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The Division Problem with Voluntary Participation

  • Gustavo Bergantiños
  • Jordi Massé
  • Alejandro Neme

The division problem consists of allocating a given amount of an homogeneous and perfectly divisible good among a group of agents with single-peaked preferences on the set of their potential shares. A rule proposes a vector of shares for each division problem. The literature has implicitly assumed that agents will find acceptable any share they are assigned to. In this paper we consider the division problem when agentsparticipation is voluntary. Each agent has an idiosyncratic interval of acceptable shares where his preferences are single-peaked. A rule has to propose to each agent either to not participate or an acceptable share because otherwise he would opt out and this would require to reassign some of the remaining agentsshares. We study a subclass of efficient and consistent rules and characterize extensions of the uniform rule that deal explicitly with agentsvoluntary participation.

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Paper provided by Barcelona Graduate School of Economics in its series Working Papers with number 437.

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Date of creation: Feb 2010
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Handle: RePEc:bge:wpaper:437
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  1. Thomson, William, 1997. "The Replacement Principle in Economies with Single-Peaked Preferences," Journal of Economic Theory, Elsevier, vol. 76(1), pages 145-168, September.
  2. Yves Sprumont, 1995. "Strategyproof Collective Choice in Economic and Political Environments," Canadian Journal of Economics, Canadian Economics Association, vol. 28(1), pages 68-107, February.
  3. Matthew O. Jackson, 2001. "A crash course in implementation theory," Social Choice and Welfare, Springer, vol. 18(4), pages 655-708.
  4. Schummer, J. & Thomson, W., 1996. "Two Derivations of the Uniform Rule and an Application to Bankruptcy," RCER Working Papers 423, University of Rochester - Center for Economic Research (RCER).
  5. Thomson William, 1994. "Consistent Solutions to the Problem of Fair Division When Preferences Are Single-Peaked," Journal of Economic Theory, Elsevier, vol. 63(2), pages 219-245, August.
  6. Sprumont, Yves, 1991. "The Division Problem with Single-Peaked Preferences: A Characterization of the Uniform Allocation Rule," Econometrica, Econometric Society, vol. 59(2), pages 509-19, March.
  7. Salvador Barberà, 2001. "An introduction to strategy-proof social choice functions," Social Choice and Welfare, Springer, vol. 18(4), pages 619-653.
  8. Dagan, Nir, 1996. "A Note on Thomson's Characterizations of the Uniform Rule," Journal of Economic Theory, Elsevier, vol. 69(1), pages 255-261, April.
  9. Herrero, Carmen & Villar, Antonio, 2000. "An alternative characterization of the equal-distance rule for allocation problems with single-peaked preferences," Economics Letters, Elsevier, vol. 66(3), pages 311-317, March.
  10. Thomson, W., 1991. "Resource-Monotonic Solutions to the Problem of Fair Divosion when Preferences are Single-Peaked ," RCER Working Papers 301, University of Rochester - Center for Economic Research (RCER).
  11. David Cantala, 2004. "Choosing the level of a public good when agents have an outside option," Social Choice and Welfare, Springer, vol. 22(3), pages 491-514, 06.
  12. Sonmez, Tayfun, 1994. "Consistency, monotonicity, and the uniform rule," Economics Letters, Elsevier, vol. 46(3), pages 229-235, November.
  13. Thomson, W., 1991. "Population-Monotonic Solutions to the Problem of Fair Division when Preferences are Single-Peaked," RCER Working Papers 302, University of Rochester - Center for Economic Research (RCER).
  14. Ching, Stephen, 1992. "A simple characterization of the uniform rule," Economics Letters, Elsevier, vol. 40(1), pages 57-60, September.
  15. Chun, Youngsub & Thomson, William, 1990. "Egalitarian solutions and uncertain disagreement points," Economics Letters, Elsevier, vol. 33(1), pages 29-33, May.
  16. Ching, Stephen & Serizawa, Shigehiro, 1998. "A Maximal Domain for the Existence of Strategy-Proof Rules," Journal of Economic Theory, Elsevier, vol. 78(1), pages 157-166, January.
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