College.

I don’t have a full account of how a system like this might work, but it seems a promising way to address current electoral anomalies.

Case study: No majority

The strongest third-party showing in recent years was the 1992 run of Ross Perot, whose cross-party appeal won him nearly 19% of the popular vote, which might have been greater were it not for a confusing mid-campaign withdrawal and re-entry. However, he did not win any states and thus failed to secure a single electoral vote. Under PEC, he fares better:

No candidate has a majority. Had the election gone to the House, then, it being solidly Democrat, Clinton would certainly have won. However, with multiple rounds the 71 Perot electors come into play. Many believed Perot cut primarily into Bush’s votes, but some polling indicated Perot voters’ second choice was almost evenly split. In any case, it seems on its face more likely that Clinton could pick up nine Perot electors than that Bush could win 64.

The 1860 election was not just a watershed but illustrative of many voting issues. It is often noted that if all non-Lincoln votes were combined under one candidate, Lincoln with less than 40% of the popular vote would still have won the College, due to the distribution of his support. While Lincoln is today a celebrated president, this is democratically an incongruous outcome. (It is also unrealistic, as there were significant divides between the other candidates.)

Under PEC we get this:

The “fusion” ticket effectively was Breckinridge, giving him 99 total. We see that Lincoln has a plurality but not a majority. A hypothetical combined non-Lincoln candidate would have won 192–111.

With the House under Republican control, a Lincoln victory might still have been inevitable. Preventing it would require 152 electors drawn from all three other sets to agree on a candidate in a round of voting, which in the prevailing climate would have been difficult.

Here are two other elections without a majority:

There is one more, 1960, discussed in the next section.

Case study: Controversy!

We shall here look at three of America’s most contentious elections.

The 2000 election is perhaps the stand-out of our time, with a margin of a few hundred votes in Florida, a protracted court battle, an arguably decisive spoiler, and a divergence from the popular vote outcome.

The last may be the impetus behind the largely Democratic push for a popular vote, rooted in the belief that Gore “would have won” had a popular vote been used. Of course, this is unknowable; if a different system were in use, the whole course of the election would have been different, in ways that could have dwarfed Gore’s small vote lead. Indeed, more equalized turnout between states would have favored Bush.⁸

Under PEC Bush wins with a somewhat higher margin, while third-party Nader gets on the board:

Nader may still be a spoiler; if all of his votes had gone to Gore, Gore wins 271–267. This is not however realistic; some Nader voters might otherwise prefer Bush, or another third-party candidate, or not voting at all.

The election of 1960 was dogged by allegations of vote fraud and even mob involvement to deliver the election to JFK, in particular in Illinois and Texas. Furthermore, three southern states put “unpledged electors” on the ballot, who were directly elected, making PEC reimaginings uncertain. In Alabama and Mississippi the electors were stated to be Democrats, but in Louisiana this was only implied. Here is my PEC attempt:

We see no candidate has a majority, but the unpledged electors, being Democrats, might favor JFK (or not, since they in fact cast protest votes for a hopeless candidate). Perhaps Nixon could have recruited three of them, or perhaps the election would go to the House, which would select Kennedy.

Finally, one of the most controversial in history is the election of 1876, which ended with a dubious compromise. PEC exactly reverses the historical outcome:

This is consonant with the popular vote. It is also stunningly close; Hayes could win by converting only 46 votes in Arkansas.

Case study: Reversals

Here are the only other elections with different outcomes under PEC:

These are both close. The 1888 results are in line with the popular vote, while the 1880 popular vote was the closest in history. The large difference from the real outcome is due to the Republicans running candidates that lost the South by large margins but won most of the numerically predominant Northern states by much less. This won the electoral vote but would be a losing strategy for PEC.

Adoption

There is of course quite a distance between me making a proposal and it being implemented nationally, although we can hope for at least incremental improvement. More generally, however, there will be resistance to reform from those who benefit from the current system.

The majority party in a state may prefer to use its influence to keep the minority party from getting any say. For example, in California Democrats outnumber Republicans about 3:2, and thus all of its 55 electoral votes consistently go to the Democrat, a situation Democrats may want to preserve. And, after Obama won one electoral vote from Nebraska in 2008 under the congressional district method, the Republican-controlled legislature passed a bill to return the state to winner-takes-all, which was vetoed by the Democratic governor.

However, the minority party is not powerless, and, perhaps in concert with other states, can leverage for a more fair voting system.

Perhaps more opposed than solid states would be swing states, who currently wield disproportionate influence, their local issues receiving greater attention. But being a swing state is a fleeting status, and anyway under PEC their influence is still more than other states due to the at-large electors. So perhaps they could be brought round.

Appendix: All other elections

What follows is a PEC reconstruction of all elections not already shown since 1828, when the current system of per-state voting was implemented almost everywhere.