Optimal ordering of heterogeneous battles

Determine the optimal ordering of heterogeneous component battles in multi-battle majority-rule team contests when the ordering is not governed by the temporal refinement relation.

Background

The paper establishes output rankings for temporal structures that are related by refinement: under convex output costs, coarser structures are weakly preferred, while under concave output costs, finer structures are weakly preferred. These results do not determine how to order heterogeneous battles when alternative orderings are not comparable under refinement.

The unresolved issue concerns identifying which ordering of battles maximizes expected total output in the presence of heterogeneous battle-specific characteristics, such as differing ability distributions, pivotality probabilities, or battle prizes, beyond the comparisons delivered by the refinement framework.