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More on Decision Rules and Policy Outcomes

Published online by Cambridge University Press:  27 January 2009

Amoz Katsa  and
Shmuel Nitzan
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Extract

An attempt to rationalize policy outcomes in voting bodies has been made by Rae and Taylor (this Journal, 1 (1971), 71–90). In that work the assumption is made that all voters' preferences are representable by ‘city block’ type utility functions. The principal result obtained in that case by the writers is that for an odd number of voters there is always a unique equilibrium point under simple majority rule, independent of the distribution of individual optimal points and independent of the dimension of the policy space. Unfortunately, the Rae and Taylor result is not correct. In particular their result holds for a one or two dimensional policy space but not in cases where the policy space has three or more dimensions. The proof given by Rae and Taylor is correct for n = 2 but is false for n ≥ 3.

Type
Notes and Comments
Information
British Journal of Political Science , Volume 7 , Issue 3 , July 1977 , pp. 419 - 422
Copyright
Copyright © Cambridge University Press 1977

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References

1 This result is also reported in Taylor, M., ‘Review Article: Mathematical Political Theory’, British Journal of Political Science, 1 (1971), 339–82.CrossRefGoogle Scholar However in Taylor's later piece, ‘The Theory of Collective Choice’, in Greenstein, F. and Polsby, N., eds., Handbook of Political Science, v (Reading, Mass.: Addison-Wesley Pub. Co., 1975), Chap. 3, pp. 413–81Google Scholar, severe reservations are expressed with regard to this assumption.

2 Although this assumption may be inappropriate in certain political circumstances we still model the problem this way since we do not feel that changing it is within the scope of this note.

3 Kramer, G. H. and Klevorick, A. K., ‘Existence of a “Local” Cooperative Equilibrium in a Class of Voting Games’, Review of Economic Studies, XLI (1974), 539–47.CrossRefGoogle Scholar

4 Kats, A. and Nitzan, S., ‘Global and Local Equilibrium in Majority Voting’, Public Choice, xxvi (1976), 105–6.CrossRefGoogle Scholar