Social choice and information: the informational structure of uniqueness theorems in axiomatic social theories

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.