If the purpose of a utility function is to provide evidence about the behavior of the group, we can preprocess the data structure into that form:
Suppose Alice may update the distribution over group decisions by ε. Then the direction she pushes in is her utility function, and the constraints “add up to 100%” and “size ε” cancel out the “affine transformation” degrees of freedom. Now such directions can be added up.
If the purpose of a utility function is to provide evidence about the behavior of the group, we can preprocess the data structure into that form: Suppose Alice may update the distribution over group decisions by ε. Then the direction she pushes in is her utility function, and the constraints “add up to 100%” and “size ε” cancel out the “affine transformation” degrees of freedom. Now such directions can be added up.