Measuring influence among players with an ordered set of possible actions
In the paper, we introduce and study generalized weighted influence indices of a coalition on a player, where players have an ordered set of possible actions. Each player has an inclination to choose one of the actions. Due to influence of a coalition of other players, a final decision of the player may be different from his original inclination. An influence in such situations is measured by the general weighted influence index. In a particular case, the decision of the player may be closer to the inclination of the influencing coalition than his inclination was. The weighted influence index which captures such a case is called the positive weighted influence index. We also consider the negative weighted influence index, where a final decision of the player goes farther away from the inclination of the influencing coalition. Some special cases of the weighted influence indices, called a possibility influence index and an equidistributed influence index, are also defined. We consider different influence functions and study their properties. A set of followers and a set of a conditional followers of a given coalition are defined, and their properties are analyzed. We define the concepts of success, decisiveness, luck, and failure for the multi-choice model of influence.
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- Agnieszka Rusinowska, 2007.
"The not-preference-based Hoede-Bakker index,"
- Agnieszka Rusinowska & Michel Grabisch, 2007.
0705, Groupe d'Analyse et de Théorie Economique (GATE), Centre national de la recherche scientifique (CNRS), Université Lyon 2, Ecole Normale Supérieure.
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- Annick Laruelle & Federico Valenciano, 2005.
"Assessing success and decisiveness in voting situations,"
Social Choice and Welfare,
The Society for Social Choice and Welfare, vol. 24(1), pages 171-197, January.
- Annick Laruelle & F. Valenciano, 2005. "Assessing success and decisiveness in voting situations," Post-Print halshs-00109417, HAL.
- MoshÊ Machover & Dan S. Felsenthal, 1997. "Ternary Voting Games," International Journal of Game Theory, Springer;Game Theory Society, vol. 26(3), pages 335-351.
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