I do not recommend reading Stewart's article since he gets it quite wrong; I was very confused by what he did, to the point of creating an incorrect implementation that was available on these pages for a very long time. You can read it for general ideas about half of the method (though Stewart presents his summary as being of the whole method), but honestly, I think it will be more confusing than elucidating.
In particular, see Chapter 10, The a priori voting strength of the electoral college, by Irwin Mann and Lloyd S. Shapley, which (it says) largely repeats  and another RAND Corp. memo.
Also see Chapter 9, A method for evaluating the distribution of power in a committee system, by Lloyd S. Shapley and Martin Shubik. That article is reprinted from American Political Science Review, Vol. 48, 1954, pgs. 787--792.
Here are some more references. The first two of these introduce themselves as being basically reproductions of the works at the RAND Corporation (such as reference  above, but that's not what I found reprinted -- yet, anyway), so they probably should be considered as having dates in the early 1960s.
Here are three more recent works. I haven't read them (yet). Note that two of them are available on the web.
Here are two mathmetics texts that discuss the Banzhaf Power Index.
I read this and it looked like a good introduction at a basic level for anyone with college-level math experience and good high school students. It doesn't go into how you could compute it for a large system, however. The whole text was apparently used for a course in the University of Georgia Math Department called Mathematics of Decision Making. One interesting note in this text is that it says that the Banzhaf Power Index was independently developed by James Coleman at RAND Corporation. It goes on to say that the Banzhaf index was used more in court cases than the Shapley-Shubik index, and theorizes that this is because John Banzhaf is a lawyer. I would guess that this probably also explains why his name is on it and why it gets a little more press.
In his new book, the mathematician John Allen Paulos continues his witty crusade against mathematical illiteracy ...... Mr. Paulos's little essay explaining the Banzhaf power index and how it relates to Lani Guinier's ideas about empowering minorities is itself worth the price of the book.
High praise, indeed. I read the essay, and it was entertaining and made a good point. But read it for yourself.
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