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Implementation of Democratic Social Choice Functions

Ferejohn, John A. and Grether, David M. and McKelvey, Richard D. (1980) Implementation of Democratic Social Choice Functions. Social Science Working Paper, 300. California Institute of Technology , Pasadena, CA. (Unpublished) https://resolver.caltech.edu/CaltechAUTHORS:20171013-145311553

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Abstract

A social choice function is said to be implementable if and only if there exists a game form such that for all preference profiles an equilibrium strategy n-tuple exists and any equilibrium strategy n-tuples of the game yield outcomes in the social choice set. A social choice function is defined to be minimally democratic if and only if whenever there exists an alternative which is ranked first by n-1 voters and is no lower than second for the last voter, then the social choice must be uniquely that alternative. No constraints are placed on the social choice function for other preference profiles. Using the usual definitions of equilibria for n-person games—namely Nash and strong equilibria—it is shown here that over unrestricted preference domains, no minimally democratic social choice function is implementable. The same result holds in certain restricted domains of the type assumed by economists over public goods spaces. We then show that a different notion of equilibrium—namely that of sophisticated equilibrium—allows for implementation of democratic social choice functions also having further appealing properties. The implication is that models of democratic political processes cannot be based on the standard equilibrium notions of Nash or strong equilibria.


Item Type:Report or Paper (Working Paper)
Related URLs:
URLURL TypeDescription
https://doi.org/10.2307/2297367Related ItemLater version published in Review of Economic Studies
Additional Information:We thank Jeff Richelson for useful comments on an earlier draft of this paper, and acknowledge the financial support of NSF grant #SOC79-21588, and #SOC78-15413. Published as Ferejohn, John A., David M. Grether, and Richard D. McKelvey. "Implementation of democratic social choice functions." The Review of Economic Studies 49.3 (1982): 439-446.
Group:Social Science Working Papers
Funders:
Funding AgencyGrant Number
NSFSOC79-21588
NSFSOC78-15413
Subject Keywords:Social choice, Mathematical functions, Nash equilibrium, Game theory, Economic theory, Voting, Public goods, Voting paradox, Private goods, Mathematical monotonicity
Series Name:Social Science Working Paper
Issue or Number:300
Record Number:CaltechAUTHORS:20171013-145311553
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20171013-145311553
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:82348
Collection:CaltechAUTHORS
Deposited By: Jacquelyn Bussone
Deposited On:16 Oct 2017 18:30
Last Modified:03 Oct 2019 18:53

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