A typical problem for groups is making a unified, collective decision when its members disagree. In response, a fair process (including, but not limited to, voting) is often used to resolve the impasse. Such a process aggregates several individual judgments by combining them into one single judgment representing the group as a whole. Unfortunately, work in the field of social choice theory formally proves that there exists no aggregation process that satisfies some relatively minimal conditions of fairness and rationality.

In this talk, I informally explain and discuss the implications of three of these “impossibility” theorems: Arrow’s Theorem, the Gibbard-Satterthwaite Theorem, and Doctrinal Paradox Theorem. (I’ll also give recommended reading for those who want to see the formal proofs for themselves.) Together, these results suggest group decision-making will inevitably have to sacrifice some element of fairness and/or rationality. However, I conclude by suggesting that may not be an altogether bad thing.