Work in computer science has established that, contrary to conventional wisdom, for a given prediction problem there are almost always multiple possible models with equivalent performance--a phenomenon often termed model multiplicity. Critically, different models of equivalent performance can produce different predictions for the same individual, and, in aggregate, exhibit different levels of impacts across demographic groups. Thus, when an algorithmic system displays a disparate impact, model multiplicity suggests that developers could discover an alternative model that performs equally well, but has less discriminatory impact. Indeed, the promise of model multiplicity is that an equally accurate, but less discriminatory algorithm (LDA) almost always exists. But without dedicated exploration, it is unlikely developers will discover potential LDAs. Model multiplicity and the availability of LDAs have significant ramifications for the legal response to discriminatory algorithms, in particular for disparate impact doctrine, which has long taken into account the availability of alternatives with less disparate effect when assessing liability. A close reading of legal authorities over the decades reveals that the law has on numerous occasions recognized that the existence of a less discriminatory alternative is sometimes relevant to a defendant's burden of justification at the second step of disparate impact analysis. Indeed, under disparate impact doctrine, it makes little sense to say that a given algorithmic system used by an employer, creditor, or housing provider is "necessary" if an equally accurate model that exhibits less disparate effect is available and possible to discover with reasonable effort. As a result, we argue that the law should place a duty of a reasonable search for LDAs on entities that develop and deploy predictive models in covered civil rights domains.

翻译：计算机科学的研究已经证实，与传统观点相反，对于给定的预测问题，几乎总是存在多个性能相当的模型——这一现象常被称为模型多重性。关键在于，性能相同的不同模型可能对同一个体产生不同的预测结果，并在总体上对不同人口群体表现出不同程度的差异性影响。因此，当某个算法系统显示出差异性影响时，模型多重性意味着开发者可能找到另一种性能相当但歧视性影响较小的模型。事实上，模型多重性的意义在于，几乎总存在一个准确率相同但歧视性更低的算法。但若没有专门的探索，开发者不太可能发现这些潜在的较少歧视性算法。模型多重性及较少歧视性算法的可获得性，对法律应对歧视性算法具有重要影响，尤其涉及差异性影响原则——该原则在评估法律责任时，长期以来都将"存在较少差异性影响的替代方案"纳入考量。通过对数十年来法律文献的细致解读可以发现，法律已多次承认：在差异性影响分析的第二阶段，较少歧视性替代方案的存在有时与被告的正当性举证责任相关。实际上，根据差异性影响原则，如果存在一个可通过合理努力发现且具有较少差异性影响的同等准确模型，那么声称雇主、信贷机构或住房供应商使用的特定算法系统是"必要"的，就缺乏合理性。因此我们认为，法律应当对在民权保护领域开发部署预测模型的主体施加一项合理搜索较少歧视性算法的义务。