In the U.S., Presidential elections are not won by the candidate who wins the popular vote nationally. (If they were won in this way, Al Gore would have become President in 2000.) Rather, each state is given a number of “electors” equal to that state’s representation in the U.S. Congress. In almost all states, the candidate that gets the most votes gets all the electors of that state —and the Presidency is won by the candidate who collects at least 270 electoral college votes.1
A: Consider a simplified version of this system in which there are only 2 states, with state 1more than twice the size of state 2 and exactly twice the Electoral College votes. Suppose all preferences are single peaked along a “left/right” continuum. Let nib be the median voter’s ideal point in state i — with n1 < n2. In the event of a state-wide tie, assume the Electoral College votes for the state are split.
(a) If the aim of two Presidential candidates is only to win, what position will they take in equilibrium?
(b) Suppose instead that there are four states, states 2 and 3 that are small (with 10% of the electoral votes each) and states 1 and 4 that are large (with 40% of the Electoral College votes each). Suppose further that the ideal points for median voters in each state are such that n1 < n2 < n3 < n4. What positions to you now expect the candidates to take?
(c) Explain how this relates to the common observation that most of the U.S. Presidential election actually takes place in a subset of states—often called “battle-ground states”, with the rest of the country largely ignored by the candidates.
(d) In exercise 28.3, we suggested that one way to view the decision of whether or not to vote is by comparing the marginal benefit of voting to the marginal cost. The marginal benefit of voting includes the probability that one’s vote will determine the outcome of the election. If this is a major consideration in people’s decision of whether to vote, how would you expect voter participation in Presidential elections to differ across states?
(e) The Electoral College system gives each state 2 electors outright plus 1 elector for each representative that the state has in the House of Representatives (where representation in the House is roughly in proportion to population). How would you evaluate the following statement: In such a system, we would expect, all else being equal, disproportionately more resources spent per voter in small states.
(f) Some states have considered switching from a state-wide winner-take-all system for electing “electors” in Presidential races to a system in which electors from the state represent each candidate in proportion to the popular vote received in the state.2 which of your answers would be affected by such a change?
(g) Prior to running in the general election as either the Democratic or the Republican candidate, a politician first needs to win a party’s presidential nomination. This is done mainly in earlier “primary” (or “caucus”) elections held in each state. In the Republican nomination fight, almost all such primary elections are “winner-take-all” (like the Electoral College system in the general election), but on the Democratic side, most primaries allocate votes to each candidate proportionally. In which party would you expect more states to be ignored during the nomination fight?
B: In exercise 28.3, we used the 2000 election and the controversy regarding Ralph Nader’s participation to suggest that the way we elect U.S. Presidents violates the spirit of Arrow’s IIA axiom. Is 2Often such proposals envision winner-take-all elections at the House of Representatives District level—which comes close to proportional allocation of electors in large states. The states of Maine and Nebraska in fact allocate some of their electors in this way, and Nebraska was the only state in the 2008 election that therefore split its electoral vote. There any reason to believe that this would be less true if the U.S. switched to a proportional system of electing its Presidents?