Protectionism and blocking power indices

摘要

We study here the protectionist role of blocking coalitions in a voting game. More precisely, we first present necessary properties that a family of coalitions must satisfy in order to be the blocking family of some game and show that they are sufficient conditions too. Furthermore, a procedure to determine all games having a given blocking family is provided. With regard to uniqueness and multiplicity, (a) the blocking families that univocally determine the game are characterized by means of a separation condition, and (b) it is shown that in the nonseparating case at least three games share each nonempty blocking family, and an upper bound is given for the number of such games. Some numerical examples illustrate our results. Finally, power indices related to the blocking structure are discussed.