The worst-total loss is subadditive

The worst-total loss over any $m+1$ states is subadditive: the worst total of a merged position never exceeds the sum of the worst totals of its parts. The reason is structural rather than computational. The functional is a maximum of linear functionals, one for each admissible set of states, and a maximum of linear functionals is always subadditive: the single set of states that realises the worst total for $X+Y$ is available to $X$ and to $Y$ separately, but neither is obliged to choose it, so each may only do better.

As throughout CoherentRisk, the development counts states and refers to no probability measure, so no confidence level is attached to $m$.