The birth of social choice theory from the spirit of mathematical logic: Arrows theorem as a model-theoretic preservation result

Arrow’s axiomatic foundation of social choice theory can be understood as an application of Tarski’s methodology of the deductive sciences which is closely related to the latter’s foundational contribution to model theory. Thus, Arrow’s celebrated impossibility theorem can be read as a model-theoretic preservation result "avant la lettre": The preservation of the …rst-order properties of weak orders under product formation is only possible in the case of ultraproducts, i.e. if the product is reduced over an ultra…lter on the index set of individuals. This perspective does not only shed new light on a well known source of dictatorship results in the …nite case, but allows to conceive of the problem of aggregation in general as a model-theoretic preservation problem.