The Complete Idiot's Guide to Game Theory by Ph.D. Edward C. Rosenthal

Author:Ph.D., Edward C. Rosenthal
Language: eng
Format: epub
Publisher: Penguin Group USA, Inc.
Published: 2010-12-28T00:00:00+00:00

Other Power Indices

The Banzhaf Power Index is not the only such measure. Lloyd Shapley and Martin Shubik proposed a different power index that predated Banzhaf’s. The Shapley-Shubik Power Index also counts swing votes, but the swing votes are counted by using the Shapley value for cooperative games that we saw in Chapter 12. In other words, the Shapley-Shubik Power Index is just the Shapley value in the special case of simple games.

NO BLUFFING

During election campaigns in the United States, political pundits talk incessantly about ʺswing states,ʺ so it is not surprising that there is a history of analytical methods to capture this notion. The first known publication on what we are calling a power index was by L. S. Penrose (a British geneticist) in 1946. Shapley and Shubik developed their index in 1954. Banzhaf, unaware of the previous work, essentially rediscovered the Penrose method in 1965, and ditto for James S. Coleman who reiterated the same technique in 1971.

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