Optimality of the ascending-descending order for odd sequential juries

Let a jury have an odd number of distinct abilities, and let the ascending-descending order (ADO) arrange the abilities by placing the more able half in increasing order followed by the less able half in decreasing order. For abilities $0\leq a_1<a_2<\dots<a_n\leq 1$ with $n=2m+1$, this order is

$$(a_{m+1},a_{m+2},\dots,a_n,a_m,a_{m-1},\dots,a_2,a_1).$$

ADO optimality conjecture. For any fixed set of an odd number of distinct abilities for a jury, the ordering that produces the highest reliability is the ADO.

For juries of size three, the ADO is the unique optimal ordering, while for larger juries the claim is supported only by limited simulations; the general optimal ordering problem remains open because reliability formulas become prohibitively complex as jury size grows.