Topological structure of a space of continuous preferences as a space of retractions and the aggregation problem
This paper shows that a procedure introduced by \textit{G. Chichilnisky} [Adv. Math. 37, 165-176 (1980; Zbl 0446.90004)], can well be used for preferences that are continuous and admit thick indifference classes and satiation points. We study two interrelated problems, (i) the choice of an appropriate topology for a class of preferences and (ii) the topological structure of the preference space. We show that the choice of the Kannai topology is adequate since it makes the preference space complete and Hausdorff. We also show that this topology coincides, on this space, with the closed convergence topology and that the conditions of \textit{G. Chichilnisky} and \textit{G. Heal} [J. Econ. Theory 31, 68-87 (1983; Zbl 0519.90012)] for the existence of continuous, anonymous and unanimous aggregation rules are met.
scientific article; zbMATH DE number 4047380