Another well-defined measure of a mountain's dominance in its vicinity is the highest peak visible above its local horizon. For peak A, we compute the angle β to every other peak with respect to the local horizon, filter out those for which it is positive, and mark the one with the highest value as the horizon parent of the peak.
Compared to isolation, this forms many isolated trees – dominant peaks often have a completely clean horizon and all other visible peaks, if any, are below the tangential plane. The horizon measure therefore does not result in a complete hierarchy. Also unlike plain slope, this hierarchy is not that shallow and results in fewer surprises.
However, there are again at least two posible meaningful definitions: the simpler one is purely geometric and does not take atmospheric refraction into account. This is easier to compute and does not change in time, however in real world the distances involved are large enough (and the angles are often small enough) so that this results in a measurable difference. A downside is that the value is not constant, and depends on temperature gradients, humidity and so on. Still, it is possible to use at least the standard value of c = 0.14. This results in an effective diameter of the Earth of R' = R / (1 - 0.14) ≈ 7408 km.
In certain pathological cases it is also possible that the highest point above the horizon is not a summit, but just a convex protrusion, however these cases are very difficult to cover and probably not worthwhile.
By default, children are sorted in descending order by angle: peaks for which the angle is high are most often just minor sub-summits, while peaks that are just enough far away to reach a small but positive values are likely still relatively important and independent summits.