David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
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Synthese 163 (2):227 - 243 (2008)
Axiomatic characterization results in social choice theory are usually compared either regarding the normative plausibility or regarding the logical strength of the axioms involved. Here, instead, we propose to compare axiomatizations according to the language used for expressing the axioms. In order to carry out such a comparison, we suggest a formalist approach to axiomatization results which uses a restricted formal logical language to express axioms. Axiomatic characterization results in social choice theory then turn into definability results of formal logic. The advantages of this approach include the possibility of non-axiomatizability results, a distinction between absolute and relative axiomatizations, and the possibility to ask how rich a language needs to be to express certain axioms. We argue for formal minimalism, i.e., for favoring axiomatizations in the weakest language possible.
|Keywords||Social choice theory Logic Judgment aggregation|
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References found in this work BETA
Herbert B. Enderton (1972). A Mathematical Introduction to Logic. New York,Academic Press.
Jaakko Hintikka (1996). The Principles of Mathematics Revisited. Cambridge University Press.
Christian List & Philip Pettit (2002). Aggregating Sets of Judgments: An Impossibility Result. Economics and Philosophy 18 (1):89-110.
Marc Pauly (2007). Axiomatizing Collective Judgment Sets in a Minimal Logical Language. Synthese 158 (2):233 - 250.
Citations of this work BETA
Philippe Mongin (2012). The Doctrinal Paradox, the Discursive Dilemma, and Logical Aggregation Theory. Theory and Decision 73 (3):315-355.
Umberto Grandi & Ulle Endriss (2013). First-Order Logic Formalisation of Impossibility Theorems in Preference Aggregation. Journal of Philosophical Logic 42 (4):595-618.
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