A result of John Harsanyi concerns the aggregation of individuals' pre
ferences into social preferences. The result states that if the indivi
duals in a society and the society as a whole have preference relation
s that compare probability distributions on a set of outcomes, and the
preference relations satisfy expected-utility conditions and Pareto c
onditions, then a utility function for the social preference relation
is a positive affine function of utility functions for the individuals
' preference relations. This paper presents an analogous result for pr
eference relations that denote intensity of preference, i.e., preferen
ce relations that compare exchanges of outcomes. This approach avoids
the difficulties of requiring that the individuals in the society have
common beliefs regarding uncertainty.