What does an Algorithmic Choice demonstrate? A formal analysis of Evidence, Comparison, and Preference Attribution

When a machine chooses A over B, what do we really know about its decision? This paper presents a formal investigation at the intersection of applied logic, computational epistemology, and algorithmic auditing methods. It examines a fundamental problem in the interpretation of algorithmic decisions: the distinction between observing what a computational procedure selects and establishing what its available evidence justifies us in concluding about that selection. An algorithm may select one action over another without having established a comparative preference between them. In systems operating under finite computational budgets, incomplete information, or architecture-specific decision procedures, an observed choice does not necessarily reveal which alternatives were compared, which comparisons were resolved, or whether the selected action was strategically optimal. From the perspective of applied logic, the paper develops a formal framework distinguishing observed selection, resolved comparison, demonstrated preference, and strategic optimality. Through explicit definitions, logical derivations, countermodels, and conditional results on identifiability, it establishes the limits of comparative inferences from algorithmic outputs. From the perspective of computational epistemology, the investigation addresses what can legitimately be known or inferred from the evidence available to an observer of an algorithmic decision. It introduces typed evidence certificates and declared comparison standards, distinguishing operational resolution, statistical support, and strategic certification. From the perspective of algorithmic auditing, the paper introduces the Attribution Audit Record, a structured method for documenting comparative claims, their evidential sources, admissible certificates, resolution levels, and the conclusions those certificates authorize. The formal analysis also examines situations in which distinct decision instances remain compatible with the same information state. It establishes a conditional non-identifiability result and derives an exact local minimax value for two indistinguishable instances with disjoint optimal-action sets under explicit assumptions. The investigation was motivated by observations of finite-budget computational search, but its formal results are independent of the empirical cases that inspired it. The proposed framework is applicable to different computational settings, including search algorithms, automated ranking systems, decision-support procedures, and generative AI, provided that the relevant evidence standards are explicitly specified. The principal contribution is a formal and methodological framework for evaluating the evidential justification of comparative attributions in algorithmic decision-making. Rather than introducing a new search algorithm or claiming a new fundamental law of logic, the paper establishes a systematic distinction between observable decisions, available comparative evidence, and the conclusions that evidence warrants. Choice is a fact. Preference is a conclusion.