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Fair Division and Collective Welfare

Author

Listed:
  • Herve Moulin

    () (Rice University)

Abstract

The concept of fair division is as old as civil society itself. Aristotle's "equal treatment of equals" was the first step toward a formal definition of distributive fairness. The concept of collective welfare, more than two centuries old, is a pillar of modern economic analysis. Reflecting fifty years of research, this book examines the contribution of modern microeconomic thinking to distributive justice. Taking the modern axiomatic approach, it compares normative arguments of distributive justice and their relation to efficiency and collective welfare. The book begins with the epistemological status of the axiomatic approach and the four classic principles of distributive justice: compensation, reward, exogenous rights, and fitness. It then presents the simple ideas of equal gains, equal losses, and proportional gains and losses. The book discusses three cardinal interpretations of collective welfare: Bentham's "utilitarian" proposal to maximize the sum of individual utilities, the Nash product, and the egalitarian leximin ordering. It also discusses the two main ordinal definitions of collective welfare: the majority relation and the Borda scoring method. The Shapley value is the single most important contribution of game theory to distributive justice. A formula to divide jointly produced costs or benefits fairly, it is especially useful when the pattern of externalities renders useless the simple ideas of equality and proportionality. The book ends with two versatile methods for dividing commodities efficiently and fairly when only ordinal preferences matter: competitive equilibrium with equal incomes and egalitarian equivalence. The book contains a wealth of empirical examples and exercises.

Suggested Citation

  • Herve Moulin, 2004. "Fair Division and Collective Welfare," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262633116, January.
  • Handle: RePEc:mtp:titles:0262633116
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    References listed on IDEAS

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    Cited by:

    1. Bettina Klaus & Flip Klijn, 2006. "Procedurally fair and stable matching," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), pages 431-447.
    2. de Marti, Joan & Zenou, Yves, 2009. "Social Networks," Working Paper Series 816, Research Institute of Industrial Economics.
    3. Fuhito Kojima & M. Ünver, 2014. "The “Boston” school-choice mechanism: an axiomatic approach," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 55(3), pages 515-544, April.
    4. Erel Segal-Halevi & Shmuel Nitzan, 2014. "Cake Cutting – Fair and Square," Working Papers 2014-01, Bar-Ilan University, Department of Economics.
    5. Birendra K. Rai, 2006. "Evolution of Division Rules," Papers on Strategic Interaction 2006-27, Max Planck Institute of Economics, Strategic Interaction Group.
    6. Arthur J. Caplan & Yuya Sasaki, 2009. "Sharing the Surplus Generated from Noncooperative Cost Sharing: The Case of Nonpoint Associations and Water Quality Trading," Working Papers 2009-09, Utah State University, Department of Economics.
    7. Maria A. Nastych, 2014. "M&A Cooperative Games," Equilibrium. Quarterly Journal of Economics and Economic Policy, Institute of Economic Research, vol. 9(1), pages 119-130, March.
    8. Vito Fragnelli & Maria Erminia Marina, 2009. "Strategic Manipulations and Collusions in Knaster Procedure," Czech Economic Review, Charles University Prague, Faculty of Social Sciences, Institute of Economic Studies, vol. 3(2), pages 143-153, July.
    9. Marco Mariotti, 2003. "Even Allocations For Generalised Rationing Problems," Working Papers. Serie AD 2003-10, Instituto Valenciano de Investigaciones Económicas, S.A. (Ivie).
    10. Yuan Ju & Peter Borm & Pieter Ruys, 2007. "The consensus value: a new solution concept for cooperative games," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 28(4), pages 685-703, June.
    11. Laurent-Lucchetti, Jérémy, 2009. "Rights on what is left," MPRA Paper 27285, University Library of Munich, Germany.
    12. van den Brink, Rene, 2007. "Null or nullifying players: The difference between the Shapley value and equal division solutions," Journal of Economic Theory, Elsevier, vol. 136(1), pages 767-775, September.
    13. De MESNARD, Louis, 2008. "On the Talmud division : equity and robustness," LEG - Document de travail - Economie 2008-07, LEG, Laboratoire d'Economie et de Gestion, CNRS, Université de Bourgogne.
    14. Laurent-Lucchetti, Jérémy & Leroux, Justin, 2009. "Axiomatic foundation for Lindahl pricing in the NIMBY context," MPRA Paper 14930, University Library of Munich, Germany.
    15. Joana Pais, 2008. "Random matching in the college admissions problem," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 35(1), pages 99-116, April.
    16. repec:spr:grdene:v:22:y:2013:i:2:d:10.1007_s10726-011-9260-8 is not listed on IDEAS
    17. Jens Leth Hougaard & Chiu Yu Ko & Xuyao Zhang, 2017. "A Welfare Economic Interpretation of FRAND," IFRO Working Paper 2017/04, University of Copenhagen, Department of Food and Resource Economics.
    18. Alain Trannoy, 2011. "Equity Dimensions of Transport Policy," Chapters,in: A Handbook of Transport Economics, chapter 26 Edward Elgar Publishing.
    19. Alessandra Casella & Sébastien Turban & Gregory Wawro, 2017. "Storable votes and judicial nominations in the US Senate," Journal of Theoretical Politics, , vol. 29(2), pages 243-272, April.
    20. Pivato, Marcus, 2010. "Approximate interpersonal comparisons of well-being," MPRA Paper 25224, University Library of Munich, Germany.
    21. Orit Arzi & Yonatan Aumann & Yair Dombb, 2016. "Toss one’s cake, and eat it too: partial divisions can improve social welfare in cake cutting," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 46(4), pages 933-954, April.
    22. Antonio Nicolò & Andrés Perea y Monsuwe & Paolo Roberti, 2012. "Equal opportunity equivalence in land division," SERIEs: Journal of the Spanish Economic Association, Springer;Spanish Economic Association, vol. 3(1), pages 133-142, March.
    23. repec:ebl:ecbull:v:4:y:2008:i:1:p:1-5 is not listed on IDEAS
    24. Balazs Sziklai & Erel Segal-Halevi, 2015. "Resource-monotonicity and Population-monotonicity in Cake-cutting," IEHAS Discussion Papers 1552, Institute of Economics, Centre for Economic and Regional Studies, Hungarian Academy of Sciences.

    More about this item

    Keywords

    fair division; collective welfare; distributive justice;

    JEL classification:

    • D31 - Microeconomics - - Distribution - - - Personal Income and Wealth Distribution
    • D63 - Microeconomics - - Welfare Economics - - - Equity, Justice, Inequality, and Other Normative Criteria and Measurement
    • B21 - Schools of Economic Thought and Methodology - - History of Economic Thought since 1925 - - - Microeconomics

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