  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.
