Comparing Power Indices

Abstract

This paper aims to give a global vision concerning the state of the art of studies on 13 power indices and to establish which of them are more suitable for describing the real situations which are, from time to time, taken into consideration. In such contexts, different comparisons have been developed in terms of properties, axiomatic grounds and so on. This analysis points out various open problems.

Indirect Control of Corporations: Analysis and Simulations

“…, f n (v)) to any simple game v with n players, where real number f i (v) is the power of player i in game v. In relation to corporate shareholding structures, we can quote Crama and Leruth (2007) that "power indices are expected to reflect the relative capacity of each shareholder (be it a firm or an individual) to impose its will to a target company, measured either by its ability to form coalitions with other shareholders to win a vote, or by its ability to change the final outcome of a vote by swinging its own vote". For some comparisons of power indices, see (Bertini et al, 2013;Bertini and Stach, 2015;Stach, 2016), for example. This paper is organized as follows.…”

“…The first three mentioned indices give more power to a player who is critical in more winning coalitions. Of course, these indices also take into account other aspects than criticality for the coalitions [see, for example, (Bertini et al, 2013)]; but here, we do not enter in these particularities. The Holler index gives more power to players belonging to more minimal winning coalitions.…”

Coalitional multinomial probabilistic values

“…It becomes a lattice under the standard composition laws given in [6] for a good survey on power indices and to [15] for the use of semivalues as such). The restriction to SG N of any value on G N is, of course, a power index, which will be denoted by the same symbol.…”

Measuring Voting Power in Convex Policy Spaces

“…In order to measure the individual's ability to influence the aggregated group decision by changing its own vote, a vast amount of so-called power indices was introduced, see, e.g., [25]. A common core is captured by: Definition 10.…”