When forming beliefs about themselves, politics, and how the world works more generally, people often face a tension between conclusions they inherently wish to reach and those which are plausible. And the likelihood of beliefs about one variable (e.g., the performance of a favored politician) depends on beliefs about other, related variables (e.g., the quality and bias of newspapers reporting on the politician). I propose a formal approach to combine these two forces, creating a tractable way to study the distortion of related beliefs. The approach unifies several central ideas from psychology (e.g., motivated reasoning, attribution) that have been applied heavily to political science. Concrete applications shed light on why successful individuals sometimes attribute their performance to luck ("imposter syndrome"), why those from advantaged groups believe they in fact face high levels of discrimination (the "persecution complex"), and why partisans disagree about the accuracy and bias of news sources.