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Fair allocation of indivisible goods: the two-agent case

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Abstract

One must allocate a finite set of indivisible goods among two agents without monetary compensation. We impose Pareto-efficiency, anonymity, a weak notion of no-envy, a welfare lower bound based on each agent’s ranking of the subsets of goods, and a monotonicity property w.r.t. changes in preferences. We prove that there is a rule satisfying these axioms. If there are three goods, it is the only rule, together with one of its subcorrespondences, satisfying each fairness axiom and not discriminating between goods.

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References

  • Beviá C (1996) Population monotonicity in economies with one indivisible good. Math Soc Sci 32: 125–137

    Article  Google Scholar 

  • Bouveret S, Lang J (2008) Efficiency and envy-freeness in fair division of indivisible goods: logical representation and complexity. J Artif Intell Res 32: 525–564

    Google Scholar 

  • Brams SJ (2006) Fair division. In: Weingast BR, Wittman D (eds) Oxford handbook of political economy. Oxford University Press, Oxford

    Google Scholar 

  • Brams SJ, Fishburn PC (2000) Fair division of indivisible items between two people with identical-preferences: envy-freeness, pareto-optimality, and equity. Soc Choice Welf 17: 247–267

    Article  Google Scholar 

  • Brams SJ, Edelman PH, Fishburn PC (2003) Fair division of indivisible items. Theory Dec 55: 147–180

    Article  Google Scholar 

  • Brams SJ, King D (2005) Efficient fair division: help the worst off or avoid envy?. Ration Soc 17: 387–421

    Article  Google Scholar 

  • Brams SP, Kilgour DM, Klamler C (2009) The undercut procedure: an algorithm for the envy-free division of indivisible items. MPRA Paper No. 12774, Munich University Library, Munich. http://mpra.ub.uni-muenchen.de/12774/

  • Brams SP, Kilgour DM, Haeringer G, Halaburda H (2011) Monotone strategyproofness, or how to rank manipulations. Mimeo

  • D’Aspremont C, Gevers L (1977) Equity and the informational basis of collective choice. Rev Econ Stud 44: 199–209

    Article  Google Scholar 

  • Demko S, Hill TP (1988) Equitable distribution of indivisible objects. Math Soc Sci 16: 145–158

    Article  Google Scholar 

  • Edelman P, Fishburn PC (2001) Fair division of indivisible items among people with similar preferences. Math Soc Sci 41: 327–347

    Article  Google Scholar 

  • Ehlers L, Klaus B (2003) Coalitional strategy-proof and resource-monotonic solutions for multiple assignment problems. Soc Choice Welf 21: 265–280

    Article  Google Scholar 

  • Fishburn PC (1970) Utility theory for decision making. Wiley, New York

    Google Scholar 

  • Grandmont JM (1978) Intermediate preferences and the majority rule. Econometrica 46: 317–330

    Article  Google Scholar 

  • Herreiner D, Puppe C (2002) A simple procedure for finding equitable allocations of indivisible goods. Soc Choice Welf 19: 415–430

    Article  Google Scholar 

  • Kemeny J, Snell J (1962) Mathematical models in the social sciences. Ginn, New York

    Google Scholar 

  • Klaus B, Miyagawa E (2001) Strategy-proofness, solidarity, and consistency for multiple assignment problems. Int J Game Theory 30: 421–435

    Article  Google Scholar 

  • Kraft CH, Pratt JW, Seidenberg A (1959) Intuitive probability on finite sets. Ann Math Stat 30: 408–419

    Article  Google Scholar 

  • Moulin H (1990) Fair division under joint ownership: recent results and open problems. Soc Choice Welf 7: 149–170

    Article  Google Scholar 

  • Moulin H (1990) Uniform externalities: two axioms for fair allocation. J Public Econ 43: 305–326

    Article  Google Scholar 

  • Moulin H (1991) Welfare bounds in the fair division problem. J Econ Theory 54: 321–337

    Article  Google Scholar 

  • Moulin H (1992) An application of the Shapley value to fair division with money. Econometrica 60: 1331–1349

    Article  Google Scholar 

  • Ramaekers E (2010) Fair allocation of indivisible goods among two agents. CORE discussion papers 2010/87. Université catholique de Louvain, Louvain-la-Neuve. http://www.uclouvain.be/cps/ucl/doc/core/documents/coredp2010_87web.pdf/

  • Sen AK (1970) Collective choice and social welfare. Holdenday, San Francisco

    Google Scholar 

  • Sprumont Y (1993) Intermediate preferences and Rawlsian Arbitration Rules. Soc Choice Welf 10: 1–15

    Article  Google Scholar 

  • Steinhaus H (1948) The problem of fair division. Econometrica 16: 101–104

    Google Scholar 

Download references

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Correspondence to Eve Ramaekers.

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Ramaekers, E. Fair allocation of indivisible goods: the two-agent case. Soc Choice Welf 41, 359–380 (2013). https://doi.org/10.1007/s00355-012-0684-0

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  • DOI: https://doi.org/10.1007/s00355-012-0684-0

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