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Fair Division and Politics

Published online by Cambridge University Press:  02 September 2013

Steven J. Brams
Affiliation:
New York University
Alan D. Taylor
Affiliation:
Union College

Extract

In the Hebrew Bible, the issue of fairness is raised in some of the best-known narratives. Cain's raging jealousy and eventual murder of Abel is provoked by what he considered unfair treatment by God, who “paid heed” to Abel's offering but ignored his (Gen. 4:4). Jacob, after doing seven years of service in return for Laban's beautiful daughter, Rachel, was told that his sacrifice was not sufficient and that he must instead marry Laban's older and plainer daughter, Leah, unless he did seven more years' service, which he regarded as not only the breaking of a contract but also flagrantly unfair.

Fairness triumphed, however, when King Solomon proposed to divide a baby, claimed by two mothers, in two. When the true mother protested and offered the baby to the other mother (whose baby had died), the truth about the baby's maternity became apparent, and “all Israel … stood in awe of the king; for they saw that he possessed divine wisdom to execute justice” (1 Kings 3:28).

Solomon's proposed solution is the first explicit mention of fair division that we know of in recorded history. But it is, of course, no solution at all. Solomon had no intention of dividing the baby in two. Instead, his purpose was to set up a game between the two women, described in Brams (1980, 118–23; 1990, 17–24), that would distinguish the mother from the impostor.

The solutions of the fair-division procedures we shall discuss are for two players.

Type
Research Article
Copyright
Copyright © The American Political Science Association 1995

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References

Blitzer, Charles. 1960. An Immortal Commonwealth: The Political Thought of James Harrington. New Haven: Yale University Press.Google Scholar
Brams, Steven J. 1980. Biblical Games: A Strategic Analysis of Stories in the Old Testament. Cambridge, MA: MIT Press.Google Scholar
Brams, Steven J. 1990. Negotiation Games: Applying Game Theory to Bargaining and Arbitration. New York: Routledge.Google Scholar
Brams, Steven J., and Fishburn, Peter C. 1995. “When Is Size A Liability? Bargaining Power in Minimal Winning Coalitions.” Journal of Theoretical Politics 7(3):301–16.CrossRefGoogle Scholar
Brams, Steven J., and Taylor, Alan D. 1996. Fair Division: From Cake-Cutting to Dispute Resolution. Cambridge, UK: Cambridge University Press.CrossRefGoogle Scholar
Cohen, I. Bernard. 1994. Interactions: Some Contacts between the Natural Sciences and the Social Sciences. Cambridge, MA: MIT Press.CrossRefGoogle Scholar
Crawford, Vincent. 1977. “A Game of Fair Division.” Review of Economic Studies 44(2):235–47.CrossRefGoogle Scholar
Crawford, Vincent. 1979. “A Procedure for Generating Pareto-Efficient Egalitarian-Equivalent Allocations.” Econometrica 47(1):4960.CrossRefGoogle Scholar
Demange, Gabrielle. 1984. “Implementing Efficient Egalitarian Equivalent Allocations.” Econometrica 52(5): 1167–77.CrossRefGoogle Scholar
Downs, Michael. 1977. James Harrington. Boston: G. K. Hall.Google Scholar
Fishburn, Peter C., and Brams, Steven J. 1996. “Minimal Winning Coalitions in Weighted-Majority Voting Games.” Social Choice and Welfare. Forthcoming.Google Scholar
Glazer, Jacob, and Ma, Ching-to Albert. 1989. “Efficient Allocation of a ‘Prize’—King Solomon's Dilemma.” Games and Economic Behavior 1(3):223–33.CrossRefGoogle Scholar
Goodwin, Barbara. 1992. Justice by Lottery. Chicago: University of Chicago Press.Google Scholar
Hardin, Russell. 1982. Collective Action. Baltimore: Johns Hopkins University Press.CrossRefGoogle Scholar
Lowry, S. Todd. 1987. The Archeology of Economic Ideas: The Classical Greek Tradition. Durham, NC: Duke University Press.Google Scholar
Kalai, Ehud, and Smorodinsky, Meir. 1975. “Other Solutions to Nash's Bargaining Problem.” Econometrica 43(3):513–18.CrossRefGoogle Scholar
Moulin, Hervé. 1984. “Implementing the Kalai-Smorodinsky Bargaining Solution.” Journal of Economic Theory 33(1): 3245.CrossRefGoogle Scholar
Nash, John. 1950. “The Bargaining Problem.” Econometrica 18, no. 2 (April): 155–62.CrossRefGoogle Scholar
Olson, Mancur Jr., 1965. The Logic of Collective Action: Public Goods and the Theory of Groups. Cambridge, MA: Harvard University Press.Google Scholar
Pocock, J. G. A., ed. 1977. The Political Works of James Harrington. Cambridge, UK: Cambridge University Press.Google Scholar
Pocock, J. G. A. 1992. “Introduction.” In Harrington, James, The Commonwealth ofOceana and A System of Politics, ed. Pocock, J. G. A.. Cambridge, UK: Cambridge University Press.Google Scholar
The Prophets. 1978. Philadelphia: Jewish Publication Society.Google Scholar
Raiffa, Howard. 1953. “Arbitration Schemes for Generalized Two-Person Games.” In Contributions to the Theory of Games, vol. 1 (Annals of Mathematics Studies 24), Kuhn, Harold and Tucker, A. W. eds. Princeton, NJ: Princeton University Press, 361–87.Google Scholar
Riker, William H. 1962. The Theory of Political Coalitions. New Haven, CT: Yale University Press.Google Scholar
Rubinstein, Ariel. 1982. “Perfect Equilibrium in a Bargaining Model.” Econometrica 50(1):97109.CrossRefGoogle Scholar
Singer, Eugene. 1962. “Extension of the Classical Rule of ‘Divide and Choose.’” Southern Economic Journal 28(4):391–94.CrossRefGoogle Scholar
Smith, H. R. Russell. 1914. Harrington and His Oceana: A Study of a 17th Century Utopia and Its Influence in America. Cambridge, UK: Cambridge University Press.Google Scholar
The Torah: The Five Books of Moses. 1967. Philadelphia: Jewish Publication Society.Google Scholar
van Damme, Eric. 1991. Stability and Perfection of Nash Equilibria. Heidelberg, Germany: Springer-Verlag.CrossRefGoogle Scholar
Yang, Chun-Lei. 1992. “Efficient Allocation of an Indivisible Good—A Mechanism Design Problem under Uncertainty.” Preprint, LS Wirschaftstheorie, University of Dortmund, Germany.Google Scholar
Young, H. Peyton. 1994. Equity in Theory and Practice. Princeton, NJ: Princeton University Press.Google Scholar