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Plea bargaining figures heavily in criminal justice systems around the globe. Its primary justification is efficiency: it allows defendants to admit their guilt in exchange for a lesser sentence, sparing both the defendant and the prosecution the cost of a trial. However, justice system reformers argue that the practice can be used in conjunction with other system features, such as pretrial detention, to force disadvantaged individuals to plead guilty even when they are innocent. In this paper, we build a formal model to consider the relationship between a criminal defendant's guilt and her likelihood of pleading guilty before trial. Our main result is that, even absent pre-trial detention or other incentives to plead guilty, the i nnocent may often plead at higher rates than the guilty. Specifically, we show that in a population characterized by a range of risk preferences, risk-acceptant individuals are more likely to commit crimes---but less likely to plead guilty if caught. As a result, in an inversion of the conventional wisdom, the defendants who plead guilty are often more likely innocent than those who go to trial. We then examine how this dynamic affects the plea bargains offered by prosecutors with different preferences and information about the guilt of defendants.