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 independent—and 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
California—roughly 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 result—that 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 contested—a
"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 wrong—the 2000 Bush victory,
say, which went against the popular vote—that ultimately had to do with
factors distinctly different from the structure of the electoral
college.
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