The theory of social choice introduced in [5,6] is robust: it is completely independent of the choice of topology on spaces of preferences. This theory has been fruitful in linking diverse forms of resource allocation: it has been shown [-17] that contractibility is necessary and sufficient for solving the social choice paradox; this condition is equivalent [11-] to another -limited arbitrage -which is necessary and sufficient for the existence of a competitive equilibrium and the core of an economy [13,14,15,16,17]. The space of monotone preferences is contractible; as shown already in ['6, 17] such spaces admit social choice rules. However, monotone preferences are of little interest in social choice theory because the essence of the social choice problem, such as Condorcet triples, rules out monotonicity.
1. Robust resource allocation
The problem of social choice introduced in [5,6] is the subject of a recent paper by Allen [1]. I welcome Allen's interest, as it indicates that the area is growing and attracting new researchers. Her paper is restricted to a rather special domain, monotone preferences, and assumes a special topology, the closed convergence topology. Allen states that social choice rules which satisfy my three axioms -continuity, anonymity and respect of unanimity -exist under these special conditions. From this she argues that my social choice paradox is easily resolved, and that it depends on the topology one chooses for space of preferences. In response, this paper will establish that: