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J. Freixas, D. Marciniako and M. Pons, “On the Ordinal Equivalence of the Johnston, Banzhaf and Shapley Power Indices,” European Journal of Operation Research, Vol. 216, No. 2, 2011, pp. 367-375. doi:10.1016/j.ejor.2011.07.028

has been cited by the following article:

• TITLE: Revenue Sharing in Hierarchical Organizations: A New Interpretation of the Generalized Banzhaf Value

  AUTHORS: Roland Pongou, Bertrand Tchantcho, Narcisse Tedjeugang

  KEYWORDS: Hierarchical Organizations; Earnings; Marginal Productivity; Generalized Banzhaf Value

  JOURNAL NAME: Theoretical Economics Letters, Vol.2 No.4, November 1, 2012

  ABSTRACT: This paper examines the distribution of earnings in a new model of hierarchical multi-task organizations. Each such organization is defined by a finite set of workers and tasks together with a production function that maps each allocation of workers to the tasks into an aggregate output. Tasks are ordered in degree of importance so that aggregate output increases when a worker climbs up the organization ladder. We show that the generalized Banzhaf value proposed by Freixas [1] can be used as a theory of revenue sharing in such organizations, and provide a new interpretation and formulation of this sharing rule, proving that a worker's pay is proportional to the difference between his marginal productivity at the top level and at the bottom level of the hierarchy summed over all the possible configurations of the organization. This new formulation also facilitates computation.