论文标题
关于本地可合理的社会选择功能
On Locally Rationalizable Social Choice Functions
论文作者
论文摘要
我们考虑了一个合理性的概念，其中合理关系可能取决于可行的替代方案。更确切地说，我们说，如果选择函数通过合理关系的家庭合理化，可以在局部合理地将其合理化，以便在删除其他替代方案时保留两个可行集合中的两个替代方案之间的严格偏好。泰森（Tyson，2008年）表明，只有在满足Sen的$γ$时，选择功能在本地可以合理化。我们通过提出$γ$的自然加强来扩展局部合理性的理论，该理论可以通过PIP转移关系来精确地表征局部合理性的特征，并通过引入选择功能的$γ$ hull作为其最好的切块，可满足$γ$。本地合理性允许对满足$γ$的社会选择功能的统一视角，包括经典的循环，例如顶级周期和未发现的集合，以及新的新闻，例如两阶段的多数批量级选择和拆分周期。我们使用局部合理性给出了其中一些的简单公理表征，并提出了系统的程序来定义满足$γ$的社会选择功能。
We consider a notion of rationalizability, where the rationalizing relation may depend on the set of feasible alternatives. More precisely, we say that a choice function is locally rationalizable if it is rationalized by a family of rationalizing relations such that a strict preference between two alternatives in some feasible set is preserved when removing other alternatives. Tyson (2008) has shown that a choice function is locally rationalizable if and only if it satisfies Sen's $γ$. We expand the theory of local rationalizability by proposing a natural strengthening of $γ$ that precisely characterizes local rationalizability via PIP-transitive relations and by introducing the $γ$-hull of a choice function as its finest coarsening that satisfies $γ$. Local rationalizability permits a unified perspective on social choice functions that satisfy $γ$, including classic ones such as the top cycle and the uncovered set as well as new ones such as two-stage majoritarian choice and split cycle. We give simple axiomatic characterizations of some of these using local rationalizability and propose systematic procedures to define social choice functions that satisfy $γ$.
