Causal Inference with Ranking Data: Application to Blame Attribution in Police Violence and Ballot Order Effects in Ranked-Choice Voting

Abstract

While rankings are at the heart of social science research, little is known about how to analyze ranking data in experimental studies. This paper introduces a potential-outcomes framework to perform causal inference when outcome data are ranking data. It introduces a class of causal estimands tailored to ranked outcomes and develops methods for estimation and inference. Furthermore, it extends the framework to partially ranked data. I show that partial rankings can be considered a selection problem and propose nonparametric sharp bounds for the treatment effects. Using the methods, I reanalyze the recent study on blame attribution in the Stephon Clark shooting, finding that people's attitudes toward officer-involved shootings are robust to contextual information. I also apply the framework to study ballot order effects in three ranked-choice voting (RCV) elections in 2022, proposing a new theory of pattern rankings in RCV. Finally, I present three applications in international relations.