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Transitive closure, proximity and intransitivities

Author

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  • Nick Baigent
  • Christian Klamler

Abstract

Assignments of weak orders to complete binary relations are considered. Firstly, it is shown that assigning the transitive closure of a complete binary relation does not always assign the closest weak order according to any reasonable metric on complete binary relations. It is then shown that the assignment of a weak order to a complete binary relation assigns its transitive closure if and only if it assigns the closest weak order according to a particular distance function that is not a metric. This permits more direct comparisons between the Transitive Closure Rule and other rules such as the Slater Rule. Copyright Springer-Verlag Berlin/Heidelberg 2003

Suggested Citation

  • Nick Baigent & Christian Klamler, 2003. "Transitive closure, proximity and intransitivities," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 23(1), pages 175-181, December.
  • Handle: RePEc:spr:joecth:v:23:y:2003:i:1:p:175-181
    DOI: 10.1007/s00199-003-0362-7
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    Citations

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    Cited by:

    1. Ceyhun Coban & M. Sanver, 2014. "Social choice without the Pareto principle under weak independence," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 43(4), pages 953-961, December.
    2. Edith Elkind & Piotr Faliszewski & Arkadii Slinko, 2015. "Distance rationalization of voting rules," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 45(2), pages 345-377, September.
    3. Burak Can & Mohsen Pourpouneh & Ton Storcken, 2021. "An axiomatic characterization of the Slater rule," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 56(4), pages 835-853, May.
    4. Christian Klamler, 2003. "Kemeny's rule and Slater''s rule: A binary comparison," Economics Bulletin, AccessEcon, vol. 4(35), pages 1-7.
    5. repec:ebl:ecbull:v:4:y:2003:i:35:p:1-7 is not listed on IDEAS
    6. Vicki Knoblauch, 2014. "Preference, topology and measure," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 43(2), pages 507-514, August.
    7. Hannu Nurmi, 2014. "Some remarks on the concept of proportionality," Annals of Operations Research, Springer, vol. 215(1), pages 231-244, April.

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