Ordinal power indeces

11 AM, Laboratory 4, Doctoral School of Social Sciences, via Verdi 26

Speaker

• Stefano Moretti, Université Paris-Dauphine

Abstract

Power indices have been widely used in the literature of cooperative games to assess the influence of single players in a setting where coalitions are winning or losing. On the other hand, many practical situations are characterized by coalitions (e.g., representing alliances of political parties, or federations of States, or football teams, etc.) that are ordered according to their “strength”, and where the notion of winning and losing groups does not apply. For instance, consider a company with three employees 1,2 and 3 working in the same department. According to the opinion of the manager of the company, the job performance of the different teams S ⊆ {1,2,3} is as follows: {1,2,3}> {3}> {1,3} >{2,3} >{2} >{1,2} >{1}  (S>T, for each non-empty  set S,T ⊆ {1,2,3}, means that the performance of S is at least as good as the performance of T). Based on this information, the manager asks us to make a ranking over his three employees showing their attitude to work with others or autonomously. Intuitively, 3 seems to be more influential than 1 and 2, as employee 3 belongs to the most successful teams in the above ranking. Can we state more precisely the reasons driving us to this conclusion? And what can we say if we have to decide who between 1 and 2 is more productive and deserves a promotion? This kind of questions are central for this talk.