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Methodologists and substantive scholars alike agree that one of process tracing’s foremost contributions to qualitative research is its capacity to adjudicate among competing explanations of a phenomenon. Existing approaches, however, only provide explicit guidance on dealing with mutually exclusive explanations, which are exceedingly rare in social science research. I develop a tripartite solution to this problem. The Relationships among Rivals (RAR) framework (1) introduces a typology of relationships between alternative hypotheses, (2) develops specific guidelines for identifying which relationship is present between two hypotheses, and (3) maps out the varied implications for evidence collection and inference. I then integrate the RAR framework into each of the main process-tracing approaches and demonstrate how it affects the inferential process. Finally, I illustrate the purchase of the RAR framework by reanalyzing a seminal example of process-tracing research: Schultz’s (2001) analysis of the Fashoda Crisis. I show that the same evidence can yield new and sometimes contradictory inferences once scholars approach comparative hypothesis testing with this more nuanced framework.

Given the increasing quantity and impressive placement of work on Bayesian process tracing, this approach has quickly become a frontier of qualitative research methods. Moreover, it has dominated the process-tracing modules at the Institute for Qualitative and Multi-Method Research (IQMR) and the American Political Science Association (APSA) meetings for over five years, rendering its impact even greater. Proponents of qualitative Bayesianism make a series of strong claims about its contributions and scope of inferential validity. Four claims stand out: (1) it enables causal inference from iterative research, (2) the sequence in which we evaluate evidence is irrelevant to inference, (3) it enables scholars to fully engage rival explanations, and (4) it prevents ad hoc hypothesizing and confirmation bias. Notwithstanding the stakes of these claims and breadth of traction this method has received, no one has systematically evaluated the promises, trade-offs, and limitations that accompany Bayesian process tracing. This article evaluates the extent to which the method lives up to the mission. Despite offering a useful framework for conducting iterative research, the current state of the method introduces more bias than it corrects for on numerous dimensions. The article concludes with an examination of the opportunity costs of learning Bayesian process tracing and a set of recommendations about how to push the field forward.

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In addition to providing crucial insights, the rebel-to-party literature exhibits an unacknowledged conceptual tension: despite remarkable agreement on what ‘rebel-to-party transition’ should capture, there are nearly as many definitions and measures as there are studies of it. I demonstrate that conceptual imprecision has an analytic ripple effect—compromising the validity of the concept, the quality of the measure, the validity of inclusion criteria, and the results of analyses. Across four existing rebel-to-party variables, scholars only agree with regard to eight transitions (out of 161) and five failures (out of hundreds). To address these limitations, I propose a novel conceptualization and measure of rebel-to-party transition—distinguishing between failures, nominal participants (the conventional benchmark for transition), and seated participants. I demonstrate that some definitions of ‘failure’ induce selection effects into samples, and that minimalist indicators of ‘transition’ introduce problematic heterogeneity into ‘successes’. My analyses reveal that nominal participants are statistically indistinguishable from failures on key traits predicting transition and, moreover, seated participants consistently drive results. As such, the new conceptual framework advances the literature on conceptual and empirical grounds.