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Axiomatic characterization of some extensions
(2009-12-12)
The general problem we are interested in this paper is of the following variety. We are given a finite universal set and a linear ordering on it. What is the minimal axiomatic characterization of a particular extension of ...
Shifts in choice problems
(2009-12-12)
In this paper we consider choice problems which are bounded both above and below and provide a new axiomatic characterization of the equal loss choice function. We subsequently turn to a study of various properties implied ...
Axiomatic characterizations of the CEA solution for rationing problems
(2009-12-12)
Situations abound in the real world, where aggregate demand for a commodity exceeds aggregate supply. When such situations of excess demand occur, what is required is some kind of rationing. The literature on rationing ...
New congruence axiom and transitive rational choice
(2009-12-12)
Rationality in choice theory has been an abiding concern of decision theorists. A rationality postulate of considerable significance in the literature is the weak congruence axiom of Richter [1971] and Sen [1971]. It is ...
Consequence of chernoff and outcasting
(2009-12-12)
The purpose of this paper is to prove by induction the theorem (in Aizerman and Malishevsi [1981]) that a choice function which satisfies Chernoff s axiom and Outcasting can always by expressed as the union of the solution ...
The equal loss choice function revisited
(2009-12-12)
Choice theory is a mathematical discipline which studies the problem of choosing a point from a set of points by studying the mathematical properties of maps assigning an outcome to each choice problem in some class of ...
A note on numerical representations of quasi-transitive binary relations
(2009-12-12)
A Binary relation is said to be quasi-transitive if its asymmetric part is transitive. A binary relation is said to be a weak-order if it is reflexive, complete and transitive. One may refer to Frensh [1986] for a synopsis ...
Rational choice correspondence in social choice problems
(2009-12-12)
This paper grew out of a reading of an interesting exposition by Danilov and Sotskov [1997], where general one to one correspondences are established between binary relations and choice correspondences. Out purpose in this ...
Theorem in utility theory revisited
(2009-12-12)
We provide in this paper a simple proof of the proposition that comparability of first differences of utility implies cardinality when the range of the utility function is a connected subset of the reals.
Extended partial orders: a note
(2009-12-12)
The purpose of this paper is to establish the equivalence of two axioms one of which appear in Nehring [1997] and the other in Nehring and Puppe [1999]. The one in Nehring and Puppe [1999] is due to Aizerman and Malishevski ...