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A New Explanation of K. J. Arrow’s Impossibility Theorem: On Conditions of Social Welfare Functions

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DOI: 10.4236/ojps.2015.51003    2,859 Downloads   3,184 Views   Citations
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ABSTRACT

Social welfare function theory belongs to the cross disciplines of economics, sociology, management science and political science. The social welfare function conditions were first proposed by Kenneth Joseph Arrow, and served as the golden criteria in this field. For a long time, “the expressions of these conditions are not satisfactory”, as Arrow said himself, and he has continued to revise them. The author of this article has attempted to structure a mathematical expression that would meet Arrow’s conditions. We found that the conditions of “unrestricted domain” and “independent alternatives independence” could not always be expressed simultaneously. This led us to conduct further research on the relationships among Arrow’s conditions. We find that there are logical conflicts among some of these conditions, and we discuss these issues in this article.

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Yuan, Z. (2015) A New Explanation of K. J. Arrow’s Impossibility Theorem: On Conditions of Social Welfare Functions. Open Journal of Political Science, 5, 26-39. doi: 10.4236/ojps.2015.51003.

References

[1] Arrow, K. J. (1951). Social Choice and Individual Values. New Heaven, CT: Cowles Foundation, Yale University.
[2] Arrow, K. J. (1970). Social Choice and Individual Values (2nd ed.). New Heaven, CT: Cowles Foundation, Yale University.
[3] Arrow, K. J. (1983). Social Choice and Justice. Cambridge, Massachusetts: The Belknap Press of Harvard University Press.
[4] Buchanan J. M., & Tullock, G. (1965) The Calculus of Consent: Logical Foundations of Constitutional Democracy. Ann Arbor, MI: University of Michigan Press.
[5] Congleton, R. (2002). The Future of Public Choice. The Sixth International Conference in Public Choice, Japan, 21 July 2002.
[6] Mueller, D. C. (1979) Public Choice. London: Cambridge University Press.
[7] Mueller, D. C. (2003) Public Choice (3th ed.). London: Cambridge University Press.
[8] Sen, A. K. (1970) Collective Choice and Social Welfare. Cambridge, Massachusetts: Belknap Press of Harvard University Press.
[9] Vickrey, W. (1960). Utility, Strategy, and Social Decision Rules. The Quarterly Journal of Economics, 74, 507-535.
http://dx.doi.org/10.2307/1884349

  
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