A strong incompatibility between efficiency and equity in non-convex economies

Maniquet, François
(1998) Journal of Mathematical Economics — Vol. 32, n° 4, p. 467-474 (1999)

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Abstract
In allocation problems of perfectly divisible goods, we study the equity property of 'no-domination', according to which no agent can receive strictly more of all goods than any other agent. We prove that no-domination is incompatible with Pareto efficiency, as soon as preferences are allowed to be non-convex.
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Maniquet, F. (1998). A strong incompatibility between efficiency and equity in non-convex economies. Journal of Mathematical Economics, 32(4), 467-474. https://doi.org/10.1016/S0304-4068(98)00067-6 (Original work published 1999)