Geodesic
Probabilistic comparison of weighted majority rules
Daniel Berend1 ; Luba Bromberg1 ; Luba Sapir1
1 Departments of Mathematics and Computer Science Ben-Gurion University 84105 Be'er Sheva, Israel
Applicationes Mathematicae, Tome 39 (2012) no. 2, pp. 151-167 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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This paper studies a bi-parametric family of decision rules, so-called restricted distinguished chairman rules, which contains several one-parameter classes of rules considered previously in the literature. Roughly speaking, these rules apply to a variety of situations where the original committee appoints a subcommittee. Moreover, the chairman of the subcommittee, who is supposed to be the most competent committee member, may have more voting power than other jurors. Under the assumption of exponentially distributed decision skills, we obtain an analytic formula for the probability of any restricted distinguished chairman rule being optimal. We also study, for arbitrary fixed voting power of the chairman, the connection between the probability of the rule being optimal and the size of the subcommittee.
DOI : 10.4064/am39-2-4
Keywords: paper studies bi parametric family decision rules so called restricted distinguished chairman rules which contains several one parameter classes rules considered previously literature roughly speaking these rules apply variety situations where original committee appoints subcommittee moreover chairman subcommittee who supposed competent committee member may have voting power other jurors under assumption exponentially distributed decision skills obtain analytic formula probability restricted distinguished chairman rule being optimal study arbitrary fixed voting power chairman connection between probability rule being optimal size subcommittee

Daniel Berend 1 ; Luba Bromberg 1 ; Luba Sapir 1

1 Departments of Mathematics and Computer Science Ben-Gurion University 84105 Be'er Sheva, Israel 
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Daniel Berend; Luba Bromberg; Luba Sapir. Probabilistic comparison of
 weighted majority rules. Applicationes Mathematicae, Tome 39 (2012) no. 2, pp. 151-167. doi: 10.4064/am39-2-4

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