Topological social choice: Reply to Le Breton and Uriarte (Q908827)

In a recent paper \textit{M. Le Breton} and \textit{J. R. Uriarte} [ibid. 7, No.2, 131-140 (1990; Zbl 0693.90010)], hereafter LBU, offer a critique of \textit{G. Chichilnisky}'s impossibility theorem [Econ. Letters 3, No.4, 347-351 (1979; Zbl 0693.90008); Adv. Math. 37, 165-176 (1980; Zbl 0446.90004); Q. J. Econ. 97, 337-352 (1982; Zbl 0479.90018)]. Of the many statements of Chichilnisky's theorem, they single out the one of the first author [Econ. Letters 16, No.1/2, 23-25 (1984; Zbl 0693.90009); J. Math. Econ. 14, 1-4 (1985; Zbl 0588.90005)] as incorrect. The first purpose of this note is to reply to this claim and argue that Baigent's formulation is not only formally correct, but also the most expeditious for its purpose. Furthermore, it will be argued that the approach advocated by LBU is not justified. Finally, it will be argued that, contrary to both Chichilnisky and LBU, the topological framework itself should be replaced by the ``old fashioned'' finite framework for the analysis of the underlying issue which Chichilnisky's theorem attempts to address.