Admissible Alternatives under Decentralized Interaction: Boundary Awareness

This paper studies the stability of decentralized admissibility. Individuals are represented by compact convex acceptance sets—capturing regions of technical feasibility, economic viability, or institutional and normative acceptability—over a continuous alternative space. Collective admissibility is determined pointwise, without central coordination or cross-alternative comparison. The object of analysis is therefore not selection among admissible alternatives, but the endogenous formation of the admissible set itself. Under minimal structural constraints, admissibility reduces to local support–counting rules. When informational granularity is limited to binary membership (Boundary Blindness), such rules are topologically fragile: arbitrarily small perturbations of individual feasibility constraints may induce discontinuous contractions of the admissible region, rendering it topologically unstable. We show that this fragility is not inherent to decentralization, but to informational coarseness. We introduce Boundary Awareness, a minimal refinement that allows the aggregation process to distinguish interior from boundary support. Under Boundary Awareness, Robust Admissibility forces admissibility to collapse to an interior-threshold form. Conversely, any signal structure that fails to distinguish interior from boundary membership cannot sustain robustness. Boundary Awareness is therefore minimal among informational regimes that restore topological stability. The results isolate informational resolution—not institutional centralization—as the determinant of robustness in decentralized interaction. JEL Classification: C02 , D02 , D83