The categorical approach to social choice theory

A number of different problems in social choice theory are given a common treatment in the framework of category theory. A social choice function is a map μ from a set Hom(A, PX) of profiles - in applications functions from a set A of agents to the set PX of linear orders on a set X of alternatives - to a set GPX the nature of which depends on the application. The main theorem established is applied to social welfare functions and strategy-proof voting schemes.     

The median procedure in cluster analysis and social choice theory

Classical approachs for fitting and aggregation problems, specially in cluster analysis, social choice theory and paired comparisons methods, consist in the minimization of a remoteness function between relational data and a relational model. The notion of median, with its algebraic, metric, geometrical and statistical aspects, allow a unified treatment of many of base problems. Properties of median procedures are organized according to four directions: stabilities and axiomatic characterizations; Arrow-like properties; combinatorial properties; effective computational possibilities. Finally, interesting mathematical problems, related to the notion of median are surveyed.