Proving Classical Theorems of Social Choice Theory in Modal Logic

A number of seminal results in the field of social choice theory demonstrate the difficulties of aggregating the preferences of several individual agents for the purpose of making a decision together. We show how to formalise three of the most important impossibility results of this kind—Arrow’s Theorem, Sen’s Theorem, and the Muller–Satterthwaite Theorem—by using a modal logic of social choice functions. We also provide syntactic proofs of these theorems in the same logic. While prior work has been successful in applying tools from logic and automated reasoning to social choice theory, this is the first human-readable formalisation of the Arrovian framework allowing for a direct derivation of the main impossibility theorems of social choice theory. This is useful for gaining a deeper understanding of the foundations of collective decision making, both in human society and in groups of autonomous software agents.