In an article from 1973, Rittel and Webber distinguished between ‘tame’ or ‘benign’ problems on the one hand and ‘wicked’ problems on the other. The authors argued that wicked problems occur in nearly all public policy issues. Since different groups adhere to different value‐sets, solutions can only be expressed as better or worse. By no means can they be viewed as definitive or objective. In this paper we consider, from this very angle, the theory of social choice which is about the aggregation of individual preferences with the aim to derive a consistent social preference. We show that collective choice offers wicked problems of various types which differ in their degree of severity. We hereby concentrate on welfare functions and voting schemes of different kinds and discuss these in the light of various criteria such as Arrow's independence condition, Condorcet consistency, monotonicity, manipulability, and other properties.