Social choice and information: the informational structure of uniqueness theorems in axiomatic social theories Marek M. Kaminski * Department of Political Science and Institute for Mathematical Behavioral Science, University of California, 3151 Social Science Plaza, Irvine, CA 92697-1869, USA Received 1 October 2001; received in revised form 1 October 2003; accepted 1 November 2003 Available online 26 February 2004 Abstract The paper introduces the category of algebraic axioms and investigates when a social rule of decision-making can be uniquely characterized with such axioms. The first result shows that every set of axioms that characterize a given rule is equivalent to a set of three algebraic axioms. The second result suggests a method for constructing an algebraic proof of uniqueness via finding an appropriate path of maps. It says that we can characterize a rule if and only if we can find a path. Both theorems are then used to prove and analyze various characterization results in May’s binary social choice, Nash bargaining theory, and Sen’s social choice theory. D 2004 Elsevier B.V. All rights reserved. Keywords: Social choice; Axiomatic method; Bargaining; Voting JEL classification: C71; C78; D71 1. Introduction Axiomatic theories created with social interpretations in mind have flourished since Nash (1950), Arrow (1951), May (1952), and Shapley (1953) made their pioneering contributions. Today, the axiomatic method is applied in bargaining theory, in game theory (cooperative and noncooperative), in social choice theory (Arrow’s, Sen’s, May’s, the 0165-4896/$ - see front matter D 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.mathsocsci.2003.11.004 *Tel.: +1-949-8242744; fax: +1-801-8805878. E-mail address: mkaminsk@uci.edu (M.M. Kaminski). www.elsevier.com/locate/econbase Mathematical Social Sciences 48 (2004) 121 – 138