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ON THE AXIOMATICS OF RESOURCE ALLOCATION: INTERPRETING THE CONSISTENCY PRINCIPLE

Published online by Cambridge University Press:  28 November 2012

William Thomson*
Affiliation:
University of Rochester, USAwth2@mail.rochester.edu

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’.

Type
Articles
Copyright
Copyright © Cambridge University Press 2012

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References

REFERENCES

Abizada, A. and Chen, S. 2011. Allocating tasks when some may get canceled or additional ones may arrive, mimeo.Google Scholar
Aumann, R. and Maschler, M. 1985. Game theoretic analysis of a bankruptcy problem from the Talmud. Journal of Economic Theory 36: 195213.Google Scholar
Balinski, M. 2005. What is just? American Mathematical Monthly 112: 502511.CrossRefGoogle Scholar
Balinski, M. and Young, P. 1982. Fair Representation. New Haven, CT: Yale University Press.Google Scholar
Chun, Y. 1986. The solidarity axiom for quasi-linear social choice problems. Social Choice and Welfare 3: 297310.Google Scholar
Chun, Y. and Thomson, W. 1988. Monotonicity properties of bargaining solutions when applied to economics. Mathematical Social Sciences 15: 1127.Google Scholar
Davis, M. and Maschler, M. 1965. The kernel of a cooperative game. Naval Research Logistics Quarterly 12: 223259.CrossRefGoogle Scholar
Ehlers, L. and Klaus, B. 2006. Efficient priority rules. Games and Economic Behavior 55: 372384.Google Scholar
Ehlers, L. and Klaus, B. 2007. Consistent house allocation. Economic Theory 30: 561574.Google Scholar
Ergin, H. 2000. Consistency in house allocation problems. Journal of Mathematical Economics 34: 7797.Google Scholar
Foley, D. 1967. Resource allocation and the public sector. Yale Economic Essays 7: 4598.Google Scholar
Huntington, E. V. 1921. The mathematical theory of the apportionment of representatives. Proceedings of the National Academy of Sciences USA 7: 123127.Google Scholar
Kalai, E. 1977. Proportional solutions to bargaining situations: interpersonal utility comparisons. Econometrica 45: 16231630.Google Scholar
Kim, H. 2004. Population monotonicity for fair allocation problems. Social Choice and Welfare 23: 5970.Google Scholar
Lensberg, T. 1985. Stability, collective choice and separable welfare. Ph.D. Dissertation, Norwegian School of Economics and Business Administration, Bergen, Norway.Google Scholar
Lensberg, T. 1988. Stability and the Nash solution. Journal of Economic Theory 45: 330341.Google Scholar
Mandelbrot, B. 1982. The Fractal Geometry of Nature. San Francisco, CA: W. H. Freeman and Company.Google Scholar
Maschler, M. and Owen, G. 1989. The consistent Shapley-value for hyperplane games. International Journal of Game Theory 18: 390407.Google Scholar
Moreno-Ternero, J. and Roemer, J. 2012. A common ground for resource and welfare egalitarianism. Games and Economic Behavior 75: 832841.Google Scholar
Moulin, H. and Thomson, W. 1988. Can everyone benefit from growth? Two difficulties. Journal of Mathematical Economics 17: 339345.Google Scholar
Nash, J.F. 1950. The bargaining problem. Econometrica 28: 155162.Google Scholar
O'Neill, B. 1982. A problem of rights arbitration from the Talmud. Mathematical Social Sciences 2: 345371.Google Scholar
Plott, C. 1973. Path independence, rationality and social choice. Econometrica 41: 10751091.Google Scholar
Rawls, J. 1971. A Theory of Justice. Cambridge, MA: Harvard University Press.Google Scholar
Roemer, J. 1986. The mismarriage of bargaining theory and distributive justice. Ethics 97: 88110.Google Scholar
Serizawa, S. 2002. Inefficiency of strategy-proof rules for pure exchange economies. Journal of Economic Theory 106: 219241.CrossRefGoogle Scholar
Shapley, L.S. 1953. A value for n-person games. Contributions to the Theory of Games 2: 307317.Google Scholar
Shimomura, K.-I. 1993. Flexible solutions to the fair division problems with single-plateaued preferences. University of Rochester mimeo.Google Scholar
Sprumont, Y. 1991. The division problem with single-peaked preferences: a characterization of the uniform allocation rule. Econometrica 59: 509519.Google Scholar
Thomson, W. 1978. Monotonic allocation mechanisms: preliminary results, University of Minnesota mimeo.Google Scholar
Thomson, W. 1983 a. Equity in exchange economies. Journal of Economic Theory 29: 217244.Google Scholar
Thomson, W. 1983 b. The fair division of a fixed supply among a growing population. Mathematics of Operations Research 8: 319326.CrossRefGoogle Scholar
Thomson, W. 1983 c. Problems of fair division and the egalitarian principle. Journal of Economic Theory 31: 211226.Google Scholar
Thomson, W. 1984. Monotonicity, stability and egalitarianism. Mathematical Social Sciences 8: 1518.Google Scholar
Thomson, W. 1988. A study of choice correspondences in economies with a variable number of agents. Journal of Economic Theory 46: 247259.Google Scholar
Thomson, W. 1994 a. Consistent solutions to the problem of fair division when preferences are single-peaked. Journal of Economic Theory 63: 219245.Google Scholar
Thomson, W. 1994 b. Consistent extensions. Mathematical Social Sciences 28: 219245.Google Scholar
Thomson, W. 1999. Welfare-domination under preference-replacement: a survey and open questions. Social Choice and Welfare 16: 373394.Google Scholar
Thomson, W. 2001. On the axiomatic method and its recent applications to game theory and resource allocation. Social Choice and Welfare 18: 327387.Google Scholar
Thomson, W. 2003. Axiomatic and game-theoretic analysis of bankruptcy and taxation problems: a survey. Mathematical Social Sciences 45: 249297.Google Scholar
Thomson, W. 2011 a. Consistent allocation rules, mimeo.Google Scholar
Thomson, W. 2011 b. On the computational implications of converse consistency, mimeo.Google Scholar
Thomson, W. 2012. Axiomatic and game-theoretic analysis of bankruptcy and taxation problems: an update, mimeo.Google Scholar
Thomson, W. and Myerson, R.B. 1980. Monotonicity and independence axioms. International Journal of Game Theory 9: 3749.Google Scholar
von Neumann, J. and Morgenstern, O. 1944. The Theory of Games and Economic Behavior. Princeton, NJ: Princeton University Press.Google Scholar
Young, P. 1987. Progressive taxation and the equal sacrifice principle. Journal of Public Economics 32: 203214.Google Scholar
Young, P. 1994. Equity in Theory and Practice. Princeton, NJ: Princeton University Press.Google Scholar