Schrödinger's Ballot: Quantum Information and the Violation of Arrow's Impossibility Theorem

Xin Sun; Feifei He; Mirek Sopek; Meiyun Guo

doi:10.3390/e23081083

Schrödinger's Ballot: Quantum Information and the Violation of Arrow's Impossibility Theorem

Entropy (Basel). 2021 Aug 20;23(8):1083. doi: 10.3390/e23081083.

Authors

Xin Sun¹, Feifei He², Mirek Sopek³, Meiyun Guo⁴

Affiliations

¹ Department of Foundation of Computer Science, Catholic University of Lublin, 20-950 Lublin, Poland.
² Institute of Logic and Cognition, Sun Yat-sen University, Guangzhou 510275, China.
³ MakoLab SA, 91-062 Lodz, Poland.
⁴ Institute of Logic and Intelligence, Southwest University, Choingqing 400715, China.

Abstract

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 in Bao and Halpern's work. Moreover, the definition of Quantum Independence of Irrelevant Alternatives (QIIA) in Bao and Halpern's work seems not appropriate to us. 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.

Keywords: Arrow’s Impossibility Theorem; quantum information; social choice; vote.