Social choice and resource allocation: a topological perspective (Q1367914)

Let \(P\) be the space of preferences on a finite-dimensional Euclidean space. This paper surveys work stemming from Chichilnisky's theorem: there is no social choice rule from \(P^k\) to \(P\) which is continuous, anonymous, and respects unanimity. This theorem has striking implications, as the following equivalences show: ``Arrow's Theorem'' iff ``Chichilnisky's Theorem'' iff ``Core equivalence with competitive equilibrium''. The 39 papers surveyed derive these equivalences, and consider extensions of them to infinite \(k\).