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Consistency and its converse: an introduction

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  • William Thomson

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Abstract

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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Suggested Citation

  • William Thomson, 2011. "Consistency and its converse: an introduction," Review of Economic Design, Springer;Society for Economic Design, vol. 15(4), pages 257-291, December.
  • Handle: RePEc:spr:reecde:v:15:y:2011:i:4:p:257-291
    DOI: 10.1007/s10058-011-0109-z
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    References listed on IDEAS

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    1. Hokari, Toru, 2005. "Consistency implies equal treatment in TU-games," Games and Economic Behavior, Elsevier, vol. 51(1), pages 63-82, April.
    2. William Thomson, 2012. "Lorenz rankings of rules for the adjudication of conflicting claims," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 50(3), pages 547-569, August.
    3. Chambers, Christopher P., 2004. "Consistency in the probabilistic assignment model," Journal of Mathematical Economics, Elsevier, vol. 40(8), pages 953-962, December.
    4. Tadenuma, Koichi & Thomson, William, 1991. "No-Envy and Consistency in Economies with Indivisible Goods," Econometrica, Econometric Society, vol. 59(6), pages 1755-1767, November.
    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. 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.
    7. 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.
    8. Oscar Volij & Nir Dagan, 1997. "Bilateral Comparisons and Consistent Fair Division Rules in the Context of Bankruptcy Problems," International Journal of Game Theory, Springer;Game Theory Society, vol. 26(1), pages 11-25.
    9. Nash, John, 1950. "The Bargaining Problem," Econometrica, Econometric Society, vol. 18(2), pages 155-162, April.
    10. Ju, Biung-Ghi, 2008. "Efficiency and consistency for locating multiple public facilities," Journal of Economic Theory, Elsevier, vol. 138(1), pages 165-183, January.
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    12. Youngsub Chun, 1999. "Equivalence of axioms for bankruptcy problems," International Journal of Game Theory, Springer;Game Theory Society, vol. 28(4), pages 511-520.
    13. Hokari, Toru & Thomson, William, 2008. "On properties of division rules lifted by bilateral consistency," Journal of Mathematical Economics, Elsevier, vol. 44(11), pages 1057-1071, December.
    14. Yeh, Chun-Hsien, 2006. "Reduction-consistency in collective choice problems," Journal of Mathematical Economics, Elsevier, vol. 42(6), pages 637-652, September.
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    23. 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.
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    28. 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.
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    35. 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.
    36. 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.
    37. 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.
    38. Lensberg, Terje, 1987. "Stability and Collective Rationality," Econometrica, Econometric Society, vol. 55(4), pages 935-961, July.
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    41. 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.
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    More about this item

    Keywords

    Consistency; Converse consistency; Elevator Lemma; Bracing Lemma; C79; D63; D74;

    JEL classification:

    • D00 - Microeconomics - - General - - - General

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