The average representation - a cornucopia of power indices?
  For the classical power indices there is a disproportion between power and relative weights, in general. We introduce two new indices, based on weighted representations, which are proportional to suitable relative weights and which also share several important properties of the classical power indices. Imposing further restrictions on the set of representations may lead to a whole family of such indices. 
Serguei Kaniovski and Sascha Kurz
cs.GT