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The not-preference-based Hoede-Bakker index

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Author Info

  • Agnieszka Rusinowska

    ()
    (GATE CNRS)

Abstract

The paper concerns a certain modification of the generalized Hoede-Bakker index - a notion defined for a social network of players. In the original Hoede-Bakker set up, preferences of players are involved. It is assumed that a player has an inclination either to accept or to reject a proposal, but due to the influence of others, his final decision may be different from his original inclination. In this paper, we propose the not-preference-based (NPB) generalized Hoede-Bakker index, where feasible strategies instead of players’ inclinations are considered. We show that if all feasible strategy profiles are equally probable, then the NPB generalized Hoede-Bakker index is a ‘net’ Success, i.e., ‘Success - Failure’, where Success and Failure of a player is defined as the probability that the player is successful and fails, respectively. Moreover, under the assumption of equal probabilities of all feasible strategy profiles, we show that the probability that a player is lucky (Luck) equals the probability that he fails (Failure). Since Success - Luck = Decisiveness, it follows that, under the same assumption, the NPB generalized Hoede-Bakker index is equal to the probability that a player is decisive.

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File URL: ftp://ftp.gate.cnrs.fr/RePEc/2007/0704.pdf
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Bibliographic Info

Paper 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 0704.

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Length: 16 pages
Date of creation: Mar 2007
Date of revision:
Handle: RePEc:gat:wpaper:0704

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Keywords: Hoede-Bakker index; feasible strategy; success; failure; decisiveness;

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References

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  1. Annick Laruelle & Federico Valenciano, 2005. "Assessing success and decisiveness in voting situations," Social Choice and Welfare, Springer, vol. 24(1), pages 171-197, January.
  2. Philip Straffin, 1977. "Homogeneity, independence, and power indices," Public Choice, Springer, vol. 30(1), pages 107-118, June.
  3. Harrie De Swart & Agnieszka Rusinowska, 2007. "On some properties of the Hoede-Bakker index," Post-Print halshs-00201414, HAL.
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Citations

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Cited by:
  1. repec:hal:cesptp:halshs-00344457 is not listed on IDEAS
  2. repec:hal:cesptp:halshs-00308741 is not listed on IDEAS
  3. Agnieszka Rusinowska, 2007. "Modifying the Hoede-Bakker index to the Shapley-Shubik and Holler-Packel indices," Working Papers 0729, Groupe d'Analyse et de Théorie Economique (GATE), Centre national de la recherche scientifique (CNRS), Université Lyon 2, Ecole Normale Supérieure.
  4. repec:hal:cesptp:hal-00519413 is not listed on IDEAS
  5. repec:hal:cesptp:halshs-00142479 is not listed on IDEAS
  6. Michel Grabisch & Agnieszka Rusinowska, 2008. "Measuring influence among players with an ordered set of possible actions," Working Papers 0801, Groupe d'Analyse et de Théorie Economique (GATE), Centre national de la recherche scientifique (CNRS), Université Lyon 2, Ecole Normale Supérieure.
  7. Michel Grabisch & Agnieszka Rusinowska, 2010. "A model of influence in a social network," Theory and Decision, Springer, vol. 69(1), pages 69-96, July.
  8. Agnieszka Rusinowska & Michel Grabisch, 2007. "Influence Indices," Working Papers 0705, Groupe d'Analyse et de Théorie Economique (GATE), Centre national de la recherche scientifique (CNRS), Université Lyon 2, Ecole Normale Supérieure.
  9. Michel Grabisch & Agnieszka Rusinowska, 2010. "A model of influence with an ordered set of possible actions," Theory and Decision, Springer, vol. 69(4), pages 635-656, October.

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