Bezalel Peleg and Hans Peters: Strategic social choice. Stable representations of constitutions

Many sincere compliments should be addressed to Bezalel Peleg and Hans Peters, the authors of the book Strategic Social Choice. Stable Representations of Constitutions published last year by Springer. Our experience with the previous books of these authors on game theory (Peleg 1984; Peleg and Sudhölter 2003; Peters 1992, 2008) induces very high expectations with respect to this jointly written monograph. And we have not been disappointed with their new project. The book studies stable representations of constitutions. The authors follow Gärdenfors (1981) who modeled constitutions as effectivity functions, a term introduced independently by Moulin and Peleg (1982) in the general context of game theory and its relation to social choice. An effectivity function assigns to each group in a society a collection of sets of social states. The manuscript is based on work that has appeared over the last thirty years, but it also contains many new results and new or improved proofs of existing results. Among various sources of the results collected in the book, the authors used, e.g., Abdou (1988), Abdou and Keiding (1991), Holzman (1986), Keiding and Peleg (2006), Peleg (1998, 2004), Peleg and Peters (2006, 2009), Peleg et al. (2002). The emphasis in the book by Peleg and Peters is on strategic stability of game forms that represent effectivity functions. As the authors mention themselves, their aim is not to contribute substantially to the purely philosophical literature on constitutions, and equity or fairness, but they focus on representation and game-theoretic stability, and rather contribute to the economic literature on mechanism design taken in a wide sense.