Tuesday, October 2, 2012

Speaking of the Electoral College

About four years ago, I made a somewhat long-winded post (not by the standards of this blog, I suppose, but generally) about the electoral college, prompted by Bernie visiting my office to ask me about it.  Of course, I had primed him by saying I had something nerdy to say about it, and he's unable to resist that kind of bait.  One of the best things about nerdy posts of this sort is that timeliness is not a big attribute, so here it is, four years on:

Bernie just came into my office because he wanted to hear my spiel on the electoral college. Put aside for the moment the question of whether this indicates he's some kind of pedagogical masochist; what started this was the question of whether voters in a big state like California suffer because their vote is diluted, or are favored because the state's electoral power is so huge. The short answer is that it's mostly the latter, but there are a few interesting wrinkles along the way.

One way to approach the question is to consider how many Missouris (11 electoral votes) it would take to match the electoral power of California (55 electoral votes). The obvious answer is five Missouris, but this assumes that the Missouris all vote as a bloc, as California would (in a presidential election). In general, assuming independent Missouris, this is unlikely. Because some of the Missouris would be likely to cancel others out, the swing power they hold would not be 11 times 5, but 11 times the square root of 5, or about 24 electoral votes. (Remember random walks and square roots?) If all Missouris were independentand why shouldn't they be?!it would take 25 Missouris to match one California (in terms of the states' electoral power).

Now, each individual voter in California has less power to impact the state's overall direction, just because there are oodles of people in Californiaroughly five times as many as in Missouri, to match the disparity in electoral votes. (It's actually a little more than that, but we'll deal with that in a bit.) That means that it takes roughly five Californians to make the same percentage impact on their state's result as one Missourian. Again, that only happens if the Californians vote as a bloc; assuming they vote independently, it would take 25 Californians to equal one Missourian.

So at first blush, it seems that these two effects cancel each other out: California has 25 times as much electoral power as Missouri, but each Missouri voter has 25 times as much individual impact on the Missouri result as a California voter has on the California result. However, there is one additional effect of California's large population: The required swing in close votes in California is smaller, percentage-wise, than it is in Missouri. It's basically the law of large numbers: In any evenly contested election, the outcome probably won't ever be exactly 50-50, but the more populous the state, the closer it will be to 50-50, and the smaller the percentage swing required to change that outcome. This factor is again equal to the square root of 5, and it's what drops out in the final resultthat a California voter has a larger impact on the national electoral result than a Missouri voter.

One complicating factor is that the number of electoral votes belonging to a state is not quite proportional to that state's population, not even when rounding is taken into account. The reason is that only the number of Representatives belonging to the state is proportional to the state's population; there are also the Senators, which are two a state. Since there is one electoral vote per Congress member (Representatives and Senators combined), small states have a much higher representation per capita than large states.

The upshot is that the most overall power is held by voters in the largest states, like California, Texas, and New York. Intermediate are voters in states with moderately large populations, such as Ohio or Illinois, as well as the smallest states. The weakest are voters in states like Arizona and Colorado, which are too large to gain much advantage from the "bonus" two electoral votes corresponding to Senators, but are too small to gain advantage from the enormous impact of a large population (and large electoral college representation).

It should be pointed out that the foregoing discussion only applies to votes where each state is contesteda "battleground" or "swing state," in recent election parlance. In practice, the impact a California voter has in the 2008 presidential election is nearly nil, since the state is almost guaranteed to go to Obama. (We'll see if I eat those words. [Obviously, I didn't. —brian]) The necessary swing is way too large for a reasonable number of California voters to overcome. That the predisposition of a state's voters is more than enough to swamp the effect of the largest population in the Union is, in my opinion, an indication that those trying to "fix" the election system (typically by replacing it with direct popular vote) are barking up the wrong tree, often in an irrational attempt to right a wrongthe 2000 Bush victory, say, which went against the popular votethat ultimately had to do with factors distinctly different from the structure of the electoral college.


  1. I’m curious what factors you think explain the 2000 Bush victory.

    I think a direct popular vote would very likely have saved us the national embarrassment of all the haggling over a few hanging chads in a few counties. It seems much less likely that the entire popular vote of the U.S., rather than just the vote of one swing state, could hinge on one such debacle.

    Whether it would have changed the result of the election is another question. It seems obvious that the distribution of efforts to “get out the vote,” and the relative likelihoods for similar people in different states to vote, would both be significantly changed by that change in the rules. And it seems at least plausible that this could significantly change the percentages of the popular vote received by each candidate. But I have no idea yet whether this would have increased, decreased, or reversed Gore’s popular-vote majority.

  2. @David: Unfortunately, four years on, I don't recall exactly what I thought the factors were.

    In a literal sense, of course, the electoral college had an impact: The result of the electoral vote was different from the result of the popular vote. However, as you point out, a lot of strategy and tactics are predicated on there being an electoral college, so it's well-nigh impossible to determine with any reliability what the end result would have been if the U.S. used the popular vote.

    As far as the embarrassment goes, I think that a lot is riding on the electoral vote having been close. A national popular vote is probably less likely to be that close, but the potential embarrassment is generally greater, since the result has to be binary. What's the probable margin on something like that? Probably wider than it is for an individual state. And while a state popular vote only occasionally has a vital impact on the result, a national popular vote by definition always does.

    My issue with many (possibly most) of the popular criticisms of the electoral college is that they make rather cavalier assumptions about what the objectives of a voting mechanism "should" be. It is by no means obvious to me that "one person, one vote" is necessarily the desired goal, yet that is essentially what the popular vote would yield. Fortunately, the founding fathers had the foresight not to put all their governmental eggs in a single presidential basket, but spread them around judiciously.