Bloomberg as a kingmaker?

President? Or Kingmaker? by Patrick Healy, in today's New York Times.

Michael Bloomberg, mayor of New York City, recently officially changed from a member of the Republican party to an independent. This has been interpreted as a harbinger of a presidential run as an independent. However, that's a long shot, even though there's speculation that Bloomberg would be willing to spend a billion dollars of his own money on his campaign.

Healy suggests that Bloomberg ought to run as a "kingmaker". He should attempt to win one or two large states (New York is the obvious choice, since he's mayor of the city that makes up nearly half that state's population) and basically forget about the others. After that, he would need to hope that neither the Republican nor the Democratic candidate has 270 electoral votes. The election then by default goes to the House of Representatives. However, electoral votes aren't cast until December 15, six weeks after the general election. So Bloomberg could make deals with one of the two major-party candidates.

This has been tried before; George Wallace attempted it in 1968, Strom Thurmond in 1948. But neither of those elections was close enough for the strategy to work.

This raises a question, though. Let's say Bloomberg can win New York (31 electoral votes). What are the chances that the other states are evenly split enough?

Let's assume that each state's winner is decided by flipping a coin. (This, of course, does not reflect the reality of American politics -- some states are much more likely to break one way or the other -- but bear with me.) Then each candidate expects to win half of the remaining electoral votes -- that's 253.5. The variance of the number of electoral votes won by, say, the Democratic candidate is the sum of the variances of the number of electoral votes won in each state. In a state with n electoral votes, that's n²/4. Adding the results up for each state, we see that the variance of the number of electoral votes won by the Democrat is 2326.25; the standard deviation is the square root of this, 48.23. I'll assume that the distribution is normal -- if all the states were the same size, this would be the Central Limit Theorem, and hopefully the fact that the states aren't all the same size doesn't kill us. So the probability that the Democrat gets 270 electoral votes in this scheme is the probability that a normally distributed random variable with mean 253.5 and standard deviation 48.23 is at least 269.5; that's 37%. Similarly for the Republican. That leaves Bloomberg a 26% chance -- barely one in four -- that this scheme would work. He might be willing to take those odds.

But, of course, there are some states that are sure to go one way or the other. Say only one-third of states (representing one-third of electoral votes) are sure to go to the Democrats, one-third to the Republicans, and one-third in play. Then the variance gets divided by 3; the standard deviation is now 27.85; Bloomberg's chances of the election being close enough for this strategy to come into play are 44%.

And this whole analysis neglects the finer points of electoral college strategy. States aren't independent of each other -- we wouldn't see an election in which Utah went Democratic while Massachusetts went Republican, or even one where Virginia went Democratic but New Jersey went Republican, to be a little more reasonable. (Both of those states are probably in play, but New Jersey is far enough left of Virginia that they shouldn't break that way.) And in the end it could come down to just a few states -- the 2004 election basically came down to Florida, Ohio, and Pennsylvania -- in which case this whole normal approximation breaks down. But we won't know whcih states those are for a long time yet.

edit, 12:09pm: Can Bloomberg Win? suggests the reverse of Healy's plan -- Bloomberg wins a few states, the Democrat and Republican split the rest of the states, and cuts a deal with electors of the party that gets less electoral votes that makes him President. Rasmussen Reports talks about possible "electoral chaos" which could fundamentally change the way we elect our Presidents.

edit, 7:47pm: As reader Elizabeth has pointed out in a comment, New York is reliably Democratic; this changes things a bit, so the chances that Bloomberg plays the spoiler by allowing neither other candidate to get 270 electoral votes (under the second set of assumptions) are more like 38%.