From a statistical standpoint, judgments about an individual are more accurate if base rates about the individual’s social group are taken into account (Eddy, 1982; Kahneman & Tversky, 1973; Bar-Hillel, 1980; Tversky & Kahneman, 1974). But from a moral standpoint, using these base rates is considered unfair and can even be illegal (Cao & Banaji, 2016; Rawls, 2001; Dworkin, 2000; Koehler, 1992; Test-Achats v. Council of Ministers, 2011). Thus, the imperative to be statistically accurate is directly at odds with the imperative to be morally fair. This conflict was resolved by creating tasks in which Bayesian rationality and moral fairness were aligned, thereby allowing social judgments to be both accurate and fair. Despite this alignment, we show that social judgments were inaccurate and unfair. Instead of appropriately setting aside social group differences, participants erroneously relied upon them when making judgments about specific individuals. This bias – which we call base rate intrusion – was robust, generalized across various social groups (gender, race, nationality, and age), and differed from analogous nonsocial judgments. Results also demonstrate how social judgments can be corrected to achieve both statistical accuracy and moral fairness. Overall, these data (total N = 5,138) highlight the pernicious effects of social base rates. Under conditions that closely approximate those of everyday life (Fiske & Neuberg, 2012; Moss-Racusin et al., 2012; Cheryan, et al., 2009), these base rates can undermine the rationality and fairness of human judgments.