Prediction algorithms assign numbers to individuals that are popularly
understood as individual "probabilities" -- what is the probability of 5-year
survival after cancer diagnosis? -- and which increasingly form the basis for
life-altering decisions. Drawing on an understanding of computational
indistinguishability developed in complexity theory and cryptography, we
introduce Outcome Indistinguishability. Predictors that are Outcome
Indistinguishable yield a generative model for outcomes that cannot be
efficiently refuted on the basis of the real-life observations produced by
Nature. We investigate a hierarchy of Outcome Indistinguishability definitions,
whose stringency increases with the degree to which distinguishers may access
the predictor in question. Our findings reveal that Outcome
Indistinguishability behaves qualitatively differently than previously studied
notions of indistinguishability. First, we provide constructions at all levels
of the hierarchy. Then, leveraging recently-developed machinery for proving
average-case fine-grained hardness, we obtain lower bounds on the complexity of
the more stringent forms of Outcome Indistinguishability. This hardness result
provides the first scientific grounds for the political argument that, when
inspecting algorithmic risk prediction instruments, auditors should be granted
oracle access to the algorithm, not simply historical predictions.

该研究通过利用复杂性理论和加密学中发展的计算不可区分性来引入结果不可区分性，调查了一系列结果不可区分性定义的等级，其严格程度随着区分器可以访问的预测器的程度而增加，并发现结果不可区分性在定性上与先前研究的不可区分性概念有所不同，从而为政治争议提供了第一批科学依据，即当检查算法风险预测工具时，审计员应被授予访问算法的 oracle，而不仅仅是历史预测。