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Monotonicity and its Cognates in the Theory of Choice

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  • Hannu Nurmi

Abstract

The standard requirement of monotonicity of a voting procedurestates that an improvement in the ranking of the winningalternative, ceteris paribus, should not make itnon-winning. A concept apparently closely linked tomonotonicity is known as the participation axiom whichrequires that it should never be advantageous for a voter toabstain rather than to vote according to his/her preferences.Situations in which a group of voters may end up with a betteroutcome by not voting at all than by voting according to theirpreferences are called instances of the no-show paradox. Astrong version of the paradox occurs when the abstainers endup with their most preferred outcome by abstaining. A thirdrelated concept is invulnerability to preference truncation.This is satisfied by such procedures that make itadvantageous for voters to always reveal their entirepreference rankings. The fourth concept, Maskin monotonicity,plays an important role in mechanism design literature. Wediscuss these requirements in the context of votingprocedures. Particular attention is paid to the plausibilityof conditions guaranteeing various forms of monotonicity. Copyright Kluwer Academic Publishers 2004

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  • Hannu Nurmi, 2004. "Monotonicity and its Cognates in the Theory of Choice," Public Choice, Springer, vol. 121(1), pages 25-49, October.
    • Handle: RePEc:kap:pubcho:v:121:y:2004:i:1:p:25-49
    DOI: 10.1007/s11127-004-4567-5
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    References listed on IDEAS

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    1. Peter Fishburn & Steven Brams, 1984. "Manipulability of voting by sincere truncation of preferences," Public Choice, Springer, vol. 44(3), pages 397-410, January.
    2. Hannu Nurmi, 1998. "Rational Behaviour and the Design of Institutions," Books, Edward Elgar Publishing, number 1487.
    3. Moulin, Herve, 1988. "Condorcet's principle implies the no show paradox," Journal of Economic Theory, Elsevier, vol. 45(1), pages 53-64, June.
    4. Jerry S. Kelly & Donald E. Campbell, 2002. "Non-monotonicity does not imply the no-show paradox," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 19(3), pages 513-515.
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    2. Roy, Sunanda & Wu, Kuan Chuen & Chandra, Abhijit, 2014. "Uncovering the "Will of the People": Heterogeneity and Polarization within electorates," Staff General Research Papers Archive 37330, Iowa State University, Department of Economics.
    3. Korpela, Ville, 2013. "A simple sufficient condition for strong implementation," Journal of Economic Theory, Elsevier, vol. 148(5), pages 2183-2193.
    4. Roy, Sunanda & Wu, Kuan Chuen & Chandra, Abhijit, 2015. "Uncovering the "Will of the People": Measuring Preference Polarization among Voters," Staff General Research Papers Archive 38358, Iowa State University, Department of Economics.
    5. Uuganbaatar Ninjbat, 2015. "Impossibility theorems are modified and unified," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 45(4), pages 849-866, December.
    6. Conal Duddy, 2014. "Condorcet’s principle and the strong no-show paradoxes," Theory and Decision, Springer, vol. 77(2), pages 275-285, August.
    7. Joaquín Pérez & José L. Jimeno & Estefanía García, 2015. "No Show Paradox and the Golden Number in Generalized Condorcet Voting Methods," Group Decision and Negotiation, Springer, vol. 24(3), pages 497-513, May.

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