Roll‐call votes are widely employed to infer the ideological proclivities of legislators. However, many roll‐call matrices are characterized by high levels of nonresponse. Under many circumstances, nonresponse cannot be assumed to be ignorable. We examine the consequences of violating the ignorability assumption that underlies current methods of roll‐call analysis. We present a basic estimation framework to model nonresponse and vote choice concurrently, build a model that captures the logic of competing principals that underlies accounts of nonresponse in many legislatures, and illustrate the payoff of addressing nonignorable nonresponse through both simulated and real data. We conclude that modeling presumed patterns of nonignorable nonresponse can yield important inferential payoffs over current models that assume random missingness, but we also emphasize that the decision to model nonresponse should be based on theoretical grounds since one cannot rely on measures of goodness of fit for the purpose of model comparison.