Previous work in the area of jury selection introduced the concept of irregular selection problems, situations in which it would be optimal for a side to give one or more peremptory challenges to its opponent. Roth, Kadane and DeGroot (RKD) (1977) introduced one model and assumed that regularity always held for their analysis. DeGroot and Kadane (DK) (1980) investigated a more general model and displayed counterexamples to regularity in this new framework. However, the examples did not apply to the simpler special case of RKD.
This paper shows that if there are only two types of jury candidates, regularity obtains in the general DK model, in section 2. However, Section 3 displays multiple counterexamples to regularity (using three candidate types) in the special RKD model, thus limiting the generality of certain results proved there. Also, one of their results under the assumption of regularity is re-examined in Section 4, where it is shown by example that the advantage claimed by RKD to going first in the regular case is more constrained than it might appear. Finally, Section 5 shows by theorem that reversibility does hold in generality.