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Decision framing in judgment aggregation
Authors:Fabrizio Cariani  Marc Pauly  Josh Snyder
Institution:(1) Department of Philosophy, University of California, Berkeley, 314 Moses Hall, Berkeley, CA 94270-2390, USA;(2) Stanford University, Stanford, CA, USA
Abstract:Judgment aggregation problems are language dependent in that they may be framed in different yet equivalent ways. We formalize this dependence via the notion of translation invariance, adopted from the philosophy of science, and we argue for the normative desirability of translation invariance. We characterize the class of translation invariant aggregation functions in the canonical judgment aggregation model, which requires collective judgments to be complete. Since there are reasonable translation invariant aggregation functions, our result can be viewed as a possibility theorem. At the same time, we show that translation invariance does have certain normatively undesirable consequences (e.g. failure of anonymity). We present a way of circumventing them by moving to a more general model of judgment aggregation, one that allows for incomplete collective judgments.
Keywords:Social choice theory  Judgment aggregation  Translation  Language dependence
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