Fair division under joint ownership: Recent results and open problems

Two microeconomic models of joint ownership are discussed: the division of unproduced commodities and the joint production of a single output by a single input. In both models the two principal interpretations of fairness are Equal Split Guarantee (ESG) and No Envy (NE). When combined with Pareto optimality these axioms are however not compatible with some appealing monotonicity properties. Resource monotonicity (more cake to share makes everyone happy) is incompatible with either ESG or NE, and Population Monotonicity (one more mouth to feed makes everyone unhappy) is incompatible with NE. This in turn suggests three disjoint classes of fair solutions. This paper contains very few new results, it is mostly a survey of recent literature.A first version of this paper was delivered in June 1989 at the University of Alicante, for the third German Bernacer Lectures. The hospitality of this institution is gratefully acknowledged. I am also thankful to Claude d'Aspremont, Louis Gevers and William Thomson for stimulating discussions and to an anonymous referee for helpful criticisms.