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Math Against Logic

Ken asked me what my thoughts were about this essay Math Against Tyranny by Will Hively that supposedly offers a mathematical proof that the electoral college is the best way to go.

Well, I have to say that I think that essay was terrible. It spends a GREAT deal of time convincing me that it's about to use math to prove it's point. No really, we have math. Our math is awesome and it totally proves our point. Let me tell you this story about how awesome our math is that proves this point, because this math? Is awesome.

The only problem is, during all of the hand waving about math, it tries to have you accept a faulty premise but keep you focused on the "math."

I'll pull out and go through several of the logical fallacies in his argument:

In baseball’s World Series, for example, the team that scores the most runs overall is like a candidate who gets the most votes. But to become champion, that team must win the most games.

The glaring error with this crack logic is of course that playing a game against the LA Dodgers counts as 1 game and playing a game against the Arizona Diamondbacks counts as 1 game. In the electoral college, winning in CA is 55 "games" and winning in Arizona is 10 "games." He's attempting to use a quaint analogy to distract from the faulty logic.

"The idea," he says, "is to give every voter the largest equal share of national voting power possible." Here’s a classic example of equal voting power: under a tyranny, everyone’s power is equal to zero.

This is wrong. Not everyone under a tyranny has equal/zero power. There is 1 person who holds 100% of the power. Everyone else shares an equal share of 0% of the power.

James Madison, chief architect of our nation’s electoral college, wanted to protect each citizen against the most insidious tyranny that arises in democracies: the massed power of fellow citizens banded together in a dominant bloc.

California is one of those democratic tyrannies. The liberal voting bloc in the 2 major urban areas of CA mass their power and force all of the rural areas of CA to vote Democratic.

If a Serb party wins national power, minorities have no prospect of throwing them out; 49 percent will never beat 51 percent. Knowing this, the majority can do as it pleases (lacking other effective checks and balances).

Our government does have checks and balances though. We elect Representatives and Senators to Congress who are supposed to balance the power of the President.

But it has worked beautifully, he insists, as a formula for converting one large national contest into 51 smaller elections in which individual voters have more clout.

More clout? Does every single voter get more clout? If so, then an increase for everyone isn't an increase, because we're all still equal. That's the point though, it does give certain voters more clout... but not all.

Two variables, Natapoff realized, profoundly affect each citizen’s voting power. One is the size of the electorate, a factor that political scientists already recognized. The other is the closeness of the contest, which most experts hadn’t taken into account.

The second part here isn't true. Most experts don't take into account the margin of win because that margin shouldn't affect my voting power. My vote should have x power where x = 1 / number of voters. Just because I happen to vote on the winning side doesn't make my vote less powerful, it just means that the stack I placed my vote in was taller.

When Natapoff computes voting power--the probability that one vote will turn the election...

I think this definition of voting power is inherently flawed. My vote isn't about turning an election, it is about deciding an election.

He wanted to know what happens when voters stop acting like ideal, perfect coins and begin to favor one candidate over the other. He could see right away that everyone’s voting power shrinks, because the probability goes down that the electorate will deadlock

This is just a silly situation question, voters aren't ever going to behave like coins. He's viewing elections backwards. There isn't a statistical model used to predict, it's a tally of the existing.

"If candidate A has a 1 percent edge on every vote," Natapoff says, "in 100,000 votes he’s almost sure to win. And that’s bad for the individual voter, whose vote then doesn’t make any difference in the outcome.

No, it isn't bad for the individual voter because in this situation, the candidate with the most votes won.

if you’re flipping a lopsided coin yet looking for an equal number of heads and tails (a deadlock), you had better keep the number of coin flips low; the longer you try with lopsided coins, the more the law of averages works against a 50-50 outcome.

Again, he's basing this on a faulty assumption. We don't want a deadlocked election. We want an election that fairly represents the wishes of the voters.

So even though districting doesn’t help in an ideal, dead-even contest, with voters acting the same all over the country, it does help, Natapoff saw, in a realistic, uneven contest.

What he's saying here is.... in a uneven election, the electoral college doesn't change the result, Most votes for A gets A elected. This means a straight up popular vote would work just as well: Most votes for A gets A elected. In close elections, however, the electoral college can give us the opposite result: Most votes for A gets B elected. I prefer the system that works in all elections instead of just the uneven ones. He says....

For a nation with millions of voters, the gap between candidates must be razor-thin for districting not to help.

"The theorem," he sums up, "essentially says that you’re better off districted in any large election, unless every voter in the country is alike and very closely balanced between candidates A and B. In that very extraordinary case, which rarely if ever occurs in our elections, it would be better to have a simple national election."

The 2000 Presidential election's popular vote was a difference of 0.5%. The electoral college failed to elect the candidate with the most votes. This last part sounds like he actually agrees with my feeling that a national popular election would be better.

Natapoff can solve his equations to find an ideal district size for the purpose of national elections, assuming that each vote, like a coin toss, is statistically independent--but the answer depends on an election’s closeness. The districts could all be the same size, but only if the preference for one candidate over another is the same everywhere in the country.

It looks like what he's trying to do here is force all of the districts to be equal, then districting won't have any lopsided effects..... He's essentially saying we just need to make the smallest logical unit be the district instead of a voter... but for it to make sense, we have to make sure all of the voters in a given district are distributed such that they all deadlock. Let's just use the voter as our smallest unit and then we don't have to figure out how to deadlock all the voters.

Every once in a while, if we use districting to jack up individual voting power, we’ll have an electoral "anomaly"--a loser like Harrison will nudge out a slightly more popular Cleveland. He sees those anomalies, as well as the more frequent close calls, not as defects but as signs that the system is working. It is protecting individual voting power by preserving the threat that small numbers of votes in this or that district can turn the election.

Ludicrous. Electing the wrong person doesn't remind us that each vote is equal, it reminds us that the system is broken because our votes were CLEARLY not equal.

"All that happens is someone with fewer votes gets elected," temporarily.

Oh? Is that all that happens. My bad. All we do is have the most powerful political office in the entire world occupied by a person who did not have the majority support. I mean... what could go wrong, right? It's not like the loser-turned-winner would lie to public to start a war with a random country, bankrupt our country and kill thousands and thousands of people in previously mentioned war...

According to this guy's logic (and I use the word lightly) the Electoral College only gives the appropriate outcome when there is an overwhelmingly majority. When the margin is close, it's better to have a national popular vote. So, screw the Electoral College because the national popular vote can get us the right outcome in both situations.

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