Journal of mathematical economics vol:24 issue:3 pages:217-237
Model theory and first-order logic are used to study aggregation of preferences. Ultraproducts and Arrow-type aggregators are shown to coincide. Los's theorem results in a rule to detect whether or not a property is preserved under aggregation. This rule explains why, unless the corresponding social welfare function is dictatorial, continuity is lost under aggregation. The abundance of free ultrafilters implies an arbitrariness in selecting decisive coalitions. A theorem of Ax indicates that this arbitrariness is characteristic for Arrow-type aggregators.