More from the Author

• Working Paper | HBS Working Paper Series | 2008

  Some Neglected Axioms in Fair Division

  John W. Pratt

  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 monotonicity 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: Resource Allocation; Valuation; Price; Cost;

  Citation:

  Pratt, John W. "Some Neglected Axioms in Fair Division." Harvard Business School Working Paper, No. 08–094, May 2008.

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• Book | 2008

  Introduction to Statistical Decision Theory

  John W. Pratt, Howard Raiffa and Robert Schlaifer

  Citation:

  Pratt, John W., Howard Raiffa, and Robert Schlaifer. Introduction to Statistical Decision Theory. Paperback ed. MIT Press, 2008.

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• Article | Journal of Risk and Uncertainty | December 2007

  Fair (and Not So Fair) Division

  John W. Pratt

  Drawbacks of existing procedures are illustrated and a method of efficient fair division is proposed that avoids them. Given additive participants' utilities, each item is priced at the geometric mean (or some other function) of its two highest valuations. The utilities are scaled so that the market clears with the participants' purchases proportional to their entitlements. The method is generalized to arbitrary bargaining sets and existence is proved. For two or three participants, the expected utilities are unique. For more, under additivity, the geometric mean separates the prices where uniqueness holds and where it fails; it holds for the geometric mean except in one case where refinement is needed.

  Keywords: Price; Management Practices and Processes; Valuation;

  Citation:

  Pratt, John W. "Fair (and Not So Fair) Division." Journal of Risk and Uncertainty 35, no. 3 (December 2007).

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