Schr\"odinger's Ballot: Quantum Information and the Violation of Arrow's Impossibility Theorem

In this paper we study Arrow’s Impossibility Theorem in the quantum setting. Our work is based on the work of Bao and Halpern, in which it is proved that the quantum analogue of Arrow’s Impossibility Theorem is not valid. However, we feel unsatisfied about the proof presented there. Moreover, the definition of Quantum Independence of Irrelevant Alternatives (QIIA) seems not appropriate to us. In this paper, we give a better definition of QIIA, which properly captures the idea of the independence of irrelevant alternatives, and a detailed proof of the violation of Arrow’s Impossibility Theorem in the quantum setting with the modified definition.