Abstract
We introduce a logic specifically designed to support reasoning about social choice functions. The logic includes operators to capture strategic ability, and operators to capture agent preferences. We establish a correspondence between formulae in the logic and properties of social choice functions, and show that the logic is expressively complete with respect to social choice functions, i.e., that every social choice function can be characterised as a formula of the logic. We prove that the logic is decidable, and give a complete axiomatization. To demonstrate the value of the logic, we show in particular how it can be applied to the problem of determining whether a social choice function is strategy-proof.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Areces, C., & ten Cate, B. (2006). Hybrid logics. In P. Blackburn, J. van Benthem, & F. Wolter (Eds.), Handbook of modal logic (Chapter 14, pp. 821–868). Elsevier Science Inc.
Arrow, K. (1950). A difficulty in the concept of social welfare. Journal of Political Economy, 58(4), 328–346.
Arrow, K. J., Sen, A. K., & Suzumura, K. (eds.) (2002). Handbook of Social Choice and Welfare (Vol. 1). Elsevier.
Bonzon, E., Lagasquie-Schiex, M.-C., & Lang, J. (2007). Efficient coalitions in Boolean games. In K. Apt & R. van Rooij (Eds.), New perspectives on games and interaction. Texts in Logic and Games (Vol. 4 , pp. 283–297). Amsterdam University Press.
Chellas, B. F. (1980). Modal logic: An introduction. Cambridge University Press.
Dasgupta, P., Hammond, P., & Maskin, E. (1979). The implementation of social choice rules: Some general results on incentive compatibiliy. Review of Economic Studies, 46, 185–216.
Gibbard, A. (1973). Manipulation of voting schemes: A general result. Econometrica, 41(4), 587–601.
May, K. (1952). A set of independent, necessary and sufficient conditions for simple majority decision. Econometrica, 20(4), 680–684.
Moulin, H. (1983) The strategy of social choice. Advanced Textbooks in Economics, North Holland.
Osborne, M. J., & Rubinstein, A. (1994). A course in game theory. The MIT Press.
Pauly, M. (2001). Logic for social software. Ph.D. thesis, University of Amsterdam. ILLC Dissertation Series 2001-10.
Satterthwaite, M. A. (1975). Strategy-proofness and arrow’s conditions: Existence and correspondence theorems for voting procedures and social welfare functions. Journal of Economic Theory, 10, 187–217.
Troquard, N., van der Hoek, W., & Wooldridge, M. (2009). A logic of games and propositional control. In K. Decker, J. Sichman, C. Sierra & C. Castelfranchi (Eds.), 8th international joint conference on autonomous agents and multi agent systems (AAMAS-09) (pp. 961–968). Budapest, Hungary.
Troquard, N., van der Hoek, W., & Wooldridge, M. (2009). A logic of propositional control for truthful implementations. In TARK ’09: Proceedings of the 12th conference on theoretical aspects of rationality and knowledge (pp. 237–246).
van der Hoek, W. & Wooldridge, M. (2005). On the logic of cooperation and propositional control. Artificial Intelligence, 164(1–2), 81–119.
Wooldridge, M., Ågotnes, T., Dunne, P. E., & van der Hoek, W. (2007). Logic for automated mechanism design—A progress report. In Proceedings of the twenty-second AAAI conference on artificial intelligence (AAAI-2007). Vancouver, British Columbia, Canada.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Troquard, N., van der Hoek, W. & Wooldridge, M. Reasoning About Social Choice Functions. J Philos Logic 40, 473–498 (2011). https://doi.org/10.1007/s10992-011-9189-z
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10992-011-9189-z