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ON THE AXIOMATICS OF RESOURCE ALLOCATION: INTERPRETING THE CONSISTENCY PRINCIPLE

  • William Thomson (a1)
Abstract

An allocation rule is ‘consistent’ if the recommendation it makes for each problem ‘agrees’ with the recommendation it makes for each associated reduced problem, obtained by imagining some agents leaving with their assignments. Some authors have described the consistency principle as a ‘fairness principle’. Others have written that it is not about fairness, that it should be seen as an ‘operational principle’. We dispute the particular fairness interpretations that have been offered for consistency, but develop a different and important fairness foundation for the principle, arguing that it can be seen as the result of adding ‘some’ efficiency to a ‘post-application’ and efficiency-free expression of solidarity in response to population changes. We also challenge the interpretations of consistency as an operational principle that have been given, and here identify a sense in which such an interpretation can be supported. We review and assess the other interpretations of the principle, as ‘robustness’, ‘coherence’ and ‘reinforcement’.

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R. Aumann and M. Maschler 1985. Game theoretic analysis of a bankruptcy problem from the Talmud. Journal of Economic Theory 36: 195213.

M. Balinski 2005. What is just? American Mathematical Monthly 112: 502511.

Y. Chun 1986. The solidarity axiom for quasi-linear social choice problems. Social Choice and Welfare 3: 297310.

Y. Chun and W. Thomson 1988. Monotonicity properties of bargaining solutions when applied to economics. Mathematical Social Sciences 15: 1127.

M. Davis and M. Maschler 1965. The kernel of a cooperative game. Naval Research Logistics Quarterly 12: 223259.

L. Ehlers and B. Klaus 2006. Efficient priority rules. Games and Economic Behavior 55: 372384.

L. Ehlers and B. Klaus 2007. Consistent house allocation. Economic Theory 30: 561574.

H. Ergin 2000. Consistency in house allocation problems. Journal of Mathematical Economics 34: 7797.

E. V. Huntington 1921. The mathematical theory of the apportionment of representatives. Proceedings of the National Academy of Sciences USA 7: 123127.

E. Kalai 1977. Proportional solutions to bargaining situations: interpersonal utility comparisons. Econometrica 45: 16231630.

H. Kim 2004. Population monotonicity for fair allocation problems. Social Choice and Welfare 23: 5970.

T. Lensberg 1988. Stability and the Nash solution. Journal of Economic Theory 45: 330341.

M. Maschler and G. Owen 1989. The consistent Shapley-value for hyperplane games. International Journal of Game Theory 18: 390407.

J. Moreno-Ternero and J. Roemer 2012. A common ground for resource and welfare egalitarianism. Games and Economic Behavior 75: 832841.

H. Moulin and W. Thomson 1988. Can everyone benefit from growth? Two difficulties. Journal of Mathematical Economics 17: 339345.

B. O'Neill 1982. A problem of rights arbitration from the Talmud. Mathematical Social Sciences 2: 345371.

C. Plott 1973. Path independence, rationality and social choice. Econometrica 41: 10751091.

J. Roemer 1986. The mismarriage of bargaining theory and distributive justice. Ethics 97: 88110.

S. Serizawa 2002. Inefficiency of strategy-proof rules for pure exchange economies. Journal of Economic Theory 106: 219241.

Y. Sprumont 1991. The division problem with single-peaked preferences: a characterization of the uniform allocation rule. Econometrica 59: 509519.

W. Thomson 1983 a. Equity in exchange economies. Journal of Economic Theory 29: 217244.

W. Thomson 1983 b. The fair division of a fixed supply among a growing population. Mathematics of Operations Research 8: 319326.

W. Thomson 1983 c. Problems of fair division and the egalitarian principle. Journal of Economic Theory 31: 211226.

W. Thomson 1984. Monotonicity, stability and egalitarianism. Mathematical Social Sciences 8: 1518.

W. Thomson 1988. A study of choice correspondences in economies with a variable number of agents. Journal of Economic Theory 46: 247259.

W. Thomson 1994 a. Consistent solutions to the problem of fair division when preferences are single-peaked. Journal of Economic Theory 63: 219245.

W. Thomson 1994 b. Consistent extensions. Mathematical Social Sciences 28: 219245.

W. Thomson 1999. Welfare-domination under preference-replacement: a survey and open questions. Social Choice and Welfare 16: 373394.

W. Thomson 2001. On the axiomatic method and its recent applications to game theory and resource allocation. Social Choice and Welfare 18: 327387.

W. Thomson 2003. Axiomatic and game-theoretic analysis of bankruptcy and taxation problems: a survey. Mathematical Social Sciences 45: 249297.

W. Thomson and R.B. Myerson 1980. Monotonicity and independence axioms. International Journal of Game Theory 9: 3749.

P. Young 1987. Progressive taxation and the equal sacrifice principle. Journal of Public Economics 32: 203214.

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Economics & Philosophy
  • ISSN: 0266-2671
  • EISSN: 1474-0028
  • URL: /core/journals/economics-and-philosophy
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