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The Borda count in n-dimensional issue space

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  • Scott Feld
  • Bernard Grofman

Abstract

We provide a natural extension of the Borda count to the n-dimensional spatial context, an algorithm to find the spatial Borda winner based on the notion of an inverse Borda count, the result that the Borda winner and the Condorcet winner coincide in unidimensional space when all alternatives on a line are feasible, results that show that in multi-dimensional space the Borda winner and the Condorcet winner (except under very implausible circumstances) will be distinct, and some results on the manipulability of outcomes under the Borda rule as a function of the domain of alternatives over which the Borda count is to be defined. Copyright Kluwer Academic Publishers 1988

Suggested Citation

  • Scott Feld & Bernard Grofman, 1988. "The Borda count in n-dimensional issue space," Public Choice, Springer, vol. 59(2), pages 167-176, November.
    • Handle: RePEc:kap:pubcho:v:59:y:1988:i:2:p:167-176
    DOI: 10.1007/BF00054452
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    References listed on IDEAS

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    1. Grofman, Bernard & Owen, Guillermo & Noviello, Nicholas & Glazer, Amihai, 1987. "Stability and Centrality of Legislative Choice in the Spatial Context," American Political Science Review, Cambridge University Press, vol. 81(2), pages 539-553, June.
    2. Richard D. McKelvey & Richard E. Wendell, 1976. "Voting Equilibria in Multidimensional Choice Spaces," Mathematics of Operations Research, INFORMS, vol. 1(2), pages 144-158, May.
    3. Chamberlin, John R. & Cohen, Michael D., 1978. "Toward Applicable Social Choice Theory: A Comparison of Social Choice Functions under Spatial Model Assumptions," American Political Science Review, Cambridge University Press, vol. 72(4), pages 1341-1356, December.
    4. Scott Feld & Bernard Grofman, 1986. "Research note Partial single-peakedness: An extension and clarification," Public Choice, Springer, vol. 51(1), pages 71-80, January.
    5. Farkas, Daniel & Nitzan, Shmuel, 1979. "The Borda Rule and Pareto Stability: A Comment," Econometrica, Econometric Society, vol. 47(5), pages 1305-1306, September.
    6. Feld, Scott L. & Grofman, Bernard, 1986. "On the Possibility of Faithfully Representative Committees," American Political Science Review, Cambridge University Press, vol. 80(3), pages 863-879, September.
    7. Norman Schofield, 1978. "Instability of Simple Dynamic Games," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 45(3), pages 575-594.
    8. Fishburn, Peter C., 1974. "Paradoxes of Voting," American Political Science Review, Cambridge University Press, vol. 68(2), pages 537-546, June.
    9. McKelvey, Richard D, 1979. "General Conditions for Global Intransitivities in Formal Voting Models," Econometrica, Econometric Society, vol. 47(5), pages 1085-1112, September.
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    Cited by:

    1. Kazuo Yamaguchi, 2016. "Borda winner in facility location problems on sphere," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 46(4), pages 893-898, April.
    2. Nehring, Klaus & Puppe, Clemens, 2019. "Resource allocation by frugal majority rule," Working Paper Series in Economics 131, Karlsruhe Institute of Technology (KIT), Department of Economics and Management.
    3. Andrei Gomberg & Francisco Marhuenda & Ignacio Ortuño-Ortín, 2004. "A model of endogenous political party platforms," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 24(2), pages 373-394, August.
    4. Cheryl L. Eavey, 1991. "Patterns of Distribution in Spatial Games," Rationality and Society, , vol. 3(4), pages 450-474, October.
    5. Yeawon Yoo & Adolfo R. Escobedo, 2021. "A New Binary Programming Formulation and Social Choice Property for Kemeny Rank Aggregation," Decision Analysis, INFORMS, vol. 18(4), pages 296-320, December.
    6. Scott L. Feld & Bernard Grofman, 1992. "Who's Afraid of the Big Bad Cycle? Evidence from 36 Elections," Journal of Theoretical Politics, , vol. 4(2), pages 231-237, April.
    7. Toyotaka Sakai, 2015. "A Search for the General Will in a Spatial Model," The Japanese Economic Review, Japanese Economic Association, vol. 66(2), pages 260-270, June.
    8. Caplin, Andrew & Nalebuff, Barry, 1997. "Competition among Institutions," Journal of Economic Theory, Elsevier, vol. 72(2), pages 306-342, February.

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