Banzhaf voting power, random elections, and the Electoral College winner’s advantage

In a recent article, Riggs et al. (2009) aim to measure the ‘Electoral College winner's advantage’—in particular, the extent to which the winner’s electoral vote margin of victory is magnified as a result of (i) the ‘two electoral vote add-on’ given to each state and (ii) the ‘winner-take-all’ mode of casting state electoral votes. Their results are based on two sets of one million simulated two-candidate elections. This note has two purposes. The first is to demonstrate that RHR’s simulation estimates can be calculated precisely using the theory of voting power measurement. The second is to correct several flaws in RHR’s analysis, the most substantial of which pertains to the effect of the two electoral vote add-on, which actually has a negative effect on the winner’s advantage.

► The ‘Electoral College winner's advantage,’ estimated through simulated random elections in a recent article, can be calculated directly and precisely on the basis of the theory of voting power measurement.
► The two electoral vote add-on actually reduces rather than enhances the winner's advantage.
► Winner-take-all does enhance the winner's advantage but primarily because it reduces the number of ‘electoral entities,’ not because the states have unequal electoral votes.