Symmetry, voting, and social choice (Q1110424)

This is a delightful introduction to social choice theory from an algebraic point of view. Among the principal results are a new proof of Arrow's theorem using the wreath product of groups, and a proof that Borda's rule is the least manipulable social choice function under symmetry conditions. Indeed, the paper makes a strong case for the claim that Borda's rule is algebraically best, in that it gives rise to a minimal number of voting paradoxes. Examples of highly paradoxical methods, including some used by the American Mathematical Society, are also included.