1. How do we aggregate many individual preference orderings into a single group or social preference ordering; or,
  2. How can rational individuals make rational choices as a group

We can define a Social welfare function (SWF) combining individual preference orderings (over social states) into a social preference ordering (over those same states).

Initial Attempts

  1. Use majority rule to aggregate individual preferences into group preferences.
    • Problem: The voting paradox. Individual preferences may be transitive but the group preference can be cyclic when we do a majority vote. The violates a Klmogorov Axiom about ordering
  2. Use maximum total utility to determine group preference
    • Different scales (equivalent vNM scales) yield a different social preference ordering
  3. Just use ordinal rankings


  1. A group is decisive with respect to some pair of social states iff by the whole group whenever everyone in prefers
  2. A group is decisive if it is decisive over all pairs of social states

See: Arrow’s Impossibility Theorem