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Threshold of median rank solutions
(2010-01-18)
In this paper we consider solutions defined on the class of transitive tournaments. Such solutions are essentially rank solutions i.e. solutions which depend on the ranks of the alternatives and not on any other physical ...
Quasitransitivity and monotonic preference for freedom
(2010-01-16)
We consider a finite universal set of alternatives and the set of all feasible sets are simply the set of all non-empty subsets of this universal set. A choice function assigns to each feasible set a non-empty subset of ...
Weighted fair division problem
(2010-01-18)
The exact problem we are concerned with in this paper is of the following nature. There are a finite number of producers each equipped with a utility function of the standard variety, which converts and input into a producer ...
Lexicographic composition of abstract games
(2010-01-18)
In this paper we begin by obtaining a necessary and sufficient condition for a quasi transitive binary relation to be transitive. Then we obtain necessary and sufficient conditions for the lexicographic composition of two ...
Consequence of chernoff and outcasting and solutions for abstract games
(2010-01-16)
The purpose of this paper is to prove by induction the theorem (in Aizerman and Malishevski [1981]) that a choice function which satisfies Chernoffs axiom and Outcasting can always by expressed as the union of the solution ...
Preservation of proximity and merging functions
(2010-01-16)
In this paper we are interested in a property due to Baigent (1987) called proximity preserving. In the conventional model of voting theory it was proposed by Baigent that aggregation procedures should be proximity preserving ...
One dimensional kakutani's fixed point theorem: a classroom capsule
(2010-01-16)
A feature of the study of such problems which is difficult to miss is that there is a clear dichotomy between the analytical methodology concerning the study of problems of fair division of just one commodity and the ...
Axiomatic characterisation of weighted voting operator
(2010-01-18)
A federation voting operator allows a finite set of coalitions to unilaterally elect any outcome. There are several special types of federation voting operators, all of which share a property: the candidates are assigned ...
Note on characterising the median
(2010-01-16)
Consider the situation where one has to choose one among three differently priced birthday cakes, to give to a friends. It is very likely, that in the absence of strong personal reasons, one would select the cake whose ...
One dimensional Kakutani's fixed point theorem in problems of fair division: a classroom capsule
(2010-01-16)
In this paper, we provide a simple proof of the one-dimensional version of the Kakutani s fixed point theorem, which is required to prove the existence of a Walrasian equilibrium in a two commodity multi-agent economy where ...