Spot It! and balanced block designs: keys to better debate architecture for a plethora of candidates in presidential primaries?

U.S. presidential primary debates are influential but under-researched. Before 2015, all of these debates, both Democratic and Republican, had 10 candidates or fewer. The first Republican debate in 2015, however, abided 17 candidates. They were split into two segments, with the 10 best-polling candidates in the main (prime-time) segment and the others in an ‘undercard’ session. A comparable pattern applied for the next six Republican debates. Concern arose not only because many candidates were crowded into a session but also because the undercard candidates were seen as receiving inferior exposure. The Democratic presidential primary debates that started four years later encountered similar difficulty. An authorized policy caused their candidates in each of the first two debates to be limited to 20, randomly divided into two groups of 10 appearing on successive nights. For remedy, this paper examines innovative debate plans, for different numbers of candidates, that feature symmetry among all candidates and entail many short segments with relatively few candidates in each. We apply combinatorial designs—balanced incomplete block designs and regular pairwise balanced designs, which are analogous to the games Spot It Jr.! Animals and (full-fledged) Spot It!, respectively.