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Consistency and its converse: an introduction

Listed author(s):
  • William Thomson

    ()

This essay is an introduction to the recent literature on the "consistency principle" and its "converse". An allocation rule is consistent if for any problem in its domain of definition and any alternative that it selects for it, then for the associated "reduced problem" obtained by imagining the departure of any subgroup of the agents with their "components of the alternative" and reassessing the options open to that subgroup.

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File URL: http://hdl.handle.net/10.1007/s10058-011-0109-z
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Article provided by Springer & Society for Economic Design in its journal Review of Economic Design.

Volume (Year): 15 (2011)
Issue (Month): 4 (December)
Pages: 257-291

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Handle: RePEc:spr:reecde:v:15:y:2011:i:4:p:257-291
DOI: 10.1007/s10058-011-0109-z
Contact details of provider: Web page: http://www.springer.com

Web page: https://sites.google.com/site/societyforeconomicdesign/

Order Information: Web: http://www.springer.com/economics/journal/10058

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  1. 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.
  2. Svensson, Lars-Gunnar, 1983. "Large Indivisibles: An Analysis with Respect to Price Equilibrium and Fairness," Econometrica, Econometric Society, vol. 51(4), pages 939-954, July.
  3. Biung-Ghi Ju, 2007. "Efficiency and Consistency for Locating Multiple Public Facilities," Discussion Paper Series 0716, Institute of Economic Research, Korea University.
  4. Yeh, Chun-Hsien, 2006. "Reduction-consistency in collective choice problems," Journal of Mathematical Economics, Elsevier, vol. 42(6), pages 637-652, September.
  5. Peleg, B, 1986. "On the Reduced Game Property and Its Converse," International Journal of Game Theory, Springer;Game Theory Society, vol. 15(3), pages 187-200.
  6. Peleg, Bezalel, 1985. "An axiomatization of the core of cooperative games without side payments," Journal of Mathematical Economics, Elsevier, vol. 14(2), pages 203-214, April.
  7. William Thomson, 2007. "Fair Allocation Rules," RCER Working Papers 539, University of Rochester - Center for Economic Research (RCER).
  8. Sasaki, Hiroo, 1995. "Consistency and Monotonicity in Assignment Problems," International Journal of Game Theory, Springer;Game Theory Society, vol. 24(4), pages 373-397.
  9. Thomson, W., 1996. "Consistent Allocation Rules," RCER Working Papers 418, University of Rochester - Center for Economic Research (RCER).
  10. 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.
  11. Thomson, William, 2003. "Axiomatic and game-theoretic analysis of bankruptcy and taxation problems: a survey," Mathematical Social Sciences, Elsevier, vol. 45(3), pages 249-297, July.
  12. Peleg, B. & Tijs, S.H., 1993. "The consistency principle for games in strategic form," Discussion Paper 1993-6, Tilburg University, Center for Economic Research.
  13. Sergiu Hart, 2006. "Shapley Value," Discussion Paper Series dp421, The Federmann Center for the Study of Rationality, the Hebrew University, Jerusalem.
  14. Sasaki, Hiroo & Toda, Manabu, 1992. "Consistency and characterization of the core of two-sided matching problems," Journal of Economic Theory, Elsevier, vol. 56(1), pages 218-227, February.
  15. Dutta, B, 1990. "The Egalitarian Solution and Reduced Game Properties in Convex Games," International Journal of Game Theory, Springer;Game Theory Society, vol. 19(2), pages 153-169.
  16. Roemer, John E., 1988. "Axiomatic bargaining theory on economic environments," Journal of Economic Theory, Elsevier, vol. 45(1), pages 1-31, June.
  17. Maniquet, Francois, 1996. "Horizontal equity and stability when the number of agents is variable in the fair division problem," Economics Letters, Elsevier, vol. 50(1), pages 85-90, January.
  18. Lars Ehlers & Bettina Klaus, 2002. "Efficient Priority Rules," UFAE and IAE Working Papers 554.02, Unitat de Fonaments de l'Anàlisi Econòmica (UAB) and Institut d'Anàlisi Econòmica (CSIC).
