I love used book shops. Back in 1980-something I found this intriguing arcane used book about politics and math, and then I lost it. A few years later I wrote the notes about the 3E Senate that eventually evolved into the website chapter ‘Rational Numbers’. I remembered the theories the book described, but not the details. Then, just recently, in sorting through some old boxes of old books, I found the book again: Paradoxes in Politics 1976 by Steven J. Brams. The byline is ‘An Introduction to the Nonobvious in Political Science’, and this is just what it is. There is a pretty good selection of counter-intuitive situations that could arise in issues related to voting, and a mathematical and game theory treatment of the situations to reveal the, well, non-obvious resulting consequences. It’s 231 pages, and pretty well written for technical approaches to social topics. In other words, I sympathize!
And, in section 7.5 the discussion turns to block voting power, and the measure I have called Decisiveness in these essays of mine are formally introduced. Paradoxes describes several ways to present the power value, and the version I am using was introduced as the Coleman index by a James Coleman in a paper in 1971. The author Brams gives as working examples the initial 1958 and later expanded 1973 Council of Ministers for the European Economic Community, and highlights the curious feature that for 15 years Luxembourg had a seat at the council but, because of the vote weight distribution of the council members, had no influence! As Brams says,
Unless its representative was able, in discussion, to influence the voting decision of representatives from other countries, he might as well have not attended Council meetings.
A friend of mine read through the whole set of the Why the 3E Senate is a Silly Idea essays and said that one thing lacking was some good footnotes or a reading list or something. He is probably right, and I will put some references in as my hobby time allows. This little post can count as one. I will probably put some in as direct links in the text, too.