From Social Choice to System Choice: A Problem for Lewis’s Best System Analysis

Abstract

One of the most important results in social choice theory is Kenneth Arrow’s impossibility theorem (1951/1963), according to which there cannot exist any rational procedure of aggregating individual preferences into a social preference. In this dissertation, I argue that the analogue of Arrow’s theorem threatens David Lewis’s Best System Account (BSA) of laws of nature, as the BSA invokes the procedure of aggregating different system-choice criteria into a resultant choice of the best system. First, I examine the formal conditions of Arrow’s impossibility theorem and its theory-choice variant. In the domain of theory choice, statistical model selection methods make different theory-choice standards commensurable. This inter-standard comparability may open up an escape route from the Arrovian impossibility for theory choice. Conducting a rigorous examination of those statistical methods, in particular, Akaike Information Criterion (AIC) and Bayesian Information Criterion (BIC), I show that these methods assume the existence of true status of nature, and that their inter-standard comparability serves as an epistemic constraint. I then argue that there is a formal analogy between social choice and system choice for the BSA and the Arrovian impossibility threatens the BSA. After rejecting various possible attempts to escape from the Arrovian impossibility for the BSA, I propose the variants of the BSA implemented with AIC and BIC as an attempt to make a case for inter-criterial comparability in system choice. I argue that, however, the proposed variants will inevitably fail to pick the best system. The failure is explained by the results in my investigation of the statistical methods. Finally, I suggest different ways in which the BSA might be able to escape from the Arrovian impossibility: a non-harmful dictatorship, a threshold-prior criterion, and the statistical method called Minimum Description Length Principle. I close the dissertation by suggesting that the BSA might have to give up the notion of ‘balancing’ in its analysis of laws of nature in order to avoid the Arrovian result in a way that is consistent with the Humean perspective on laws of nature.