Election 2012: What if the House were bigger?

As usual after a presidential election, there have been a lot of maps showing how the vote went in the US electoral college. One thing that I haven't seen get much discussion is the effect of limiting the size of the college itself.

Thanks to Nate Silver, lots of people now know the number of votes in the US electoral college (whether they realize it or not): 538. With the exception of the three given to Washington, DC, the electors are distributed to each state according to the number of congressmen it has. (DC's total is equal to the number it would have were it a state, not to exceed the number held by the least populous state.) This formula sets a minimum of three electors for each state, equal to its two senators and one House representative. Currently the seven least populous states have three electors. This minimum perpetuates the equality of states' voting power in the senate, where population is irrelevant and every state gets two votes. It's also the case that every state must have at least one representative, no matter how few citizens it has. In other words, the smallest states have more voting power than their populations would warrant otherwise. (There's also an inherent inequality in that there needs to be a whole number of electors, which means there will be other inequalities due to rounding.)

So what would happen if the House were bigger and there were therefore more electors and also a more proportionate relationship between a state's population and the number of its electors? In effect this would give more influence to the more populous states.

To check this out, I made a little spreadsheet to recreate the distribution of electors. The tricky part is assigning members to the House of Representatives. This assignment isn't quite straightforward (here's a nice little paper on alternatives to the current method), and my reconstruction spreadsheet of the current situation (435 members total) doesn't quite get it right (MN and RI are missing one member each), so my projection of what the House would look with more members is likely a tiny bit off too. (I could spend some more time on this, but I think I'm close enough and a little internet searching hasn't helped me out. Suggestions welcome in the comments.)

So what happens? In this election, Obama with 50.5% of the national vote got 332 electoral votes to Romney's 48% and 206. Had the House 485 members (an average of one more per state), Obama would have gotten 364 and Romney 224. Throw in another 50 and Obama's at 396 and Romney 243 (you'll note that my model is one over the real total of 638). In all cases, Obama wins a rounded-off 62% of the electoral college, so no change in that metric.

That doesn't mean that there would no changes at all in the way the election might go. For example, it might be possible to put together a different collection of states to win, or to neglect more of the smaller states and still win. It does however look like the picture wouldn't change much even with a much bigger House.

(It would be interesting to consider what would happen to the split between the parties in a bigger House, but given all the complications with drawing districts, that's far from straightforward to work out.)