The not-preference-based Hoede-Bakker index
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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References listed on IDEAS
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- Annick Laruelle & Federico Valenciano, 2005.
"Assessing success and decisiveness in voting situations,"
Social Choice and Welfare,
Springer;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.
- Philip Straffin, 1977. "Homogeneity, independence, and power indices," Public Choice, Springer, vol. 30(1), pages 107-118, June.
- Harrie De Swart & Agnieszka Rusinowska, 2007. "On some properties of the Hoede-Bakker index," Post-Print halshs-00201414, HAL. Full references (including those not matched with items on IDEAS)