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.
KeywordsSocial choice theory Judgment aggregation Translation Language dependence
Unable to display preview. Download preview PDF.
- Bovens, L., & Rabinowicz, W. (2004). Democratic answers to complex questions—an epistemic perspective. In M. Sintonen (Ed.), The socratic tradiction—questioning as philosophy and as method. Kluwer Academic Publishing.Google Scholar
- Brams, S., & Fishburn, P. (1983). Approval voting. Birkhauser.Google Scholar
- Dietrich, F., & List, C. (2007). Judgment aggregation by quota rules. Journal of Theoretical Politics, 19(4), (in press).Google Scholar
- Leininger W. (1992). The fatal vote: Berlin versus Bonn. Finanzarchiv 50: 1–20Google Scholar
- List C., Pettit P. (2002). Aggregating sets of judgments: An impossibility result. Economics and Philosophy 18: 89–110Google Scholar
- Oddie, G. (2007). Truthlikeness. Edward N. Zalta (Ed.), The Stanford Encyclopedia of Philosophy (Summer 2007 Edition), http://plato.stanford.edu/archives/sum2007/entries/truthlikeness/.
- Popper K. (1963). Conjectures and refutations. London, RoutledgeGoogle Scholar
- Zwart, S. (1998). Approaches to truth. Ph.D. thesis, ILLC Amsterdam.Google Scholar