For most Americans, the concept of trial by jury means a unanimous verdict by 12 members. Historically, however, juries have varied in size and decision requirements, with smaller juries and the absence of a unanimity requirement relatively common in civil cases. The task of the jury is to evaluate the evidence and determine the criminal defendant's guilt or innocence. This task can be conceptualized in terms of some well known results in the theory of signal detectability. Signal detection models contain two components. One component is a model of the observer as a sensor, that is, of his ability to discriminate stimuli. The second component is a model of the observer as a decisionmaker, that is, of the effects of his values and expectations on his responses. In criminal trials, jurors may be confronted with multiple verdict options when they are given the option of convicting the defendant of a lesser included offense. What options jurors open to them may have important verdict consequences. In addition to the signal detection theory model, nondeliberative models for aggregating juror choices as a function of jury size and jury quorum rule may be applied. Based on the available limited evidence, it appears that jury size can make a discernible difference with regard to verdict. Mathematical models can be extremely useful in analyzing the nature of jury decisionmaking and in drawing normative policy implications. Twelve figures, 6 tables, 25 footnotes, numerous equations, and over 100 references are provided.