Tuesday, November 6, 2012

No, the electoral college is not a good system

Oh come on, obviously you can't think about anything but the election today anyway! You might as well keep reading, even though you probably already agree. Do not be attempted to check nytimes or cnn, as the election results are still not in. And don't worry, Fivethirtyeight still has Obama above 90%.

Anyway, yesterday, courtesy of Sarah (hi Sarah!) I was pointed to this interesting argument in favor of the electoral college (update! see this one from today in Slate, especially point 1 which is basically the same as the previous link). At first it seemed persuasive. But then I realized the entire argument rests upon a basic flaw of sampling and statistics!

Weingarten says that a close election in 1 or 2 states is a manageable disaster, but a close election nationally would be an unmanageable disaster because every vote would be contested, not just every vote in FL, or every vote in OH, or whatever. This is an appealing point—it would be a nightmare if the campaigns were suing for votes all over the country—but it ignores the fact that the likelihood of a close and contestable election in the statistical sense (explained below) decreases sharply with the number of votes cast. A 0.5% margin of victory nationally is equally likely to, but much more robust, than a 0.5% margin of victory in any one state. A more precise formulation of this same idea: if a candidate wins by 0.5% in a single state, it's much more likely that his victory in that state is a result of random vote-counting errors than if the candidate wins the national popular vote by 0.5%.

How much more likely? It depends on the relative size of the state vs. the national population, but the general relationship is that the statistical robustness of a given margin of victory grows like the square root of the sample size. So if a state has 1/100th the voting population of the country as a whole (like, say, CT), then a given margin of victory is equivalent to a national margin of victory that's only 1/10th as large (since 10 is the square root of 100).

The margin of victory of Florida in the 2000 election was about 500 votes out of over 5 million, or less than 0.01% of the total votes cast.  In order for a national victory in the popular vote to be as narrow statistically, it would have be a margin of less than 0.002%, or just 3000 votes out of about 140 million. Although one Presidential election has been this close (1880), it was way back when the population was much smaller, and that election was dubious for lots of other reasons. And no other popular vote result before or since has been anywhere near as questionable. In general, it remains true that the chance of a close election in one or more decisive electoral states is much more likely than the national popular vote being similarly questionable. Therefore a national popular vote is a much more reliable way to arrive at a clear, decisive winner.

Weingarten's other argument is that the electoral college ultimately legitimizes the electoral process by amplifying the margin of victory, since the winner typically wins a much larger fraction of the 538 electoral votes than of the total votes cast. But this contention seems neither desirable, nor true for any election that's close enough for it to really be an issue. Again, think back to the election of 2000. In that year, the election went to Bush by a mere 537 votes! Does that really legitimize the electoral process? No, it makes it seem incredibly arbitrary, because a national popular vote victory will simply never be that close!

Of course, as far as I know, no state has ever been decided that narrowly either, and so it was probably a one-time fluke as well. But the basic point remains: a narrow-enough margin to be dubious in a decisive electoral state is more likely than a narrow-enough margin nationally, because of the much bigger vote sample nationally.

And then there's all those other traditional reasons to dislike the electoral college. But I won't get into that.

Time to call some Ohians!


  1. I'd say more but I have to go refresh nate silver's blog 600 times.