In the realm of algorithmic economics, voting systems are evaluated and compared by examining the properties or axioms they satisfy. While this pursuit has yielded valuable insights, it has also led to seminal impossibility results such as Arrow's and Gibbard-Satterthwaite's Impossibility Theorems, which pose challenges in designing ideal voting systems. Enter the domain of quantum computing: recent advancements have introduced the concept of quantum voting systems, which have many potential applications including in security and blockchain. Building on recent works that bypass Arrow's Impossibility Theorem using quantum voting systems, our research extends Quantum Condorcet Voting (QCV) to counter the Gibbard-Satterthwaite Impossibility Theorem in a quantum setting. To show this, we introduce a quantum-specific notion of truthfulness, extend ideas like incentive compatibility and the purpose of onto to the quantum domain, and introduce new tools to map social welfare functions to social choice functions in this domain.

翻译：在算法经济学领域，投票系统通过检验其满足的性质或公理来进行评估与比较。尽管这一研究路径已取得宝贵洞见，但也催生了如阿罗不可能定理和吉巴德-萨特斯韦特不可能定理等具有开创性的不可能性结论，这些定理对设计理想投票系统构成了根本性挑战。随着量子计算领域的介入，近期进展引入了量子投票系统的概念，其在安全及区块链等领域具有众多潜在应用。基于近期利用量子投票系统绕过阿罗不可能定理的研究，我们扩展了量子康多赛投票方法，以在量子框架下对抗吉巴德-萨特斯韦特不可能定理。为证明这一点，我们提出了量子特有的诚实性概念，将激励相容性和满射目的等思想拓展至量子领域，并引入了在该领域中将社会福利函数映射为社会选择函数的新工具。