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Acyclic Choice without the Pareto Principle

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  • David Kelsey

Abstract

In this paper we prove some versions of the Arrow Impossibility Theorem, with the collective rationality condition weakened from transitivity to acyclicity, and the Pareto condition replaced by weaker conditions. Thus this result has weaker assumptions than versions of the Arrow Theorem which have previously appeared in the literature. Consequently it is one of the strongest impossibility theorems. Our result is an extension of a recent theorem of Blair and Pollak.

Suggested Citation

  • David Kelsey, 1984. "Acyclic Choice without the Pareto Principle," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 51(4), pages 693-699.
    • Handle: RePEc:oup:restud:v:51:y:1984:i:4:p:693-699.
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    File URL: http://hdl.handle.net/10.2307/2297787
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    Citations

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    Cited by:

    1. Wesley H. Holliday & Mikayla Kelley, 2020. "A note on Murakami’s theorems and incomplete social choice without the Pareto principle," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 55(2), pages 243-253, August.
    2. Susumu Cato, 2015. "Conditions on social-preference cycles," Theory and Decision, Springer, vol. 79(1), pages 1-13, July.
    3. Susumu Cato, 2013. "Quasi-decisiveness, quasi-ultrafilter, and social quasi-orderings," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 41(1), pages 169-202, June.
    4. Sholomov, Lev A., 2000. "Explicit form of neutral social decision rules for basic rationality conditions," Mathematical Social Sciences, Elsevier, vol. 39(1), pages 81-107, January.
    5. Jérémy Picot, 2012. "Random aggregation without the Pareto principle," Review of Economic Design, Springer;Society for Economic Design, vol. 16(1), pages 1-13, March.
    6. Susumu Cato & Daisuke Hirata, 2010. "Collective choice rules and collective rationality: a unified method of characterizations," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 34(4), pages 611-630, April.
    7. Susumu Cato, 2012. "Social choice without the Pareto principle: a comprehensive analysis," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 39(4), pages 869-889, October.
    8. Wesley H. Holliday & Mikayla Kelley, 2021. "Escaping Arrow's Theorem: The Advantage-Standard Model," Papers 2108.01134, arXiv.org, revised Nov 2022.
    9. Donald Campbell & Jerry Kelly, 2014. "Universally beneficial manipulation: a characterization," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 43(2), pages 329-355, August.
    10. Quesada, Antonio, 2003. "(100-200/m)% veto power," Research in Economics, Elsevier, vol. 57(2), pages 83-92, June.

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