What is a good introductory book on Rational Choice Theory for a mathematician?

Question

I'm interested in Rational Choice Theory as an approach to political science. Amongst other, related subjects, I'd like to know a thing or two about Arrow's impossibility theorem (and other aspects of voting theory), the logic behind collective action by Mancur Olson and the veto power model of Tjebelis. Do you know a good introductory book on this subject (for a mathematician)? I'm also interested in historical examples in which the abstract mathematics is concretised in actual political discourse.

Answer 1

At first, I am sorry for bumping an old post.

Now, one must consider that the mentioned authors, even though as a part of Rational Choice as an approach, work on different, but relatable, things.

Arrow contributions on politics may be resumed as a fundamental part of Social Choice Theory. If one is interested solely on Arrow Impossibility Theorem, then, one may as well read his Social Choice and Individual Values( 1963, reprinted on 2012 ). Otherwise, I would recommend Wulf Gaertner's textbook: A Primer In Social Choice Theory( 2006 ), where he presents not only Axiomatic Social Choice( including Arrow, Gibbart-Satterthwaite theorem, etc. ), but also Empirical Social Choice. There is also Alan D. Taylor, with both "Mathematics and Politics: Strategy, Voting, Power, and Proof"( 2009 ) and "Social Choice and the Mathematics of Manipulation"( 2005 ).

About Collective Action, I cannot remember, besides Mancur Olson's book itself, of any book or author that does a job similar to Gaertner's job on his Primer. The literature strictly on this topic comes mainly from Garret Hardin's paper, The Tragedy Of The Commons( 1968 ), and Elinor Ostrom's( and her Husband, Vincent ) Governing The Commons( 1990 ). None of those can be considered mathematically intense.( Apart from the mentioned books, contributions to this area were made by researchers from Game Theory, mostly cooperative Game Theory; and computational social scientists ).

Now, Tsebelis' work can be considered as a using both Social Choice and Game Theory( he uses the notion of Nested Games ). There are a lot of textbooks on Game Theory, where many of them have as prerequisite a good base on mathematics( probability theory, linear algebra, calculus, and, maybe, for the hardest ones, real analysis ): Roger B. Myerson - Game Theory: Analysis of Conflict( 1997 ); Ken Binmore - Playing For Real: A Text on Game Theory( 2007 ); Steven Tadelis - Game Theory: An Introduction( 2013 ).

I hope it helps!