Decision framing in judgment aggregation

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 its normative desirability. We show that in the canonical judgment aggregation model, no reasonable judgment aggregation functions are translation invariant. These results motivate a more general model of judgment aggregation, which gives up the requirement that judgment sets be complete.