Axiomatizing collective judgment sets in a minimal logical language
Axiomatizing collective judgment sets in a minimal logical language
复制标题
用最小的逻辑语言公理化集体判断集
作者：
M. Pauly
摘要我们调查在什么情况下，一组给定的集体判断可以从特定的投票程序中产生。为了回答这个问题，我们引入了一种类似于模态逻辑的语言来推理判断聚合过程。在这种语言中，公式
$$Square varphi$$表示$$varphi$$被集体接受，或表示$$varphi$$是基于投票的集体判断。不同的判断汇总程序可能是群体决策的基础。在这里，我们研究多数投票，如果大多数人接受$$varphi$$，则$$Square varphi$$成立；共识投票，如果所有个人接受$$varphi$$，则$$square varphi$$成立；以及独裁。我们给出了由这三个集结过程产生的判断集的完全公理。
AbstractWe investigate under what conditions a given set of collective judgments can arise from a specific voting procedure. In order to answer this question, we introduce a language similar to modal logic for reasoning about judgment aggregation procedures. In this language, the formula
$$square varphi$$ expresses that$$varphi$$ is collectively accepted, or that$$varphi$$ is a group judgment based on voting. Different judgment aggregation procedures may be underlying the group decision making. Here we investigate majority voting, where$$square varphi$$ holds if a majority of individuals accepts$$varphi$$, consensus voting, where$$square varphi$$ holds if all individuals accept$$varphi$$, and dictatorship. We provide complete axiomatizations for judgment sets arising from all three aggregation procedures.