Continuous linear representability of binary relations

Summary A very general result on continuous linear representability of binary relations on topological vector spaces is presented. Applications of this result include individual decision making under uncertainty, i.e. expected utility theory and collective decision making, in particular, utilitaristic social welfare functions.Thanks are due for helpful comments to Manfred Nermuth, David Schmeidler, Antonio Villar, and anonymous referees. Financial support from the DFG under Tr 120/4-2 is gratefully acknowledged.