Hiroaki Terao
(Tokyo Metropolitan University)
Arrangement of hyperplanes and the ranking problem in statistics
Abstract: A psychologist C. H. Coombs, in 1950, initiated study of the "1-dimensional ideal point model" in the social choice theory. The ranking problem, which naturally occurs in the study, can be interpreted as a problem in the theory of hyperplane arrangements. Actually H. Kamiya and A. Takemura(1997), two statisticians, applied the theory of hyperplane arrangements to the "higher-dimensional ideal point model." In this talk we propose a new approach to the ranking problem after we briefly review its history.