We consider the implications of the definition of juror bias offered in Schwartz and SchwartzEdward P. Schwartz & Warren F. Schwartz, The Challenge of Peremptory Challenges. Paper presented at the annual meeting of the Public Choice Society, Long Beach, California, March 24–26, 1995. for optimal use of juror challenges to improve the accuracy of the jury process. For them, bias consists of a juror assinging more/less weight to the evidence for guilt than would be assigned by the median juror in a fully representative pool of jurors. When juror assessments of the evidence have a probabilistic component to them, we show that this notion of bias does not imply that we necessarily would wish to use challenges to eliminate the most biased jurors. We also explain how understanding juror verdict accuracy requires an analysis of the interaction between the threshold rule that the juror uses to determine what level of belief in the guilt of the defendant is sufficient for “guilt beyond a reasonable doubt” and the probative force of the evidence in the cases that the prosecution chooses to bring to trial. Whether we use the Schwartz and Schwartz definition or other more standard legal approaches to defining juror bias (and grounds for challenge for cause) we come away highly skeptical of the expanded voir dire and extended use of peremptories that, in a number of recent highly publicized criminal trials, have had the consequences of eliminating from the jury pool the most highly educated and the most knowledgeable jurors.