How do people approach international conflicts or crises with foreign leaders they believe are irrational? According to Schelling’s famous argument about the ‘rationality of irrationality,’ an irrational image enhances the credibility of threats thereby making it easier to coerce or deter counterparts without resorting to actual violence, disincentivizes adversaries from making threats or using force against the apparent madman, and provides many other boons besides. Yet despite its fame this claim is theoretically underdeveloped and empirically untested. In this dissertation I provide a novel conceptual spectrum as a framework for dealing with perceived irrationality, and theorize how variation on this spectrum effects actors' preferences and choices in interstate conflicts or crises. I argue that a dichotomous conception of perceived irrationality is unhelpful and not reflective of reality, and that to gain useful insight scholars must break perceived irrationality down into its constituent dimensions. Rather than treating perceived irrationality in isolation, I treat it as one extreme on a spectrum that I call beliefs about judgment, which I simplify to two dimensions: perceived objectivity (objective/biased) and perceived competence (competent/incompetent). I argue that perceived irrationality functions precisely counter to the expectations of the ‘rationality of irrationality’ theory: leaders who are apparently irrational on the objectivity or competence dimensions of my spectrum are more likely to be subject to threats or force and to experience unfavorable outcomes in interstate negotiations. Specifically, actors who perceive an adversary leader as biased are more likely to conduct diplomacy through coercion, threats, and violence than through rational dialogue, information sharing, and argument, since they a purely informational approach to persuasion is expected to be less effective with biased leaders. Actors who perceive an adversary leader as incompetent are less likely to make concessions, more likely to ‘stand firm,’ and more likely to exit negotiations and escalate violence if their desired settlement is not achieved, since conflict with incompetent leaders is expected to be less costly. I test my theory with a mixed methods approach: I experimental and case study methodology to examine the veracity of my theory at the public and elite level, respectively.