11 June 2018, Computational Social Choice Seminar, Michael Morreau
A jury theorem is presented for range voting, where individuals contribute judgements in the form of scores or grades. Unlike the Condorcet jury theorem for majority voting, this one does not require that individuals are competent to choose among the options before them. Instead there is a requirement concerning the distribution of errors among all the voters. According to the grading jury theorem, a sufficiently large group of voters that satisfies this holistic condition can be almost certain to judge correctly -- even if its individual members are vanishingly unlikely to do so by themselves. Nor does the group need to be large: 6000 (a quorum in the ancient Athenian assembly) can do nicely, and the more voters there are the better. All this casts an optimistic light on the possibilities for epistemically sound democratic decisions in an age of polarization, media bubbles and alternate facts.