Measuring Power and Satisfaction in Societies with Opinion Leaders: Properties of the Qualified Majority Case

Groupe d'Analyse et de Théorie Économique (GATE) Working Paper No. 09-01

22 Pages Posted: 28 Jan 2009 Last revised: 15 Apr 2011

See all articles by René van den Brink

René van den Brink

VU University Amsterdam - Department of Economics; Tinbergen Institute; Tinbergen Institute

Agnieszka Rusinowska

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

Frank Steffen

University of Liverpool - Management School (ULMS); University of Bayreuth - Faculty of Law, Business and Economics

Date Written: January 1, 2009

Abstract

A well known and established model in communication policy in sociology and marketing is that of opinion leadership. It is based on the idea of a two-step flow of communication. Opinion leaders are actors in a society who are able to affect the behavior of other members of the society called followers. Hence, opinion leaders might have a considerable impact on the behavior of markets and other social agglomerations being made up of individual actors choosing among a number of alternatives. For marketing purposes it appears to be interesting to investigate the effect of different opinion leader-follower structures in markets or any other collective decision-making situations in a society. We study a two-action model in which the members of a society are to choose one action, for instance, to buy or not to buy a certain joint product, or to vote yes or no on a specific proposal. Each of the actors has an inclination to choose one of the actions. By definition opinion leaders have some power over other actors, their followers, and they exercise this power by influencing the behavior of their followers, i.e. their choice of action. After all actors have chosen their actions, a decision-making mechanism determines the collective choice resulting out of the individual choices. The structure of the relations between the actors can be represented by a bipartite digraph. We analyze such digraphs investigating satisfaction and power distributions within societies with and without the opinion leaders. Moreover, we study common properties of the satisfaction and power measures and illustrate our findings and some marketing implications for a society with five members.

Keywords: Bipartite digraph, influence, inclination, collective choice, opinion leader, follower, satisfaction, power

JEL Classification: C7, D7

Suggested Citation

van den Brink, J.R. (René) and Rusinowska, Agnieszka and Steffen, Frank, Measuring Power and Satisfaction in Societies with Opinion Leaders: Properties of the Qualified Majority Case (January 1, 2009). Groupe d'Analyse et de Théorie Économique (GATE) Working Paper No. 09-01, Available at SSRN: https://ssrn.com/abstract=1334122 or http://dx.doi.org/10.2139/ssrn.1334122

J.R. (René) Van den Brink (Contact Author)

VU University Amsterdam - Department of Economics ( email )

De Boelelaan 1105
1081 HV Amsterdam
Netherlands

Tinbergen Institute ( email )

Burg. Oudlaan 50
Rotterdam, 3062 PA
Netherlands

Tinbergen Institute ( email )

Burg. Oudlaan 50
Rotterdam, 3062 PA
Netherlands

Agnieszka Rusinowska

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

93, chemin des Mouilles
Ecully, 69130
France

Frank Steffen

University of Liverpool - Management School (ULMS) ( email )

Chatham Street
Liverpool, L69 7ZH
Great Britain

University of Bayreuth - Faculty of Law, Business and Economics ( email )

Universitätsstraße 30
Bayreuth, 95447
Germany