Abstract
In the problem of judgment aggregation, a panel of judges has to evaluate each proposition in a given agenda as true or false, based on their individual evaluations and subject to the constraint of logical consistency. We elaborate on the relation between this and the problem of aggregating abstract binary evaluations. For the special case of truth-functional agendas we have the following main contributions: (1) a syntactical characterization of agendas for which the analogs of Arrow’s aggregation conditions force dictatorship; (2) a complete classification of all aggregators that satisfy those conditions; (3) an analysis of the effect of weakening the Pareto condition to surjectivity.
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This is a sequel to the paper “Aggregation of binary evaluations.” The contents of both papers were presented, under the title “An Arrovian impossibility theorem for social truth functions,” at the Second World Congress of the Game Theory Society, Marseille, July 2004. The first version of “Aggregation of binary evaluations” was completed in June 2005. That working paper was subsequently split into two parts, of which this is the second. The comments of an anonymous referee are gratefully acknowledged. Part of R. Holzman’s work was done while he was a Fellow of the Institute for Advanced Studies at the Hebrew University of Jerusalem.
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Dokow, E., Holzman, R. Aggregation of binary evaluations for truth-functional agendas. Soc Choice Welf 32, 221–241 (2009). https://doi.org/10.1007/s00355-008-0320-1
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DOI: https://doi.org/10.1007/s00355-008-0320-1