Proving the Incompatibility of Efficiency and Strategyproofness via SMT Solving

TL;DR

This paper proves that no randomized preference aggregation mechanism can be both efficient and strategyproof by formulating the problem as an SMT satisfiability check, providing a computer-aided impossibility proof.

Contribution

It introduces a novel computer-aided proof method using SMT solving to establish an impossibility result in social choice theory.

Findings

Every efficient mechanism can be manipulated.

The proof is verified via SMT and higher-order logic.

First application of SMT in computational social choice.

Abstract

Two important requirements when aggregating the preferences of multiple agents are that the outcome should be economically efficient and the aggregation mechanism should not be manipulable. In this paper, we provide a computer-aided proof of a sweeping impossibility using these two conditions for randomized aggregation mechanisms. More precisely, we show that every efficient aggregation mechanism can be manipulated for all expected utility representations of the agents' preferences. This settles an open problem and strengthens a number of existing theorems, including statements that were shown within the special domain of assignment. Our proof is obtained by formulating the claim as a satisfiability problem over predicates from real-valued arithmetic, which is then checked using an SMT (satisfiability modulo theories) solver. In order to verify the correctness of the result, a minimal unsatisfiable set of constraints returned by the SMT solver was translated back into a proof in higher-order logic, which was automatically verified by an interactive theorem prover. To the best of our knowledge, this is the first application of SMT solvers in computational social choice.