The Replacement Principle in Economies with Single-Peaked Preferences

Abstract Our objective is to investigate the implications of the “replacement principle” for the fair allocation of an infinitely divisible commodity among agents with single-peaked preferences. The principle says that when one of the components of the data entering the description of the problem to be solved changes, all of the relevant agents should be affected in the same direction: they all gain or they all lose. We apply it to situations in which the preferences of one of the agents may change, under the name ofwelfare-domination under preference-replacement. We show that there is no selection from the no-envy and Pareto solution satisfying it. Then, we weaken it by limiting its application to situations in which the change is not so disruptive that it turns the economy from one in which there is “too little” of the commodity to one in which there is “too much,” or conversely. We show that there is only one selection from the no-envy and Pareto solution satisfying this property andreplication-invariance. It is the “uniform rule,” a solution that has played a central role in previous analyses of the problem.Journal of Economic LiteratureClassification Numbers: D51, D63, D70.

[1]  Hans Peters,et al.  Two characterizations of the uniform rule for division problems with single-peaked preferences , 1996 .

[2]  Alvin E. Roth,et al.  Risk Aversion and Solutions to Nash's Bargaining Problem , 1981 .

[3]  Core convergence without monotone preferences and free disposal , 1991 .

[4]  Andreu Mas-Colell,et al.  Equilibrium Theory with Possibly Satiated Preferences , 1992 .

[5]  Stephen Ching,et al.  A simple characterization of the uniform rule , 1992 .

[6]  H. Moulin.  A Core Selection for Regulating a Single-Output Monopoly , 1987 .

[7]  W. Thomson.  Population-monotonic solutions to the problem of fair division when preferences are single-peaked , 1995 .

[8]  R. Myerson,et al.  Monotonicity and independence axioms , 1980 .

[9]  H. Polemarchakis,et al.  Competitive equilibria without free disposal or nonsatiation , 1993 .

[10]  William Thomson,et al.  Two characterizations of the Raiffa solution , 1980 .

[11]  S. Ching.  An alternative characterization of the uniform rule , 1994 .

[12]  William Thomson,et al.  Consistent Solutions to the Problem of Fair Division When Preferences Are Single-Peaked , 1994 .

[13]  E. Kalai.  Proportional Solutions to Bargaining Situations: Interpersonal Utility Comparisons , 1977 .

[14]  D. Foley.  Resource allocation and the public sector , 1967 .

[15]  William Thomson,et al.  Monotonicity properties of bargaining solutions when applied to economics , 1988 .

[16]  J. Roemer.  Equality of Resources Implies Equality of Welfare , 1986 .

[17]  Hervé Moulin,et al.  The Pure Compensation Problem: Egalitarianism Versus Laissez-Fairism , 1987 .

[18]  Yves Sprumont.  Axiomatizing Ordinal Welfare Egalitarianism When Preferences May Vary , 1996 .

[19]  Marc Fleurbaey.  Reward patterns of fair solutions , 1996 .

[20]  Mukul Majumdar,et al.  Equilibrium and Dynamics , 1992 .

[21]  Hervé Moulin,et al.  Egalitarian-equivalent cost sharing of a public good , 1987 .

[22]  Lu Hong,et al.  Division Rules and Migration Equilibria , 1996 .

[23]  William Thomson,et al.  Resource-monotonic solutions to the problem of fair division when preferences are single-peaked , 1994 .

[24]  Yves Sprumont.  The Division Problem with Single-Peaked Preferences: A Characterization of the Uniform Allocation Rule , 1991 .

[25]  Y. Chun.  The solidarity axiom for quasi-linear social choice problems , 1986 .

[26]  Tayfun Sönmez,et al.  Consistency, monotonicity, and the uniform rule , 1994 .

[27]  W. Thomson,et al.  The fair allocation of an indivisible good when monetary compensations are possible , 1993 .

[28]  J. Benassy,et al.  The economics of market disequilibrium , 1982 .

[29]  Hervé Moulin,et al.  Public Ownership of the External World and Private Ownership of Self , 1989, Journal of Political Economy.

[30]  William Thomson,et al.  The replacement principle in public good economies with single-peaked preferences , 1993 .

[31]  H. Moulin,et al.  Can everyone benefit from growth?: Two difficulties , 1988 .

[32]  William Thomson,et al.  The Fair Division of a Fixed Supply Among a Growing Population , 1983, Math. Oper. Res..