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Influence Indices

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Author Info
Michel Grabisch () (CES - Centre d'économie de la Sorbonne - CNRS : UMR8174 - Université Panthéon-Sorbonne - Paris I)
Agnieszka Rusinowska () (GATE - Groupe d'analyse et de théorie économique - CNRS : UMR5824 - Université Lumière - Lyon II - Ecole Normale Supérieure Lettres et Sciences Humaines)

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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.

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Paper provided by HAL in its series Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) with number halshs-00142479_v1.

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Date of creation: Mar 2007
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Handle: RePEc:hal:cesptp:halshs-00142479_v1

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Related research
Keywords: Hoede-Bakker index ; influence function ; influence indices;

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References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
  1. Hsiao Chih-Ru & Raghavan T. E. S., 1993. "Shapley Value for Multichoice Cooperative Games, I," Games and Economic Behavior, Elsevier, vol. 5(2), pages 240-256, April. [Downloadable!] (restricted)
  2. Annick Laruelle & Federico Valenciano, 2005. "Assessing success and decisiveness in voting situations," Social Choice and Welfare, Springer, vol. 24(1), pages 171-197, January. [Downloadable!] (restricted)
  3. Agnieszka Rusinowska, 2007. "The not-preference-based Hoede-Bakker index," Working Papers 0704, Groupe d'Analyse et de Théorie Economique (GATE), Centre national de la recherche scientifique (CNRS), Université Lyon 2, Ecole Normale Supérieure. [Downloadable!]
  4. MoshÊ Machover & Dan S. Felsenthal, 1997. "Ternary Voting Games," International Journal of Game Theory, Springer, vol. 26(3), pages 335-351.
  5. R J Johnston, 1978. "On the measurement of power: some reactions to Laver," Environment and Planning A, Pion Ltd, London, vol. 10(8), pages 907-914, August. [Downloadable!] (restricted)
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