Abstract
Previous investigations have shown that a social choice function which is partially implementable must be characterized by pervasive veto power. This paper investigates how much additional latitude in the design of social choice functions, and how much relief from this vetoers result, can be achieved by examining multi-valued social choice rules and relaxing the requirement of partial implementability to a requirement that we call weak partial implementability. We find that the power structures which characterize partially implementable social choice functions, including the veto properties, also characterize weakly partially implementable social choice rules. The conclusion is that invoking multi-valuedness and implementation of appealing social choice rules in strong Nash equilibria. Our results apparently exhaust the possibilities for implementation in strong Nash equilibrium. If any implementation possibility results are to be achieved, they can apparently come only by weakening the equilibrium requirement.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Arrow, K. J.: 1963, Social Choice and Individual Values, Wiley, New York.
Bandyopadhyay, T.: 1984, ‘On the frontier between possibility and impossibility theorems in social choice’, Journal of Economic Theory 32, 52–66.
Bandyopadhyay, T.: 1985, ‘Pareto optimality and the decisive power structure with expansion consistency conditions’, Journal of Economic Theory 35, 366–375.
Bandyopadhyay, T.: 1986a, ‘Rationality, path independence, and the power structure’, Journal of Economic Theory 40, 338–348.
Bandyopadhyay, T.: 1986b, ‘Strategy-proofness of social choice rules’, European Journal of Political Economy, 2, 61–76.
Barbera', S.: 1977, ‘Manipulation of social choice mechanisms that do not leave “Too Much” to chance,’ Econometrica 45, 1573–1588.
Blair, D. H., Bordes, G., Kelly, J. S. and Suzumura, K.: ‘Impossibility without collective rationality’, Journal of Economic Theory 13, 361–379.
Dasgupta, P., Hammond, P. J., and Maskin, E.: 1979, ‘The implementation of social choice rules: some general results on incentive compatibility’, Review of Economic Studies 46, 181–216.
Dutta, B. and Pattanaik, P. K.: 1978, ‘On nicely consistent voting systems’, Econometrica 46, 163–170.
Ferejohn, J. A. and Grether, D. M.: 1977, ‘Weak path-independence’, Journal of Economic Theory 14, 19–31.
Ferejohn, J. A., Grether, D. M. and McKelvey, R. D.: 1982, ‘Implementation of democratic social choice functions’, Review of Economic Studies 49, 439–446.
Gibbard, A.: 1973, ‘Manipulation of voting schemes: a general result’, Econometrica 41, 587–601.
Hurwicz, L. and Schmeidler, D.: 1978, ‘Construction of outcome functions guaranteeing existence and pareto optimality of Nash equilibria’, Econometrica 46, 1447–1474.
Ishikawa, S. and Nakamura, K.: 1979, ‘The strategy-proof social choice functions,’ Journal of Mathematical Economics 6, 283–295.
Maskin, E.: 1977, ‘Nash equilibrium and welfare optimality’, mimeo, Massachusetts Institute of Technology.
Maskin, E.: 1979, ‘Implementation and strong Nash equilibrium’, in J. J. Laffont (ed.), Aggregation and Revelation of Preferences, North-Holland, Amsterdam.
McKelvey, R. D.: 1985, ‘Game forms for Nash implementation of general social choice correspondences’, California Institute of Technology Social Science Working Paper 579.
Moulin, H. and Peleg, B.: 1980, ‘Stability and implementation of effectivity functions’, mimeo, Virginia Polytechnic Institute and Hebrew University of Jerusalem.
Pattanaik, P. K.: 1978, Strategy and Group Choice, North-Holland, Amsterdam.
Pattanaik, P. K. and Sengupta, M.: 1978a, ‘On consistent voting systems’, Discussion Paper, La Trobe University.
Peleg, B.: 1978a, ‘Consistent voting systems’, Econometrica 46, 153–161.
Peleg, B.: 1978b, ‘Representation of simple games by social choice functions’, International Journal of Game Theory 7, 81–94.
Plott, C. R.: 1973, ‘Path independence, rationality and social choice’, Econometrica 41, 1075–1091.
Roberts, K. W. S.: 1974, ‘Implementable social choice functions’, in J. J. Laffont (ed.), Aggregation and Revelation of Preference, North-Holland, Amsterdam.
Saari, D. G.: 1985, ‘The optimal ranking method is the Borda count’, Northwestern University Center for Mathematical Studies in Economics and Management Science Discussion Paper 638.
Satterthwaite, M. A.: 1975, ‘Strategy-proofness and Arrow conditions: existence and correspondence theorems for voting procedures and social welfare functions’, Journal of Economic Theory 10, 187–217.
Sen, A.: 1977, ‘Social choice theory: a re-examination’, Econometrica 45, 53–89.
Sengupta, M.: 1983, ‘Implementation of social choice rules: characterization and correspondence theorems under strong Nash-Equilibrium’, Journal of Mathematical Economics 11, 1–24.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Bandyopadhyay, T., Samuelson, L. Weakly implementable social choice rules. Theor Decis 33, 135–151 (1992). https://doi.org/10.1007/BF00134093
Issue Date:
DOI: https://doi.org/10.1007/BF00134093