218 Figure 8: Fifth and final step of realization: at both hierarchies, the space not allocated in the previous steps is allocated to category 4 (orange). 5. DISCUSSION The results of this experiment demonstrate that hierarchical ordering in HSIS is not a neutral or purely operational choice, but a fundamental modeling decision that directly controls how uncertainty is translated into spatial outcomes. Although both simulations are conditioned to the same dataset, share identical variogram models, neighborhood parameters, and random seeds, the change in the decision tree ordering alone leads to markedly different spatial allocations. The divergence observed from the third simulation step onward highlights a key property of HSIS: once a category is allocated at a given node, it removes probability mass and spatial opportunity from all lower priority categories. Consequently, early decisions have a disproportionate influence on the final spatial configuration. This path dependency implies that hierarchical ordering implicitly encodes a modeling hypothesis about which propositions should be tested first and which uncertainties are resolved earlier in space. The comparison between hierarchies based on raw sample proportions and declustered proportions further illustrates how preprocessing choices propagate into decision structures. A relatively small change in global proportions, caused by declustering, was sufficient to swap the ranking of two categories and trigger a branching in the decision tree. This branching, in turn, produced spatial patterns that differ not only locally but across the entire modeled domain. Such sensitivity underscores that hierarchy definition aggregates assumptions about representativeness, support, and spatial bias, even when these assumptions are not explicitly stated. From a decision theoretical perspective, the HSIS workflow can be interpreted as a stochastic decision tree evaluated in space, where each indicator represents a binary proposition and each realization represents one possible resolution of uncertainty. Under this interpretation, different hierarchical orderings correspond to different decision policies applied to the same information set. The results presented here show that these policies are not equivalent and may lead to different spatial alternatives, even when all probabilistic inputs remain unchanged. 1 1 1 1 2 3 3 4 4 4 4 4 5 5 5 5 1 1 1 1 2 3 3 4 4 4 4 4 5 5 5 5
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