Some Neglected Axioms in Fair Division

HBS Working Paper No. 08-094

9 Pages Posted: 5 May 2008

Date Written: April 30, 2008


Conditions one might impose on fair allocation procedures are introduced. Nondiscrimination requires that agents share an item in proportion to their entitlements if they receive nothing else. The "price" procedures of Pratt (2007), including the Nash bargaining procedure, satisfy this. Other prominent efficient procedures do not. In two-agent problems, reducing the feasible set between the solution and one agent's maximum point increases the utility cost to that agent of providing any given utility gain to the other and is equivalent to decreasing the dispersion of the latter's values for the items he does not receive without changing their total. One-agent monotonnicity requires that such a change should not hurt the first agent, limited monotonicity that the solution should not change. For prices, the former implies convexity in the smaller of the two valuations, the latter linearity. In either case, the price is at least their average and hence spiteful.

Keywords: Fair division, efficient allocation, nondiscrimination axiom, monotonicity axioms, envy-free, spite, bargaining solutions.

Suggested Citation

Pratt, John W., Some Neglected Axioms in Fair Division (April 30, 2008). HBS Working Paper No. 08-094, Available at SSRN: or

John W. Pratt (Contact Author)

Harvard Business School ( email )

Soldiers Field Road
Morgan 270C
Boston, MA 02163
United States

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