An Abstract Result on Projective Aggregation Functions

Abstract

Abstract:A general characterization result of projective aggregation functions is shown, the proof of which makes use of the celebrated Arrow's theorem, thus providing a link between aggregation functions theory and social choice theory. The result can be viewed as a generalization of a theorem obtained by Kim (1990) for real-valued aggregation functions defined on the n-dimensional Euclidean space in the context of measurement theory. In addition, two applications of the core theorem of the article are shown. The first is a simple extension of the main result to the context of multi-valued aggregation functions. The second offers a new characterization of projective bijection aggregators, thus connecting aggregation operators theory with social choice.

Quantiles in Abstract Convex Structures

“…We propose also a particular version of Arrow's theorem thus considering a link between aggregation theory and social choice theory as in [6]. It appears that there are many connections between the work presented here with the results of [3,4,[7][8][9][10][11][12].…”