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

Sun, Xin; He, Feifei; Sopek, Mirek; Guo, Meiyun

doi:10.3390/e23081083

Open AccessArticle

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

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

^*

Author to whom correspondence should be addressed.

Entropy 2021, 23(8), 1083; https://doi.org/10.3390/e23081083

Submission received: 1 July 2021 / Revised: 1 August 2021 / Accepted: 13 August 2021 / Published: 20 August 2021

(This article belongs to the Special Issue Quantum Communication)

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

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MDPI and ACS Style

Sun, X.; He, F.; Sopek, M.; Guo, M. Schrödinger’s Ballot: Quantum Information and the Violation of Arrow’s Impossibility Theorem. Entropy 2021, 23, 1083. https://doi.org/10.3390/e23081083

AMA Style

Sun X, He F, Sopek M, Guo M. Schrödinger’s Ballot: Quantum Information and the Violation of Arrow’s Impossibility Theorem. Entropy. 2021; 23(8):1083. https://doi.org/10.3390/e23081083

Chicago/Turabian Style

Sun, Xin, Feifei He, Mirek Sopek, and Meiyun Guo. 2021. "Schrödinger’s Ballot: Quantum Information and the Violation of Arrow’s Impossibility Theorem" Entropy 23, no. 8: 1083. https://doi.org/10.3390/e23081083

APA Style

Sun, X., He, F., Sopek, M., & Guo, M. (2021). Schrödinger’s Ballot: Quantum Information and the Violation of Arrow’s Impossibility Theorem. Entropy, 23(8), 1083. https://doi.org/10.3390/e23081083

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

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