  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.
