Revisiting J. S. Mill’s methods: causal inference and social choice theory
从社会选择理论视角重新审视密尔的实验探究方法，发现批准投票和Leximax规则分别一致且中立地扩展了密尔的第一和第二准则，并揭示了因果推断与社会选择理论之间的深层联系。
Abstract In his work “A System of Logic”, John Stuart Mill presented four methods of experimental inquiry, structured into five canons, aimed at determining the circumstances that relate to the considered phenomenon by an invariable law. This study delves into Mill’s methods through the lens of social choice theory and discovers the synchronicity between these theories. Our primary finding is that Approval Voting and the Leximax rule are characterized by consistently (and neutrally) extending Mill’s first canon (the method of agreement) and his second canon (the method of difference). Furthermore, we explore the interplay among the five canons. Our findings demonstrate that the Leximax rule successfully adheres to the first four canons while maintaining consistency and neutrality. These results underscore the intricate connection between causal inference and social choice theory, establishing a foundational link for the application of preference aggregation theory to data aggregation in causal inference and vice versa.