It was September 1954, fifty years ago this month, that the Americna Political Science Review published its first article that used significant mathematics, apart from articles using statistics.
It was "A Method for Evaluating the Distribution of Power in a Committee System" by Lloyd Shapley and Martin Shubik. It defined a measure of the theoretical power that a committee member has by virtue of the voting rules and nothing else, e.g., not the person's connections or charisma, etc. For example, considering the US legislative process as one big committee, the powers of a president, senator and member of the house were calculated as having the ratio of 350:9:2. Shapley and Shubik were graduate students at Princeton. The latter told me that he and Shapley sent the paper in on the advice of a professor in the political science department, never thinking it would be accepted, but after three weeks the news came that it was in. He thinks the referee who blessed it must have been a Very Important Person. Years later he asked Herbert Simon if it was him, but it wasn't. The method has generated hundreds of articles, most of which use it prescriptively -- as a guide to how to set up fair rules when some members should have more power than others. It could set voting weights in a body like the European Council of Ministers where some of the countries have more population. The approach is a counterexample to the idea that mathematical methods make political science non-normative. Martin Shubik was Nash's roommate at Princeton -- in the movie A Beautiful Mind, the roommate is named Martin, but he turns out to be imaginary -- this is not so! A modification to the method that has been used in metropolitan councils is the Banzhaf Index, invented by John Banzhaf, a lawyer who now crusades against fast food, and who appeared in the movie Supersize Me. -------------------------------------------------------------- Please Note: Due to Florida's very broad public records law, most written communications to or from College employees regarding College business are public records, available to the public and media upon request. Therefore, this e-mail communication may be subject to public disclosure.
