By sheer chance, I came across the book Predicting Party Sizes by Rein Taagepera, a political scientist who was trained as a physicist. I was interested to run into a "theorem" (I'm not sure whether I can call it this, because the derivation in the book is rather heuristic) which states the following. Let V be the number of voters in a country like the United States which elects its president through an electoral college, and let E be the number of states in that country. Then let n = (log V)/(log E). For the United States at present, V is about 121 million (I'm using the turnout in the 2004 election), E is 51 (the District of Columbia is a "state" for the purposes of this discussion), and so n is about 4.7.
This quantity n is called the "responsiveness" of the system, and its rough interpretation is that if the party in control receives (1/2 + ε) of the popular vote, then it will receive (1/2 + nε) of the electoral vote, for small ε. More generally, let VD and VR be the number of popular votes obtained by the Democratic and Republican candidates, respectively; let ED and ER be their numbers of electoral votes. Then ED/ER is approximately (VD/VR)n. When VD/VR = 1 this reduces to the first statement.
Anyway, Nate Silver at fivethirtyeight.com showed the results of some of his simulations about a month ago and claimed that a one-percent swing in the popular vote corresponds to 25 electoral votes. It turns out that 25 electoral votes is 4.6 percent of the electoral college at a whole, so based on his simulations n = 4.6. I take this as evidence that Silver is doing something right. (n is also in this neighborhood for data from actual elections.)