VJE Seminar: Frederik Herzberg (U Bielefeld)
Expertise vs. unanimity, anonymity vs. linearity: News from probabilistic opinion pooling
Abstract: The problem of aggregating (i.e. "merging" or "pooling") probabilistic opinions has been studied for several decades (e.g. McConway 1981, Lehrer & Wagner 1981). A new direction in this research program is the connection with the recent literature on (binary logical) judgement aggregation theory (survey: List & Puppe 2009). In this paper, we shall first generalise the classical results on linear probabilistic opinion pools to the case of infinite (both countably and uncountably) electorates. We will see that the existence of aggregation rules satisfying certain desiderata is independent from the axioms of standard mathematics (Zermelo-Fraenkel set theory with Choice). In the second part of the talk, we will provide a probabilistic version of the famous paradox of a Paretian liberal (Sen 1970): If one seeks an aggregation rule with universal domain for entangled decision problems, one has to choose between following expertise and respecting unanimity.