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); AbstractIn \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.
