AbstractIn 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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Bibliographic InfoPaper provided by Groupe d'Analyse et de Théorie Economique (GATE), Centre national de la recherche scientifique (CNRS), Université Lyon 2, Ecole Normale Supérieure in its series Working Papers with number 0705.
Length: 33 pages
Date of creation: Mar 2007
Date of revision:
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Hoede-Bakker index; influence function; influence indices;
Other versions of this item:
- Michel Grabisch & Agnieszka Rusinowska, 2007. "Influence Indices," UniversitÃ© Paris1 PanthÃ©on-Sorbonne (Post-Print and Working Papers) halshs-00142479, HAL.
- C7 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory
- D7 - Microeconomics - - Analysis of Collective Decision-Making
This paper has been announced in the following NEP Reports:
- NEP-ALL-2007-03-24 (All new papers)
- NEP-GTH-2007-03-24 (Game Theory)
- NEP-POL-2007-03-24 (Positive Political Economics)
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.:
- Annick Laruelle & Federico Valenciano, 2005. "Assessing success and decisiveness in voting situations," Social Choice and Welfare, Springer, vol. 24(1), pages 171-197, January.
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- Agnieszka Rusinowska, 2007.
"The not-preference-based Hoede-Bakker index,"
0704, Groupe d'Analyse et de Théorie Economique (GATE), Centre national de la recherche scientifique (CNRS), Université Lyon 2, Ecole Normale Supérieure.
- MoshÊ Machover & Dan S. Felsenthal, 1997. "Ternary Voting Games," International Journal of Game Theory, Springer, vol. 26(3), pages 335-351.
- Michel Grabisch & Agnieszka Rusinowska, 2008.
"Measuring influence among players with an ordered set of possible actions,"
0801, Groupe d'Analyse et de Théorie Economique (GATE), Centre national de la recherche scientifique (CNRS), Université Lyon 2, Ecole Normale Supérieure.
- Michel Grabisch & Agnieszka Rusinowska, 2008. "Measuring influence among players with an ordered set of possible actions," UniversitÃ© Paris1 PanthÃ©on-Sorbonne (Post-Print and Working Papers) halshs-00260863, HAL.
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