  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.
