U.S. Electoral College, Power In

The president of the United States is elected not by a direct national popular vote, but by an electoral college system in which the popular votes in each separate state are aggregated by adding up electoral votes awarded on a winner-take-all basis to the plurality winner in each state. State electoral votes vary with population and at present range from 3 to 55. The U.S. Electoral College therefore generates the kind of weighted voting game susceptible to a priori voting power analysis using the various power indices; in particular, the question arises of whether and how much the power of voters varies from state to state.

The U.S. Constitution provides that states have electoral votes equal in number to their total representation in Congress. Each state has two senators, while representatives are apportioned among the states on the basis of population (though every state is guaranteed at least one representative). The resulting apportionment of electoral votes gives a distinct advantage to small states relative to straight apportionment by population. The size of the House of Representatives is now fixed at 435 members, there are 50 states, and the 23rd Amendment gives three electoral votes to the District of Columbia, so the total number of electoral votes at present is 435 + 100 + 3 = 538, with 270 votes required for election. (If no candidate receives this required majority, other provisions in the Constitution come into effect.) The Constitution leaves the mode of selection of presidential electors (the officials who actually cast electoral votes) up to each state to decide. Since the mid-1830s, the almost universal state practice has been that each party nominates a slate of elector candidates, equal in number to the state's electoral votes and pledged to vote for the party's presidential candidate. The voters choose between the two slates. The slate that wins the most votes is elected and casts its bloc of electoral votes as pledged, producing the weighted voting game noted at the outset. This practice has been widely believed to give larger states an advantage in voting power that in some measure counterbalances the small-state advantage in apportionment.

The development in the mid-1950s of the Shapley-Shubik voting power index provided a tool for evaluating a priori voting power in the Electoral College. While it is not possible to apply the Shapley—Shubik Index directly to weighted voting games of the magnitude of the Electoral College, early computer simulations indicated that the expected bias in favor of larger states was quite modest. Since then other mathematical and computational techniques have been developed that can provide highly accurate estimates. Moreover, the rival Banzhaf (or Penrose-Banzhaf) voting power measure has since been proposed, which is (arguably) more appropriate than Shapley-Shubik for evaluating a priori voting power. Table 1 shows both the Shapley-Shubik and Banzhaf voting power of states in the present Electoral College, from which it is apparent that (a) the two indices provide very similar estimates of state voting power, and (b) state voting power is approximately proportional to electoral votes, though (c) the largest states—and especially the largest of all (California)—is somewhat advantaged relative to the apportionment of electoral votes. The last column shows the absolute Banzhaf value for each state, which has the following direct and useful interpretation. Suppose we know nothing about the workings of the Electoral College other than its formal rules, so our a priori expectation must be that states vote randomly, that is, as if independently flipping fair coins (the random voting or Bernoulli model). On this assumption, the absolute Banzhaf value is the probability that a state casts a decisive bloc of electoral votes that determines the outcome of the election.

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