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 or liberal rights. Dietrich and List

(2008) have generalised this result to the setting of binary judgement

aggregation. This paper proves that the liberal paradox holds even in

the framework of probabilistic opinion pooling and discusses options to

circumvent this impossibility result: restricting the aggregator domain

to profiles with no potential for conflicting rights, or considering agendas

whose issues are not all mutually interdependent.