EXAMPLE 17 The Jury

A jury of 12 members must reach a unanimous verdict. This means that the only winning coalition is the grand coalition. The Banzhaf power index of each member of the jury is 1. Thus the probability that a juror will be a critical voter is . One might think that most criminal trials would end as mistrials, since it is so unlikely that the jurors would agree. But the Banzhaf model only touches on the voting system. it does not consider all of the evidence that the jurors see before they vote.