Two perspectives on consensus for (Bayesian) inference and decisions
T. Seidenfeld, M.J. Schervish · IEEE Transactions on Systems Man and Cybernetics · 1990
Questions of consensus among Bayesian investigators are discussed with regard to: (1) inference and (2) decisions. Concerning topic (1), results about asymptotic consensus and certainty with increasing evidence are reported. The findings deal with extending a conclusion of D. Blackwell and L. Dubins (1962) from pairs of agents to larger communities. Increasing evidence creates (almost sure) certainty of the truth and, depending upon the size of the community, it leads to varieties of consensus for conditional (posterior) distributions. Concerning topic (2), results are reported on the shared agreements of two Bayesian decision makers who have some differences in their probabilities for events and some differences in their utilities for outcomes. The results are couched in a setting where acts are so-called horse lotteries, with coherence defined by axiomatic restrictions on preferences over such acts. Subject to a weak Pareto condition, it is established that the only coherent preference schemes are the two agents' preferences themselves. Moreover, stronger Pareto conditions exclude even these extreme solutions.>