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

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 clarifies the structure and multi-dimensionality of ranking data, introduces causal estimands tailored to ranked outcomes, and develops methods for estimation and inference. Furthermore, it extends the framework to partially ranked data by building on principal stratification. 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 responses to officer-involved shootings are robust to the contextual information about police brutality and reform. I also apply the methods to an experimental design for quantifying ballot order effects in ranked-choice voting.