Conditional legitimacy: How turnout, majority size, and outcome affect perceptions of legitimacy in European Union membership referendums

Survey experiments are a core tool for causal inference. Yet, the design of classical survey experiments prevents them from identifying which components of a multidimensional treatment are influential. Here, we show howconjoint analysis, an experimental design yet to be widely applied in political science, enables researchers to estimate the causal effects of multiple treatment components and assess several causal hypotheses simultaneously. In conjoint analysis, respondents score a set of alternatives, where each has randomly varied attributes. Here, we undertake a formal identification analysis to integrate conjoint analysis with the potential outcomes framework for causal inference. We propose a new causal estimand and show that it can be nonparametrically identified and easily estimated from conjoint data using a fully randomized design. The analysis enables us to propose diagnostic checks for the identification assumptions. We then demonstrate the value of these techniques through empirical applications to voter decision making and attitudes toward immigrants.

The authors suggest that procedural and distributive factors interactively combine to influence individuals' reactions to their encounters with other people, groups, and organizations. Results from 45 independent samples (reviewed herein) show that (a) level of procedural justice is more positively related to individuals' reactions when outcome fairness or valence is relatively low and (b) level of outcome fairness or valence is more positively related to individuals' reactions when procedural justice is relatively low. They present various explanations of the interaction effect. Theoretical progress may be achieved through future efforts to delineate the conditions under which each of the explanations is more versus less likely to account for the interaction.