Evidence from psychology and economics indicates that many individuals overestimate their ability, both absolutely and relatively. We test three different theories about observed relative overconfidence. The first theory notes that simple statistical comparisons (for example, whether the fraction of individuals rating own skill above the median value is larger than half) are compatible (Benoît and Dubra, 2007) with a Bayesian model of updating from a common prior and truthful statements. We show that such model imposes testable restrictions on relative ability judgments, and we test the restrictions. Data on 1,016 individuals' relative ability judgments about two cognitive tests rejects the Bayesian model. The second theory suggests that self-image concerns asymmetrically affect the choice to get new information about one's abilities, and this asymmetry produces overconfidence (Kőszegi, 2006; Weinberg, 2006). We test an important specific prediction of these models: individuals with a higher belief will be less likely to search for further information about their skill, because this information might make this belief worse. Our data also reject this prediction. The third theory is that overconfidence is induced by the desire to send positive signals to others about one's own skill; this suggests a either a bias in judgment, strategic lying, or both. We provide evidence that personality traits strongly affect relative ability judgments in a pattern that is consistent with this third theory. Our results together suggest that overconfidence in statements is most likely to be induced by social concerns than by either of the other two factors.