In this paper, we develop a set-theoretic and possible worlds approach to counterfactual analysis in case-study explanation. Using this approach, we first consider four kinds of counterfactuals: necessary condition counterfactuals, SUIN condition counterfactuals, sufficient condition counterfactuals, and INUS condition counterfactuals. We explore the distinctive causal claims entailed in each, and conclude that necessary condition and SUIN condition counterfactuals are the most useful types for hypothesis assessment in case-study research. We then turn attention to the development of a rigorous understanding of the 'minimal-rewrite' rule, linking this rule to insights from set theory about the relative importance of necessary conditions. We show why, logically speaking, a comparative analysis of two necessary condition counterfactuals will tend to favour small events and contingent happenings. A third section then presents new tools for specifying the level of generality of the events in a counterfactual. We show why and how the goals of formulating empirically important versus empirically plausible counterfactuals stand in tension with one another. Finally, we use our framework to link counterfactual analysis to causal sequences, which in turn provides advantages for conducting counterfactual projections.

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This article develops a set-theoretic approach to Bayes’s theorem and Bayesian process tracing. In the approach, hypothesis testing is the procedure whereby one updates beliefs by narrowing the range of states of the world that are regarded as possible, thus diminishing the domain in which the actual world can reside. By explicitly connecting Bayesian analysis to its set-theoretic foundations, the approach makes process tracing more intuitive and thus easier to apply for qualitative researchers. Moreover, the set-theoretic approach provides new tools for assessing both the consequentialness and expectedness of evidence when conducting process tracing. It also provides a new way to classify and interpret process-tracing tests, such as hoop tests and smoking gun tests, by viewing them as zones in a continuous space whose dimensions reflect the magnitude of changes in sets. The article shows that Bayesian process tracing and set-theoretic process tracing are not alternatives to each other but rather two sides of the same coin.

RESUMENEste artículo es una revisión del devenir político peruano durante el 2013. El Perú es una democracia sin partidos sostenida en un Estado débil, lo que si bien limita la capacidad de los políticos para establecer vínculos estables con la ciudadanía, no ha afectado seriamente la estabilidad del régimen político. Por un lado, una élite política desprestigiada, precaria y fragmentada coexiste con una influyente tecnocracia económica, fortalecida por los buenos resultados económicos del país en los últimos años. Por otro, esta brecha entre Estado y sociedad hace que la sorprendente (y precaria) estabilidad peruana coexista con signos de descontento entre sectores urbanos que rechazan el sistema político y se ven asediados por la inseguridad ciudadana, mientras que en zonas rurales se registren fragmentados episodios de movilización que dan cuenta de la contracara del crecimiento económico, sostenido en la extracción y exportación de materias primas.Palabras clave: Perú, democracia, conflictos sociales, elecciones, partidos políticos. ABSTRACT This paper is a review of the main political events of 2013 in Peruvian politics. Peru is a democracy without parties sustained in a weak