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Re: Math and the electoral college's virtue
Posted:
Nov 20, 2000 6:53 AM
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Keith Ramsay wrote:
> I don't think you can get very far in trying to describe who is
> "favored" by a system without considering some notion of what
> constitutes a fair, equitable such distribution of power, not that
> this is really the place to do it.
I meant "favored" relative to electing the president on a plurality
of the popular vote.
> |Most people who look at the issue superficially note that even the
> |least populous state gets three electors, and conclude (quite wrongly)
> |that the system gives disproportionate power to the small states
> |because their ratio of electoral votes to population is higher.
>
> Note that various attempts to eliminate the electoral college have
> been foiled in the U.S. senate, where those small states get even
> more disproportionate representations. I don't think these senators
> are just being dumb; I think they have a different issue in mind. They
> want a system that results in outcomes they prefer (basically).
Perhaps. I don't think it's a good long-term strategy, though.
The states that have the unit rule and vote predictably, can be
and are essentially ignored by the candidates. Therefore, if
Wyoming is in G.W.B's pocket from the moment he's nominated, he
has no incentive to address Wyomingan concerns, even ideologically.
> Giving Wyoming 5 times the electoral college vote as proportional to
> its size moves the point of balance point (as far as presidential
> politics goes) to the right. It's no coincidence that we tend to get
> presidents and Senates to the right of Houses of Representatives.
The argument wrt presidents would be more convincing if there'd been
a candidate *between* Tilden and Gore who won the popular vote and
didn't become president. As for the Senate, it's not winner-take-all
in a state, so my argument doesn't apply there.
> |In fact, it's easy to see that other things being equal (the "other
> |things" are e.g. the closeness of the race in your state and the
> |proportion of undecideds), your chance of deciding the election
> |is proportional to 1/sqrt(n) where n is the number of voters.
> |Since the number of electoral votes is (roughly) proportional to n,
> |it follows that your power is approximately proportional to sqrt(n).
> |That is, the system gives disproportionate power to voters in *large*
> |states.
>
> But the proportionality to 1/sqrt(n) (for this measure of power) is
> only when the race *is* balanced. (Ha, and you thought there wasn't
> going to be any math here.) Suppose all voters have .51 probability
> for voting in favor of a measure. The distribution of vote totals is
> roughly Gaussian with standard of deviation proportional to sqrt(n),
> but falling all the way to a tie is proportional to 0.01*sqrt(n)
> standard deviations from the mean. On a Gaussian, that decreases the
> density much more rapidly than the 1/sqrt(n) you get from the curve
> spreading out; it's going down with population like an exponential
> divided by sqrt(n).
Yeah, you've got me here. It doesn't invalidate the argument entirely,
but it does definitely restrict its applicability.
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