Abstract
In a (Econ. Theory 22:557–568, 2003) paper, Campbell and Kelly correctly stated that if the number of individuals is odd and there are at least three alternatives then a social choice function with full range on the Condorcet domain must always select the majority winner if the rule is non-dictatorial and strategy-proof. This note corrects an error in the proof.
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Notes
The claim is not true when \(n\) is even (Merrill 2011). Campbell and Kelly (2015) prove that, regardless of the parity of \(n\), if there are at least four alternatives then a social choice function with full range on the Condorcet domain must always select the majority winner if it is strategy-proof and also satisfies anonymity and neutrality.
References
Campbell, D.E., Kelly, J.S.: A strategy-proofness characterization of majority rule. Econ. Theory 22, 557–568 (2003)
Campbell, D. E., Kelly, J. S.: Anonymous, neutral, and strategy-proof social choice functions on the Condorcet domain (2015) forthcoming
Gibbard, A.: On the manipulation of voting schemes: a general result. Econometrica 4, 587–602 (1973)
Merrill, L.N.: Parity dependence of a majority rule characterization on the Condorcet domain. Econ. Lett. 112, 259–261 (2011)
Satterthwaite, M.: Strategy-proofness and arrow’s conditions: existence and correspondence theorems for voting procedures and social welfare functions. J. Econ. Theory 10, 187–217 (1975)
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Campbell, D.E., Kelly, J.S. Correction to “A Strategy-proofness Characterization of Majority Rule”. Econ Theory Bull 4, 121–124 (2016). https://doi.org/10.1007/s40505-015-0066-8
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DOI: https://doi.org/10.1007/s40505-015-0066-8