Dept. Math, Hokkaido Univ. EPrints Server

Faces of arrangements of hyperplanes and Arrow's impossibility theorem

Preprint Series # 805
Abe, Takuro Faces of arrangements of hyperplanes and Arrow's impossibility theorem. (2006);

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Abstract

In \cite{T}, Terao introduced an admissible map of chambers of a real central arrangement, and completely classified it. An admissible map is a generalization of a social welfare function and Terao's classification is that of Arrow's impossibility theorem in economics. In this article we consider an admissible map not of chambers but faces, and show that an admissible map of faces is a projection to a component if an arrangement is indecomposable and its cardinality is not less than three. From the view point of Arrow's theorem, our result corresponds to the impossibility theorem of a welfare function which permits the ''tie" choice.

Item Type:Preprint
Additional Information:30
Uncontrolled Keywords:Arrow's impossibility theorem, arrangements of hyperplanes, faces
Subjects:91-xx GAME THEORY, ECONOMICS, SOCIAL AND BEHAVIORAL SCIENCES
52-xx CONVEX AND DISCRETE GEOMETRY
05-xx COMBINATORICS
ID Code:1620