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Quality and Quantity

, Volume 29, Issue 4, pp 433–438 | Cite as

On the fundamental thought behind voting rules

  • Björn S. Stefánsson
Research Note

Abstract

The theme is Arrow's requirement in his theorem of 1951 on methods for group choice, that the choice be independent of irrelevant alternatives. The attention is drawn to (1) his own explanation of this requirement in 1972, which is a quite different understanding than has been discussed in the voluminous literature on the theorem, (2) that Arrow, in fact, in 1985 showed an understanding for how “irrelevant alternatives” might in a meaningful way influence the group choice, (3) that admittedly the border-line between irrelevant and relevant alternatives in Arrow's original statement is arbitrary, and (4) that Arrow, if he had observed the final thought in the origin of the group theory by Borda, which he admittedly did not, might have realized that Borda's method stringently estimates the relevance of each alternative for the result.

The author expresses his surprise that a theoretical conclusion based on an arbitrary fundament has been admired so long.

Keywords

Theoretical Conclusion Group Choice Irrelevant Alternative Fundamental Thought 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. Arrow, K. J. (1972). ‘General economic equilibrium: purpose, analytic techniques, collective choice’, pp. 209–31 inLex Prix Nobel en 1972.Google Scholar
  2. Arrow, K. J. (1951).Social Choice and Individual Values. New York: John Wiley.Google Scholar
  3. Arrow, K. J. (1963).Social Choice and Individual Values (2nd edn.). New Haven: Yale University Press.Google Scholar
  4. Bentzel, R. (1972). ‘The prize for economic science, in memory of Alfred Nobel’, pp. 203–3 inLes Prix Nobel en 1972.Google Scholar
  5. Hansson, B. (1970). ‘Valsystem och besludsprocesser,’Minerva's kvartalsskrift 14: 190–198.Google Scholar
  6. Höglund, B. (1991). ‘Rangordning och vinnare inom tÄvlingsidrott’, pp. 113–136 inGruppbeslut och rangordning — om demokratiska röstningsmetoder, ForskningsrådsnÄmnden, Stockholm.Google Scholar
  7. MacKay, A. (1980).Arrow's Theorem. The Paradox of Social Choice. A Case Study in the Philosophy of Economics. New Haven: Yale University Press.Google Scholar
  8. Newenhizen, J. V. (1992). ‘The Borda method is most likely to respect the Condorcet principle’,Economic Theory 2: 69–83.Google Scholar
  9. Nurmi, H. (1991), ‘Preferences, choices, tournaments: alternative foundations for the evaluation of voting schemes’,Quality & Quantity 25: 393–405.Google Scholar
  10. University of Oxford (1989). Faculty of social studies. Social Studies Faculty Centre, Working Paper 1/89.The Political Theory of Condorcet.Google Scholar
  11. Riker, W. H. (1982).Liberalism Against Populism. A Confrontation between the Theory of Democracy and the Theory of Social Choice. San Francisco: W. H. Freeman and Company.Google Scholar
  12. Sen, A. (1977). ‘Social choice theory: A re-examination’,Econometrica 45: 53–89.Google Scholar
  13. Stefánsson, B. S. (1982). ‘Group choice among three or more alternatives’,Quality & Quantity 16: 433–54.Google Scholar
  14. Stefánsson, B. S. (1991a). ‘Borda's method applied — The right to make a proposal. A historical note’,Quality & Quantity 25: 389–92.Google Scholar
  15. Stefánsson, B. S. (1991b). ‘On irrelevant and infeasible alternatives’,Quality & Quantity 25: 297–306.Google Scholar

Copyright information

© Kluwer Academic Publishers 1995

Authors and Affiliations

  • Björn S. Stefánsson
    • 1
  1. 1.University of IcelandReykjavíkIceland

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