Arrow's Impossibility Theorem

Result in economics. Solving economics is just a matter of allocating resources to people in the most efficient possible way, right? What happens if you try to do that?

This result proves that at least one reasonable-seeming way to model that situation is a dead-end.

Properties of the model:

• Universality - allocation function is complete of the space of resources and people' preferences

• Pareto-optimality - all possible Pareto improvements are made: that is, allocations A where there exists no allocations A' that are preferred by at least one person and equivelently good per everybody else.

• Independence of Irrelevant Alternatives or i.i.d) - people's preferences are consistent across the subset relation - if R = P_Alice({A,B}) = A >= B, then for all \phi, R' = P_Alice({A,B} \bigcup \phi) must be such that A R_2 B is A >= B.

• (No) Dictatorship - No single person in the allocation function is empowered to "choose among allocations" - that is, there should be no person whose preferences completely determine the entire allocation function.

There exist no allocation functions with all four of these properties.

todo write out the proof of Arrow's impossibility theorem.

Proof in Sen