Topological social choice
The author surveys the main results on topological social choice theory as initiated by Chichilnisky. In topological social choice, individual preferences are assumed to be smooth over some Euclidean space. The main result in the field is that under suitable conditions, a continuous, anonymous, and unanimous social choice rule exists if and only if the preference space is contractible. The author gives very clear descriptions of both the social choice theory and the topological background required to prove the theorem. The author also discusses more recent refinements of this central result and the work of Baryshnikov on `topologizing' the discrete Arrovian model. Towards the end of the paper, the author outlines some other recent results in topological social choice theory. The paper focuses on the applications of homotopy theory to social choice, but at the end, the author indicates some possible uses of other areas in topology. The paper serves as an admirable introduction to the field. It could be read profitably both by workers in social choice theory wanting to acquire some useful topology, and by topologists interested in applications of their field to an area few of them often visit. The 75 references provide a good entry to the field for those wishing to pursue their interests further.
scientific article; zbMATH DE number 1491045
scientific article