Power indices of players in systems with weighted voting (Q1348542)

The problem of constructing of power indices of players in a scheme of weighted voting is considered. The method of normalized weighting vectors produces (for a some quota -- a beforehand established number of voices) a set of gained alliances. For each player a sufficiently sharp segment of possible weights is determined so that each point of the segment is an estimate of the power and its length is proportional of the in-accuracy of this notion. An apriori estimate of the in-accuracy in terminology of a minimizing function is found. An essential difference of the indices emerges from the use of normalized weighting vectors minimising a function. Some additional properties of the scheme of a weighted voting are disscused.