Generalizing and Modifying the Hoede-Bakker Index

The Not-Preference-Based Hoede-Bakker Index

“…This result is in the line with the result obtained in Rusinowska and De Swart (2006), where using a different method it was shown that the generalized Hoede-Bakker index of a player is equal to the probability that the player is decisive, and consequently, that the generalized Hoede-Bakker index coincides with the absolute Banzhaf index. This result was shown under assumptions that all vote configurations (coalitions) as well as all inclination vectors are equally probable.…”

“…In Rusinowska and De Swart (2006), instead of imposing (3), the authors adopted the following two axioms (together with (4)):…”

“…In Section 2, we recapitulate the concepts of the Hoede-Bakker index (Hoede and Bakker 1982) and the generalized Hoede-Bakker index (Rusinowska and de Swart 2006). Section 3 concerns a modification of the HoedeBakker index, introducing the not-preference-based version of this index.…”

“…Some properties of the Hoede-Bakker index, including its sensitivity to voting power paradoxes, have been analyzed by Rusinowska and De Swart (2007). In Rusinowska and De Swart (2006), a natural generalization of the Hoede-Bakker index, coinciding with the absolute Banzhaf index (Banzhaf 1965) has been presented. Moreover, the authors proposed several modifications of the Hoede-Bakker index that coincide with the Rae index (Rae 1969), the Coleman indices (Coleman 1971(Coleman , 1986, and the König-Bräuninger index (König and Bräuninger 1998).…”

Influence functions, followers and command games

“…in [9][10][11][25][26][27]. We consider a social network with the set of players (agents, voters) denoted by N := {1, ..., n}.…”