Contributions of social choice theory for the analysis of democracy

The objective of this paper is to present the main results of the social choice theory and to briefly comment on them. The most famous result of this theory is still Condorcet's paradox. It shows that, even if the individual preferences on a set of alternatives are transitive, the social preference obtained through the majority rule may not lead to a transitive outcome. Each alternative can be beaten by another one in pairwise comparisons and there is no clear collective winner. In 1951, Arrow showed that the majority rule is not the unique voting mechanism which suffers from important drawbacks: All the voting rules fail to satisfy simultaneously a set of four a priori benign requirements. Following Arrow's tradition, other important impossibility results are due to Sen (1970), Gibbard (1973) and Satterthwaite (1975). However, solutions also exist: Some voting rules have been characterized axiomatically and the impossibility theorems are no longer valid if we use some domain restriction.