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Integer Programming on Domains Containing Inseparable Ordered Paris

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  • Busetto, Francesca
  • Codognato, Giulio
  • Tonin, Simone

Abstract

Using the integer programming approach introduced by Sethuraman, Teo, and Vohra (2003), we extend the analysis of the preference domains containing an inseparable ordered pair, initiated by Kalai and Ritz (1978). We show that these domains admit not only Arrovian social welfare functions \without ties," but also Arrovian social welfare functions \with ties," since they satisfy the strictly decomposability condition introduced by Busetto, Codognato, and Tonin (2012). Moreover, we go further in the comparison between Kalai and Ritz (1978)'s inseparability and Arrow (1963)'s single-peak restrictions, showing that the former condition is more \respectable," in the sense of Muller and Satterthwaite (1985).

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  • Busetto, Francesca & Codognato, Giulio & Tonin, Simone, 2014. "Integer Programming on Domains Containing Inseparable Ordered Paris," SIRE Discussion Papers 2015-22, Scottish Institute for Research in Economics (SIRE).
    • Handle: RePEc:edn:sirdps:610
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    References listed on IDEAS

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    1. Ritz, Zvi, 1983. "Restricted domains, arrow-social welfare functions and noncorruptible and non-manipulable social choice correspondences: The case of private alternatives," Mathematical Social Sciences, Elsevier, vol. 4(2), pages 155-179, April.
    2. Kalai, Ehud & Ritz, Zvi, 1980. "Characterization of the private alternatives domains admitting arrow social welfare functions," Journal of Economic Theory, Elsevier, vol. 22(1), pages 23-36, February.
    3. Francesca Busetto & Giulio Codognato & Simone Tonin, 2012. "Integer Programming and Nondictatorial Arrovian Social Welfare Functions," EconomiX Working Papers 2012-36, University of Paris Nanterre, EconomiX.
    4. Jay Sethuraman & Teo Chung Piaw & Rakesh V. Vohra, 2003. "Integer Programming and Arrovian Social Welfare Functions," Mathematics of Operations Research, INFORMS, vol. 28(2), pages 309-326, May.
    5. Blair, Douglas & Muller, Eitan, 1983. "Essential aggregation procedures on restricted domains of preferences," Journal of Economic Theory, Elsevier, vol. 30(1), pages 34-53, June.
    6. Sethuraman, Jay & Teo, Chung-Piaw & Vohra, Rakesh V., 2006. "Anonymous monotonic social welfare functions," Journal of Economic Theory, Elsevier, vol. 128(1), pages 232-254, May.
    7. Ritz, Zvi, 1985. "Restricted domains, arrow social welfare functions and noncorruptible and nonmanipulable social choice correspondences: The case of private and public alternatives," Journal of Economic Theory, Elsevier, vol. 35(1), pages 1-18, February.
    8. Kalai, Ehud & Muller, Eitan, 1977. "Characterization of domains admitting nondictatorial social welfare functions and nonmanipulable voting procedures," Journal of Economic Theory, Elsevier, vol. 16(2), pages 457-469, December.
    9. Kim, Ki Hang & Roush, Fred W., 1981. "Effective nondictatorial domains," Journal of Economic Theory, Elsevier, vol. 24(1), pages 40-47, February.
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