Conundrums for nonconsequentialists

There are a number of single-profile impossibility theorems in social choice theory and welfare economics that demonstrate the incompatibility of unanimity/dominance criteria with various nonconsequentialist principles given some rationality restrictions on the rankings being considered. This article is concerned with examining what they have in common and how they differ. Groups of results are identified that have similar formal structures and are established using similar proof strategies. This article is based on the first part of my Presidential Address to the Society for Social Choice and Welfare that I delivered on June 19, 2008 at Concordia University in Montreal. An expanded version of the second part has appeared as Weymark (2014). I am grateful for the comments received from Franz Dietrich, Marc Fleurbaey, Paolo Piacquadio, and an anonymous referee. I have also benefited from the discussion of my article in Montreal and at the Munich Center for Mathematical Philosophy Conference on Social Choice and Its Philosophical Applications held at Venice International University.