Respect for experts vs. respect for unanimity: The liberal paradox in probabilistic opinion pooling

- A formal framework for discussing expert rights in the context of probabilistic opinions is developed.
- An analogue of Amartya Sen's paradox of a Paretian liberal is formulated and proved.
- Escape strategies for avoiding the paradox are discussed.

Amartya Sen (1970) has shown that three natural desiderata for social choice rules are inconsistent: universal domain, respect for unanimity, and respect for some minimal rights-which can be interpreted as either “expert rights” (an expert's right to have her competence respected) or liberal rights. Dietrich and List (2008) have generalised this result to the setting of binary judgement aggregation. This paper proves that the paradox of a Paretian liberal holds even in the framework of probabilistic opinion pooling and discusses options to circumvent this impossibility result: (i) restricting the aggregator domain to profiles with no potential for conflicting rights; (ii) avoiding agendas where all issues are pairwise entangled (interdependent).