The Donation Paradox for Peremptory Challenges

A donation paradox occurs when a player gives an apparently valuable prerogative to another player, but does better, according to some criterion. Peremptory challenges, used in choosing a American jury, permit each side to veto a certain number of potential jurors. With even a very simple model of jury selection, it is shown that for one side to give a peremptory challenge to the other side may lead to a more favorable jury, an instance of the donation paradox. Both a theorem and examples are given concerning the existence of the donation paradox in the optimal use of peremptory challenges.