吉伯德-萨特思韦特防策略不可能性定理的逻辑初探

Preliminary Study on Logic of Gibbard-Satterthwaite Strategy-Proof Impossibility Theorem

自20世纪70年代吉伯德-萨特思韦特防策略不可能性定理确立后,引起了数学、经济学、计算机科学和哲学等诸多领域中学者的广泛关注。然而,在国内外文献中,对吉伯德-萨特思韦特防策略不可能性定理的逻辑研究还比较少。基于此,借助公理化的方法探讨吉伯德-萨特思韦特防策略不可能性定理,并形式化地给出定理的内容和证明,力图把精细的逻辑推理应用于复杂的过程分析中,使防策略投票这一过程形式化、清晰化,以期能指导人们进行合理、有效的决策活动。

Since Gibbard-Satterthwaite strategy-proof impossibility theorem was established in the1970 s,it has drawn the widespread attention of scholars in fields of mathematics,economics,computer science and philosophy. However,it is seldom found the research on logics of the Gibbard-Satterthwaite theorem. This paper discussed Gibbard-Satterthwaite strategy-proof impossibility theorem with the axiomatic method,and elaborated the content and proving process of this theorem formally. It is trying to apply the fine logical reasoning to the complex processes analysis to make the strategy-proof voting process more formal and clear,hoping to guide people to make rational and effective decisionmaking activities.