A difference preorder is a (possibly incomplete) preorder on a space of state changes (rather than the states themselves); it encodes information about preference intensity, in addition to ordinal preferences. We find necessary and sufficient conditions for a difference preorder to be...

In formal utilitarian voting, each voter assigns a numerical value to each alternative, and society chooses the alternative with the highest total value. Range voting is similar, except that each voter’s values are constrained to lie in the interval [0,1]. We characterize these rules via the...