I was curious: how will the electoral vote apportionment change between now and 2012? (Reapportionment is done after each census, and censuses take place in years divisible by 10; the apportionment takes effect the year after the census. Thus the 2004 and 2008 presidential elections were done under one apportionment, and the 2012, 2016, and 2020 elections will be done under another one.)
I don't know (my first attempt at programming the apportionment gave some really strange-looking results) but I wanted to share an amusing fact.
Each of the 50 states receives a number of electoral votes equal to its number of Representatives, plus two. So the question is really one of determining the number of Representatives that each state gets. The way this works is as follows. First, each state receives one seat. Then, let the populations of the states be P1, P2, ..., P50; let
Qi,j = Pi / (j(j-1))1/2
for 1 ≤ i ≤ 50 and all positive integers j. Sort these numbers, and take the 385 largest of these numbers. Now state i (the state with population Pi) gets r = ri representatives, where r is the unique integer such that Qi,r is one of the 385 largest Q's, and Qi,r+1 is not. (385 is 435-50; 435 is the number of seats in the House of Representatives, and 50 seats were already assigned in the previous step, one for each state.) Essentially, this assigns the seats in the House "in sequence", so we can speak of the 51st seat, 52nd seat, ..., 435th seat.
So what if there's a tie for 385th place in that ordering? This can occur, of course, if two states have the same population, and I bet some tiebreaker is written into the law. But what if two states have different populations, but after dividing by the square root factor, two of the Qi,j are the same? Surprisingly, this can happen. Let P1 = 6P2. Then it's not hard to see Q1,9 = Q2,2; that is, state 1 gets its ninth seat "simultaneously with" state 2 getting its second seat. More generally, if
P1 / (m(m-1))1/2 = P2 / (n(n-1))1/2
then state 1 gets its mth seat simultaneously with state 2 getting its nth seat. Note that P1/P2 is rational. So a tie can only occur when (m(m-1)/n(n-1))1/2 is rational; when does this happen?
When n = 2, this amounts to asking when (m(m-1)/2) is a square; this happens for m = 2, 9, 50, ... (the indices of the square-triangular numbers in the sequence of triangular numbers) So one state can receive its second seat at the same time another one gets its 9th seat, its 50th seat, ... if the larger state has 6, 35, ... times the population of the smaller one.
Somehow I doubt the law covering apportionment has a provision for this. I suspect the provision taken would be similar to what happens if there's a tie in an election; I know there are some jurisdictions that just flip a coin in that case.
Edit, 10:53 pm: Boris points out in the comments that somebody's done the projection. Texas gains 4, Florida and Arizona each gain 2; the Carolinas, Georgia, Utah, Nevada, and Oregon each gain 1. New York and Ohio each lose 2; Massachusetts, New Jersey, Pennsylvania, Michigan, Illinois, Minnesota, Iowa, Missouri, Louisiana, and California each lose 1. At first glance this shift seems like it would favor the Republicans in the presidential race; nine of the seats created are in states that voted for McCain in '08, and only two of the seats destroyed are. But I'm not sure about this analysis; states are made of people, so as a state's population grows or shrinks its political makeup changes as well. Maybe Nate Silver will have something to say about this?