IDEAS home Printed from https://ideas.repec.org/a/kap/pubcho/v47y1985i2p349-370.html
   My bibliography  Save this article

The vulnerability of point-voting schemes to preference variation and strategic manipulation

Author

Listed:
  • Shmuel Nitzan

Abstract

This essay measures and analyzes for a special class of point-voting schemes (the Borda method, plurality rule and the unrestricted point-voting scheme) sensitivity to preference variation (a simple change in the socially winning alternative resulting from alteration of a single voter's preferences) and vulnerability to individual strategic manipulation (a change in the winning alternative that benefits the voter whose preferences are altered). Assuming that society (n voters with linear preference orders on a finite set of m alternatives) satisfies the impartial-culture assumption, that is, each randomly selected voter is equally likely to hold any one of the randomly picked possible preference orders on the alternatives, we demonstrate: (i) for a given rule and a fixed number of voters, the sensitivity to individual preference variation and the vulnerability to individual strategic manipulation are greater, the larger the total number of alternatives. (ii) For a given rule and a fixed number of alternatives, the vulnerability to individual strategic manipulation, in general, is not greater the smaller the total number of voters. Such a relationship does hold, however, if n is sufficiently large. (iii) For any given combination of number of voters and number of alternatives, the unrestricted point-voting scheme is more sensitive to preference variation than the Borda method, which, in turn, is more exposed to such variation relative to the plurality rule. A similar conclusion does not hold with respect to vulnerability to individual strategic manipulation, unless the number of voters is sufficiently small. Copyright Martinus Nijhoff Publishers 1985

Suggested Citation

  • Shmuel Nitzan, 1985. "The vulnerability of point-voting schemes to preference variation and strategic manipulation," Public Choice, Springer, vol. 47(2), pages 349-370, January.
  • Handle: RePEc:kap:pubcho:v:47:y:1985:i:2:p:349-370
    DOI: 10.1007/BF00127531
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1007/BF00127531
    Download Restriction: Access to full text is restricted to subscribers.

