The Computational Challenge of Amartya Sen’s Social Choice Theory in Formal Philosophy

A significant chapter of the short history of formal philosophy is related with the notion and the theory of the so-called “Social Welfare Functions (SWFs)”, as a substantial component of the “social choice theory”. One of the main uses of SWFs is aimed, indeed, at representing coherent patterns (effectively, algebraic structures of relations) of individual and collective choices/preferences, with respect to a fixed ranking of alternative social/economical states. Indeed, the SWF theory is originally inspired by Samuelson’s pioneering work on the foundations of mathematical economic analysis. It uses explicitly Gibbs’ thermodynamics of ensembles “at equilibrium” based on statistical mechanics as the physical paradigm for the mathematical theory of economic systems. In both theories, indeed, the differences and the relationships among individuals are systematically considered as irrelevant. On the contrary, in the mathematical theory of “Social Choice Functions” (SCFs) developed by Amartya Sen, the interpersonal comparison and the real-time information exchanges among different social actors and their environments—different—ethical values and constraints, included—play an essential role. This means that the inspiring physical paradigm is no longer “gas” but “fluid thermodynamics” of interacting systems passing through different “phases” of fast “dissolution/aggregation of coherent behaviors”, and then staying persistently in far from equilibrium conditions. These processes are systematically studied by the quantum field theory (QFT) of “dissipative systems”, at the basis of the physics of condensed matter, modeled by the “algebra doubling” of coalgebras. This coalgebraic modeling is highly significant for making computationally effective Sen’s SCF theory, because both based on a dynamic and not statistical weighing of the variables for interacting systems, respectively in the physical and in the social realms.