Social Choice Rules

In this chapter we are going to start fresh. Now that we have reasons to look beyond simple majority voting, we want to explore a range of possible social choice procedures. We must reintroduce a lot of earlier ideas in a broader context of general social choice rules. We are going to be very precise and very formal. Partly we are doing this because some of the ideas are both subtle and slippery and can not be well conveyed just by examples and hand waving but require precise definition. But more important is preparation for Chapters like 7, 8 and 10 where we are going to prove impossibility theorems. Impossibility theorems tell us there are no social choice rules satisfying a certain list of appealing criteria. Now it is usually easy to show that a given social choice rule satisfies a list of clear criteria or fails to satisfy it. But to prove no rule satisfies such a list, you must work with all logically possible social choice rules and you can’t even make a beginning on that unless you have a clear, precise, rigorous notion of what a social choice rule is. Our theorem goal forces us to be rather formal.