Influence Indices

Documents De Travail Working Paper No. 07-05

33 Pages Posted: 24 May 2007 Last revised: 11 May 2010

See all articles by Michel Grabisch

Michel Grabisch

Université Paris I Panthéon-Sorbonne - CERMSEM

Agnieszka Rusinowska

University of Lyon 2 - Groupe d'Analyse et de Théorie Economique (GATE)

Date Written: March 1, 2007

Abstract

In the paper, we investigate the Hoede-Bakker index - the notion which computes the overall decisional 'power' of a player in a social network. It is assumed that each player has an inclination (original decision) to say 'yes' or 'no' which, due to influence of other players, may be different from the final decision of the player. The main drawback of the Hoede-Bakker index is that it hides the actual role of the influence function, analyzing only the final decision in terms of success and failure. In this paper, we further investigate the Hoede-Bakker index, proposing an improvement which fully takes into account the mutual influence among players. A global index which distinguishes an influence degree from a 'power' index is analyzed. We define weighted influence indices, in particular, a possibility influence index which takes into account any possibility of influence, and a certainty influence index which expresses certainty of influence. We consider different influence functions and study their properties.

Keywords: Hoede-Bakker index , influence function , influence indices

JEL Classification: C7 , D7

Suggested Citation

Grabisch, Michel and Rusinowska, Agnieszka, Influence Indices (March 1, 2007). Documents De Travail Working Paper No. 07-05, Available at SSRN: https://ssrn.com/abstract=988301 or http://dx.doi.org/10.2139/ssrn.988301

Michel Grabisch (Contact Author)

Université Paris I Panthéon-Sorbonne - CERMSEM ( email )

106-112, Boulevard de l'Hôpital
Paris, 75647
France

Agnieszka Rusinowska

University of Lyon 2 - Groupe d'Analyse et de Théorie Economique (GATE) ( email )

93, chemin des Mouilles
Ecully, 69130
France