A robust theory of resource allocation

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.