Tutorial on Power indices next Tuesday (reminder)
Francis Bloch
This tutorial provides a rigorous and unified treatment of power measurement in collective decision-making environments. The central objective is to develop a precise mathematical understanding of power indices in simple voting games and in games with multiple levels of approval, with a particular focus on ordinal comparisons of players. The course emphasizes formal definitions, axiomatic characterizations, and careful distinctions between cardinal measurements of power and ordinal rankings induced by different indices. We mainly focus on the most common power indices (including The Shapley-Shubik, Banzhaf-Coleman, Deegan Packel and Johnston power indices) and the desirability relation, originally defined in voting games and extended later on to the more general classes of games with multiple levels of approval in the input. A key goal is to identify conditions under which distinct power indices lead to the same ordering of players, and to understand structurally why and when ordinal equivalence fails.