Social Choice Problem
- How to aggregate many individual preference orderings into a single group or social preference ordering; or,
- How to have 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).
- 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
- Use maximum total utility to determine group preference
- Different scales (equivalent vNM scales) yield a different social preference ordering
- Just use ordinal rankings
- A group $D \in G$ is decisive with respect to some pair of social states $(a,b)$ iff $a \succ b$ by the whole group $G$ whenever everyone in $D$ prefers $a \succ b$
- A group is decisive if it is decisive over all pairs of social states