John W. Pratt

William Ziegler Professor of Business Administration, Emeritus

John W. Pratt is a professor of business administration, emeritus, at Harvard Business School. He was educated at Princeton and Stanford, specializing in mathematics and statistics. Except for two years at the University of Chicago, and a sabbatical in Kyoto on a Guggenheim fellowship, Pratt has been at Harvard for his entire professional career. Editor of the Journal of the American Statistical Association from 1965 to 1970, he is a fellow of five professional societies and has chaired National Academy of Sciences committees on environmental monitoring, census methodology, and the future of statistics. His recent research has been on risk aversion, risk sharing incentives, and the nature and discovery of stochastic laws, statistical relationships that describe the effects of decisions. He is co-author of a book entitled: Introduction to Statistical Decision Theory, published by MIT Press, 1995.

Books

  1. Introduction to Statistical Decision Theory

    Citation:

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

    Keywords: Mathematical Methods; Decision Making; Theory;

    Citation:

    Pratt, John W., Howard Raiffa, and Robert Schlaifer. Introduction to Statistical Decision Theory. MIT Press, 1995.
  3. Principals and Agents: The Structure of Business

    Keywords: Organizational Structure;

    Citation:

    Pratt, John W., and Richard Zeckhauser, eds. Principals and Agents: The Structure of Business. Harvard Business School Press, 1991.

Journal Articles

  1. Fair (and Not So Fair) Division

    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).
  2. How Many Balance Functions Does It Take To Determine A Utility Function?

    Citation:

    Pratt, John W. "How Many Balance Functions Does It Take To Determine A Utility Function?" Journal of Risk and Uncertainty 31 (2005): 109–127. (Article in Honor of Paul Samuelson's 90th Birthday.)
  3. Efficient Risk Sharing: The Last Frontier

    Keywords: Risk and Uncertainty;

    Citation:

    Pratt, John W. "Efficient Risk Sharing: The Last Frontier." Management Science 46, no. 12 (December 2000): 1545–1553. (Japanese version, translated by Fumiko Seo, in Modeling and Decision Making in Ambiguous Environments, Fumiko Seo and Takao Fukuchi, eds., 2002 (Kyoto U. Press).)
  4. A New Interpretation of the F Statistic

    Citation:

    Pratt, John W., and Robert Schlaifer. "A New Interpretation of the F Statistic." American Statistician 52 (1998): 141–143.
  5. Increasing Risk: Some Direct Constructions

    Keywords: Risk and Uncertainty;

    Citation:

    Pratt, John W., and Mark J. Machina. "Increasing Risk: Some Direct Constructions." Journal of Risk and Uncertainty 14 (1997): 103–127.
  6. Willingness to Pay and the Distribution of Risk and Wealth

    Keywords: Risk and Uncertainty; Wealth;

    Citation:

    Pratt, John W., and Richard Zeckhauser. "Willingness to Pay and the Distribution of Risk and Wealth." Journal of Political Economy 104 (August 1996): 747–763.
  7. The Contraction Mapping Approach to the Perron-Frobenius Theory: Why Hilbert's Metric?

    Keywords: Theory; Measurement and Metrics;

    Citation:

    Kohlberg, Elon, and John W. Pratt. "The Contraction Mapping Approach to the Perron-Frobenius Theory: Why Hilbert's Metric?" Mathematics of Operations Research, no. 7 (1982): 198–210.
  8. Evaluating and Comparing Projects: Simple Detection of False Alarms

    Keywords: Performance Evaluation;

    Citation:

    Hammond, John S., and John W. Pratt. "Evaluating and Comparing Projects: Simple Detection of False Alarms." Journal of Finance 34, no. 5 (December 1979): 1231–1242.

Working Papers

  1. Some Neglected Axioms in Fair Division

    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.
  2. Correlated Equilibrium and Nash Equilibrium as an Observer's Assessment of the Game

    Noncooperative games are examined from the point of view of an outside observer who believes that the players are rational and that they know at least as much as the observer. The observer is assumed to be able to observe many instances of the play of the game; these instances are identical in the sense that the observer cannot distinguish between the settings in which different plays occur. If the observer does not believe that he will be able to offer beneficial advice then he must believe that the players are playing a correlated equilibrium, though he may not initially know which correlated equilibrium. If the observer also believes that, in a certain sense, there is nothing connecting the players in a particular instance of the game then he must believe that the correlated equilibrium they are playing is, in fact, a Nash equilibrium.

    Keywords: Decision Choices and Conditions; Game Theory; Cooperation;

    Citation:

    Hillas, John, Elon Kohlberg, and John W. Pratt. "Correlated Equilibrium and Nash Equilibrium as an Observer's Assessment of the Game." Harvard Business School Working Paper, No. 08-005, July 2007.

Cases and Teaching Materials

  1. Rubicon Rubber Co.

    Keywords: Rubber Industry;

    Citation:

    Pratt, John W. "Rubicon Rubber Co." Harvard Business School Case 171-330, January 1971. (Revised March 1992.)