Elizabeth Maggie Penn

A social choice theory of legitimacy

We develop a formal theory of legitimate collective choice. In our theory a policy choice is legitimate if the process through which the final choice was determined is consistent with some principle that can be used to (perhaps partially) rank the potential policy choices. The set of principles in any choice situation is taken to be exogenous, but a decision-making process is defined so as to deal with any nontrivial set of principles. Such a process is itself referred to as legitimate if it is guaranteed to select a legitimate outcome for each possible exogenous set of principles. We characterize the class of procedures that are legitimate, prove that legitimate policy decisions consistent with principles always exist and characterize the set of policy decisions that are legitimate for a any given set of principles. As we do not require the principles to be weak orders of the alternatives, our theory provides a notion of legitimacy that can be satisfied even when the guiding principles are potentially cyclic or incomplete. Accordingly, our theory illustrates one nontautological means by which majoritarian principles can be reconciled with legitimacy.

Measuring the Latent Quality of Precedent: Scoring Vertices in a Network

In this chapter, we consider the problem of estimating the latent influence of vertices of a network in which some edges are unobserved for known reasons. We present and employ a quantitative scoring method that incorporates differences in “potential influence” between vertices. As an example, we apply the method to rank Supreme Court majority opinions in terms of their “citability,” measured as the likelihood the opinion will be cited in future opinions. Our method incorporates the fact that future opinions cannot be cited in a present-day opinion. In addition, the method is consistent with the fact that a judicial opinion can cite multiple previous opinions.

Scoring from Contests

This article presents a new model for scoring alternatives from “contest” outcomes. The model is a generalization of the method of paired comparison to accommodate comparisons between arbitrarily sized sets of alternatives in which outcomes are any division of a fixed prize. Our approach is also applicable to contests between varying quantities of alternatives. We prove that under a reasonable condition on the comparability of alternatives, there exists a unique collection of scores that produces accurate estimates of the overall performance of each alternative and satisfies a well-known axiom regarding choice probabilities. We apply the method to several problems in which varying choice sets and continuous outcomes may create problems for standard scoring methods. These problems include measuring centrality in network data and the scoring of political candidates via a “feeling thermometer.” In the latter case, we also use the method to uncover and solve a potential difficulty with common methods of rescaling thermometer data to account for issues of interpersonal comparability.