Axiomatic characterizations of threshold choice functions for comparison functions. (Q1867658)

The threshold choice functions associated with comparison functions (reciprocal fuzzy relations) are characterized. A special type of these functions is the Orlovsky choice function (with threshold \(1/2\)). This family is somewhat larger than the family of choice functions which select only those alternatives that secure a certain pre-specified proportion of the votes against all other alternatives. It also includes functions which select only those alternatives that exceed a certain pre-specified proportion of the votes against all other alternatives. The authors axiomatically characterize the same choice functions using some assumptions that have been used by \textit{K. Sengupta} [Soc. Choice Welfare 16, 259--272 (1999)] except continuity.