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Kelly, Jerry S, 1977. "Strategy-Proofness and Social Choice Functions without Singlevaluedness," Econometrica, Econometric Society, vol. 45(2), pages 439-446, March.
    2. Satterthwaite, Mark Allen, 1975. "Strategy-proofness and Arrow's conditions: Existence and correspondence theorems for voting procedures and social welfare functions," Journal of Economic Theory, Elsevier, vol. 10(2), pages 187-217, April.
    3. Pattanaik, Prasanta K., 1974. "Stability of sincere voting under some classes of non-binary group decision procedures," Journal of Economic Theory, Elsevier, vol. 8(2), pages 206-224, June.
    4. Tullock, Gordon & Campbell, Colin D, 1970. "Computer Simulation of a Small Voting System," Economic Journal, Royal Economic Society, vol. 80(317), pages 97-104, March.
    5. Pattanaik, Prasanta K., 1973. "On the stability of sincere voting situations," Journal of Economic Theory, Elsevier, vol. 6(6), pages 558-574, December.
    6. Klahr, David, 1966. "A Computer Simulation of the Paradox of Voting," American Political Science Review, Cambridge University Press, vol. 60(2), pages 384-390, June.
    7. DeMeyer, Frank & Plott, Charles R, 1970. "The Probability of a Cyclical Majority," Econometrica, Econometric Society, vol. 38(2), pages 345-354, March.
    8. Kannai, Yakar & Peleg, Bezalel, 1984. "A note on the extension of an order on a set to the power set," Journal of Economic Theory, Elsevier, vol. 32(1), pages 172-175, February.
    9. Kelly, Jerry S, 1974. "Voting Anomalies, the Number of Voters, and the Number of Alternatives," Econometrica, Econometric Society, vol. 42(2), pages 239-251, March.
    10. Gehrlein, William V. & Fishburn, Peter C., 1976. "The probability of the paradox of voting: A computable solution," Journal of Economic Theory, Elsevier, vol. 13(1), pages 14-25, August.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Green-Armytage, James, 2011. "Strategic voting and nomination," MPRA Paper 32200, University Library of Munich, Germany.
    2. Dominique Lepelley & Boniface Mbih, 1997. "Strategic Manipulation in Committees Using the Plurality Rule: Alternative Concepts and Frequency Calculations," Group Decision and Negotiation, Springer, vol. 6(2), pages 119-138, March.
    3. Mostapha Diss, 2015. "Strategic manipulability of self-selective social choice rules," Annals of Operations Research, Springer, vol. 229(1), pages 347-376, June.
    4. Eyal Baharad & Leif Danziger, 2018. "Voting in Hiring Committees: Which “Almost” Rule is Optimal?," Group Decision and Negotiation, Springer, vol. 27(1), pages 129-151, February.
    5. Sébastien Courtin & Boniface Mbih & Issofa Moyouwou, 2014. "Are Condorcet procedures so bad according to the reinforcement axiom?," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 42(4), pages 927-940, April.
    6. Yuliya Veselova, 2016. "The difference between manipulability indices in the IC and IANC models," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 46(3), pages 609-638, March.
    7. Yuliya A. Veselova, 2016. "Does Incomplete Information Reduce Manipulability?," HSE Working papers WP BRP 152/EC/2016, National Research University Higher School of Economics.
    8. Steven Brams & Peter Fishburn & Samuel Merrill, 1988. "The responsiveness of approval voting: Comments on Saari and Van Newenhizen," Public Choice, Springer, vol. 59(2), pages 121-131, November.
    9. Jean-François Laslier, 2015. "Heuristic voting under the Alternative Vote: the efficiency of “sour grapes" behavior," PSE Working Papers halshs-01168670, HAL.
    10. Bednay, Dezső & Moskalenko, Anna & Tasnádi, Attila, 2019. "Dictatorship versus manipulability," Mathematical Social Sciences, Elsevier, vol. 101(C), pages 72-76.
    11. Eyal Baharad & Leif Danziger, 2018. "Voting in Hiring Committees: Which "Almost" Rule is Optimal?," CESifo Working Paper Series 6851, CESifo Group Munich.
    12. Baharad, Eyal & Danziger, Leif, 2018. "Voting in Hiring Committees: Which "Almost" Rule Is Optimal?," IZA Discussion Papers 11287, Institute of Labor Economics (IZA).
    13. James Green-Armytage & T. Nicolaus Tideman & Rafael Cosman, 2016. "Statistical evaluation of voting rules," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 46(1), pages 183-212, January.
    14. James Green-Armytage & T. Tideman & Rafael Cosman, 2016. "Statistical evaluation of voting rules," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 46(1), pages 183-212, January.
    15. Jean-François Laslier, 2016. "Heuristic Voting Under the Alternative Vote: The Efficiency of “Sour Grapes” Behavior," Homo Oeconomicus: Journal of Behavioral and Institutional Economics, Springer, vol. 33(1), pages 57-76, August.
    16. Matías Núñez & Jean Laslier, 2014. "Preference intensity representation: strategic overstating in large elections," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 42(2), pages 313-340, February.
    17. Jean-François Laslier, 2016. "Heuristic Voting Under the Alternative Vote: The Efficiency of “Sour Grapes” Behavior," Homo Oeconomicus: Journal of Behavioral and Institutional Economics, Springer, vol. 33(1), pages 57-76, August.
    18. Matias Nunez & Laslier Jean François Author-Workplace-Name : Ecole Polytechnique, 2010. "Overstating: A tale of two cities," THEMA Working Papers 2010-05, THEMA (THéorie Economique, Modélisation et Applications), Université de Cergy-Pontoise.
    19. James Green-Armytage, 2015. "Direct voting and proxy voting," Constitutional Political Economy, Springer, vol. 26(2), pages 190-220, June.
    20. Baharad, Eyal & Danziger, Leif, 2018. "Voting in Hiring Committees: Which "Almost" Rule Is Optimal?," GLO Discussion Paper Series 185, Global Labor Organization (GLO).
    21. Jean-François Laslier, 2015. "Heuristic voting under the Alternative Vote: the efficiency of “sour grapes" behavior," PSE - Labex "OSE-Ouvrir la Science Economique" halshs-01168670, HAL.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:kap:pubcho:v:47:y:1985:i:2:p:349-370. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Sonal Shukla) or (Springer Nature Abstracting and Indexing). General contact details of provider: http://www.springer.com .

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.