In a bitterly contested U.S. presidential election, like the one last year, the question often comes up about the perceived unfairness of the Electoral College, the system of indirect democracy we use for electing presidents. Every state is entitled to choose a number of electors equal to its combined representation in the House of Representatives and the Senate — this has the effect of giving voters in small states approximately three times the voting power of voters in California. There are, on the other hand, many many more people in California, so maybe it balances out.

If you actually believe in democracy, you probably think the chief executive ought to be chosen by direct election — preferably using a ranked-choice voting system like STV (Single Transferable Vote). But to enact such a change would require a constitutional amendment, and the small states — those with artificially boosted representation in the Electoral College — have a double veto on such changes, due to the requirement of a supermajority of both the Senate and the 50 state legislatures. So people have looked at alternative ways of choosing electors that wouldn’t require a constitutional amendment. One such is the National Popular Vote Interstate Compact, which — if adopted by states representing at least 270 electoral votes and assuming no faithless electors — would give the presidency to the winner of the popular vote by voting a majority of electors for whoever that was. Currently, the NPV compact is still far from its goal of a majority of electoral college seats — unsurprisingly, the large states have ratified the compact and the small states mostly haven’t. It highlights the sort of collective-action problem inherent in fixing presidential voting: if the legislature of a member state saw partisan advantage in switching their vote, they could simply do so, by ordinary state law, and leave everyone else in the lurch.

Naturally, the question arises over whether it would be possible to have everyone’s votes count while maintaining the unfair advantage of the small states. One way to do this — which would also require collective action, since it doesn’t benefit the large states to enact it if the small states refuse to go along — would be apportion each state’s electors in accordance with the popular vote in that state. There are ways to do this which would be tolerably democratic, and there are ways to do it which are very undemocratic:

1. You could randomly assign every voter to an “electoral district”, and give the winner of each district one elector. This only works if it’s truly random, and would be difficult to implement given how elections are implemented in most states (it’s assumed that everyone at the same polling place gets the same ballot).
2. You could use any of a number of proportional representation systems to assign electors to candidates.
3. You could do what Maine and Nebraska do already, and have separate electors for each Congressional District plus two at-large electors who, like Senators, represent the state-wide winner.

It should be clear that, so long as gerrymandering is permitted, option 3 is Very Bad: essentially it means that whoever controls the state legislature determines the outcome of the presidential election, but with a veneer of democracy that hides the essential corruptness of the system. Better for the legislature to just decide who the state will be voting for, as in the Old Days. So I’m focusing on option 2.

One of the common ways of apportioning representatives in a system of proportional representation is a system called the “d’Hondt Count”. It’s mathematically equivalent to what is known as “Jefferson’s method”, which Thomas Jefferson used to propose the (ultimately enacted) first apportionment of Congress after the 1790 Census. It’s not the system used for Congressional apportionment today (called the “method of equal proportions”) but it is popular around the world for legislative elections. I implemented a script that takes as input a CSV file with the state-by-state popular vote in a presidential election and outputs the results of apportioning the electors using this method. With a small modification, it’s possible to subtract out the “small state bonus” (two electors per state), and see whether that actually has an impact on the outcome or not. I then created data files representing the popular vote from the last five presidential elections (using a variety of sources), to see how things would have turned out if we had done it this way (source and data files on Github).

You’ll notice that only in the hotly contested 2000 and 2016 elections would third-party candidates have received electors under this scheme. We can recompute the assignment of electors without third-party candidates, and it turns out that the results are indeed different. In 2016, without the third-party vote, but with the current “small state bonus”, Trump and Pence win a bare majority (270 EV); if the bonus is removed, Clinton and Kaine win a two-EV majority (220 EV to 216 EV). In 2000 with the third-party vote removed, the “no bonus” scenario sends the election to the House, but the current-law scenario gives a bare majority to Gore and Lieberman.

In the title of this piece, I questioned whether this would be a better way to choose electors. Having actually worked out the results in a number of important recent cases, I have to conclude that it would not be a significant improvement over the existing system, and that we are better off demanding a true popular vote (hopefully by preference voting). About the only positive thing I can say about doing it the way I’m suggesting above is that it would make it much more clear that nearly all of the country is actually some shade of “purple” — run the scripts and you’ll see just how few states give all of their electors to a single candidate when they are allocated proportionally.

I would gladly accept data files from additional presidential elections by Github pull request.