  We propose a quantum voting system, in the spirit of quantum games such as
the quantum Prisoner's Dilemma. Our scheme enables a constitution to violate a
quantum analog of Arrow's Impossibility Theorem. Arrow's Theorem is a claim
proved deductively in economics: Every (classical) constitution endowed with
three innocuous-seeming properties is a dictatorship. We construct quantum
analogs of constitutions, of the properties, and of Arrow's Theorem. A quantum
version of majority rule, we show, violates this Quantum Arrow Conjecture. Our
voting system allows for tactical-voting strategies reliant on entanglement,
interference, and superpositions. This contribution to quantum game theory
helps elucidate how quantum phenomena can be harnessed for strategic advantage.
