Duality, Logic and Judgment Aggregation

Alessandra Palmigiano (ILLC) gives a talk at the MCMP Colloquium (10 January, 2013) titled "Duality, Logic and Judgment Aggregation". Abstract: In the last decades, logic has facilitated the build-up of a critical mass of results and insights generalizing the original Arrovian problem in Social Choice, and culminating in the formation of judgment aggregation theory. Within this framework, the Arrovian-type impossibility results are obtained as consequences of characterization theorems, which provide necessary and su_cient conditions for agendas to have aggregator functions on them satisfying given axiomatic conditions. Methodologically, there are two tools, both derived from logic, underlying these generalizations: one is the ultra_lter argument, occurring both in a model-theoretic and in an algebraic setting; the other tool, providing a unifying framework for the agenda-based characterization theorems, is the notion of property space. Duality theory can provide insights into, and connections between, these two tools. In the present talk, Stone-type duality theory will be illustrated, as well as its main logical signi_cance: namely, providing a systematic, triangular connection between logical languages, their model-theoretic semantics and their algebraic semantics. Then, applications of duality theory will be discussed to the ultrafilter argument and property spaces.