用格理论设计不带选择权的预测系统，避免自我实现预言的偏见。
Unbiased Canonical Set-Valued Oracles Via Lattice Theory
- 用信用集替代点估计，通过格论保证答案自洽且无选择余地。
- 答案恒非空，可从下界迭代计算，若问题无表演性则等同于传统点估计。
- 适用于概率、连续统计量，适合需消除人为判断的科学智能场景。
一个能预测未来事件概率的预言者会因人们的行动而改变该概率本身。我们主张这种表演性是合理的，因为人们咨询预言者是为了被其答案影响。但更需警惕的是，要求预言者给出自洽的答案（即公布后仍成立）可能使其在多个答案中选择，而这个选择过程可能被学习利用。为此，我们提出让预言者报告一个信用集而非点估计，将预言者的反应函数提升为格上的保序算子。预言者报告该算子的最小不动点——由Knaster-Tarski定理保证存在。由于此答案由预先规则决定，无需额外选择。我们证明该解存在、自洽、永不为空，可通过从下界迭代计算，并在问题无表演性时等于传统点估计。对简单概率查询，我们建议将答案限制为区间，在温和单调性假设下，答案即为从无信息基线到自我实现均衡的区间。由于本方法纯基于序理论，可直接推广至任意随机变量和其分布的有界连续统计量。最后我们证明，有限个单纯形族足以均匀逼近所有答案，使构造变为可终止计算。文章结尾将其置于科学家人工智能计划中，提供一种无需人工审计即可执行的关键步骤的无选择标准。
原文摘要 · Abstract (English)
An oracle that tells you the probability of some future event can change that very probability because you act on the answer. We argue that this performativity is OK as people consult oracles to be informed, and hence moved, by the answer. We worry about instead that asking for a self-consistent answer, one that still holds once it has been announced, may leave the oracle with several answers to pick from, and whichever rule it uses to pick is a lever it could learn to pull. We propose to take away that choice: The oracle reports a credal set instead of a point estimate, which lifts the oracle's reaction function to an isotone operator on a lattice. We make the oracle report that operator's least fixed point, which exists because of Knaster and Tarski. As that answer is fixed by a rule laid down in advance, nothing is left to choose by the oracle. We show that solution exists, is self-consistent, is never empty, can be computed by iterating from below, and equals the ordinary point estimate if the question is not performative after all. For simple queries about probabilities, we propose to restrict answers to intervals and show that, under a mild monotonicity assumption, the answer is simply the interval from the no-information baseline to the self-fulfilling equilibrium one would end up at by iteratively querying a point oracle until the answer is self-consistent. As our proposal is purely order-theoretic, it carries over unchanged to arbitrary random variables and to bounded continuous statistics of their law. Finally we show that a fixed finite family of polytopes suffices to approximate every answer uniformly, which turns the construction into a terminating computation. We close by placing the construction inside the Scientist AI programme, where it offers a choice-free criterion for a step that programme currently hands to audited human judgement.
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