  19. Youngsub Chun, 2011. "Consistency and monotonicity in sequencing problems," International Journal of Game Theory, Springer;Game Theory Society, vol. 40(1), pages 29-41, February.
  20. Bettina Klaus & Alexandru Nichifor, 2010. "Consistency in one-sided assignment problems," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 35(3), pages 415-433, September.
  21. Thomson, William, 1988. "A study of choice correspondences in economies with a variable number of agents," Journal of Economic Theory, Elsevier, vol. 46(2), pages 237-254, December.
  22. Lensberg, Terje, 1988. "Stability and the Nash solution," Journal of Economic Theory, Elsevier, vol. 45(2), pages 330-341, August.
  23. Tadenuma, Koichi & Thomson, William, 1993. "The fair allocation of an indivisible good when monetary compensations are possible," Mathematical Social Sciences, Elsevier, vol. 25(2), pages 117-132, February.
  24. Chun, Youngsub, 2002. "The Converse Consistency Principle in Bargaining," Games and Economic Behavior, Elsevier, vol. 40(1), pages 25-43, July.
  25. Hokari, Toru, 2005. "Consistency implies equal treatment in TU-games," Games and Economic Behavior, Elsevier, vol. 51(1), pages 63-82, April.
  26. William Thomson, 2007. "Lorenz rankings of rules for the adjudication of conflicting claims," RCER Working Papers 538, University of Rochester - Center for Economic Research (RCER).
  27. Chambers, Christopher P., 2004. "Consistency in the probabilistic assignment model," Journal of Mathematical Economics, Elsevier, vol. 40(8), pages 953-962, December.
  28. Tadenuma, Koichi & Thomson, William, 1991. "No-Envy and Consistency in Economies with Indivisible Goods," Econometrica, Econometric Society, vol. 59(6), pages 1755-1767, November.
  29. Fleurbaey, Marc & Maniquet, Francois, 1996. "Fair allocation with unequal production skills: The No Envy approach to compensation," Mathematical Social Sciences, Elsevier, vol. 32(1), pages 71-93, August.
  30. Dagan, N. & Volij, O.C., 1994. "Bilateral Comparisons and Consistent Fair Division Rules in the Context of Bankruptcy Problems," Discussion Paper 1994-23, Tilburg University, Center for Economic Research.
  31. Nash, John, 1950. "The Bargaining Problem," Econometrica, Econometric Society, vol. 18(2), pages 155-162, April.
  32. Tadenuma, K, 1992. "Reduced Games, Consistency, and the Core," International Journal of Game Theory, Springer;Game Theory Society, vol. 20(4), pages 325-334.
  33. Youngsub Chun, 1999. "Equivalence of axioms for bankruptcy problems," International Journal of Game Theory, Springer;Game Theory Society, vol. 28(4), pages 511-520.
  34. Toru Hokari & William Thomson, 2007. "On properties of division rules lifted by bilateral consistency," RCER Working Papers 536, University of Rochester - Center for Economic Research (RCER).
  35. Manabu Toda, 2006. "Monotonicity and Consistency in Matching Markets," International Journal of Game Theory, Springer;Game Theory Society, vol. 34(1), pages 13-31, April.
  36. Youngsub Chun, 1999. "Equivalence of Axioms for Bankruptcy Problems," Working Paper Series no1, Institute of Economic Research, Seoul National University.
  37. Young, H. P., 1988. "Distributive justice in taxation," Journal of Economic Theory, Elsevier, vol. 44(2), pages 321-335, April.
  38. Aumann, Robert J. & Maschler, Michael, 1985. "Game theoretic analysis of a bankruptcy problem from the Talmud," Journal of Economic Theory, Elsevier, vol. 36(2), pages 195-213, August.
  39. Carmen Bevia, 1996. "Identical preferences lower bound solution and consistency in economies with indivisible goods," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 13(1), pages 113-126, January.
  40. Ergin, Haluk I., 2000. "Consistency in house allocation problems," Journal of Mathematical Economics, Elsevier, vol. 34(1), pages 77-97, August.
  41. Thomson, William, 1994. "Consistent extensions," Mathematical Social Sciences, Elsevier, vol. 28(1), pages 35-49, August.
  42. Lensberg, Terje, 1987. "Stability and Collective Rationality," Econometrica, Econometric Society, vol. 55(4), pages 935-961, July.
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