Equivalence of axioms for bankruptcy problems

Abstract. The bankruptcy problem is concerned with how to divide the net worth of the bankrupt firm among its creditors. In this paper, we investigate the logical relations between various axioms in the context of bankruptcy. Those axioms are: population-and-resource monotonicity, consistency, converse consistency, agreement, and separability. In most axiomatic models, they are not directly related. However, we show that they are equivalent on the class of bankruptcy problems under minor additional requirements.

[1]  Barry O'Neill,et al.  A problem of rights arbitration from the Talmud , 1982, Math. Soc. Sci..

[2]  R. Aumann,et al.  Game theoretic analysis of a bankruptcy problem from the Talmud , 1985 .

[3]  Nir Dagan,et al.  Bilateral comparisons and consistent fair division rules in the context of bankruptcy problems , 1997 .

[4]  Yves Sprumont.  Population monotonic allocation schemes for cooperative games with transferable utility , 1990 .

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

[6]  Y. Chun.  The proportional solution for rights problems , 1988 .

[7]  Hervé Moulin,et al.  Priority Rules and Other Inequitable Rationing Methods , 1998 .

[8]  H. Young,et al.  Distributive justice in taxation , 1988 .

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

[10]  Youngsub Chun.  Agreement, separability, and other axioms for quasi-linear social choice problems , 2000, Soc. Choice Welf..

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

[12]  H. Moulin.  Equal or proportional division of a surplus, and other methods , 1987 .

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

[14]  W. Thomson,et al.  Constrained Egalitarianism: A New Solution for Claims Problems , 1998 .

[15]  N. Dagan.  New characterizations of old bankruptcy rules , 1996 .

[16]  H. Peyton Young,et al.  On Dividing an Amount According to Individual Claims or Liabilities , 1987, Math. Oper. Res..

[17]  William Thomson,et al.  Welfare-domination under preference-replacement: A survey and open questions , 1999 .

[18]  Carmen Herrero,et al.  PREEMINENCE AND SUSTAINABILITY IN BANKRUPTCY PROBLEMS , 1998 .

[19]  N. Dagan,et al.  A Noncooperative View of Consistent Bankruptcy Rules , 1994 .

[20]  W. Thomson.  Problems of fair division and the Egalitarian solution , 1983 .