Consider that we could easily consider ensembles of fairness definitions which are stated in somewhat different languages. Responding to these sorts of questions, Chouldechova proves that we cannot satisfy equal false negative rates , equal false positive rates , and equal positive predictive values , except under the condition of perfect prediction or equal base rates. Kleinberg et al. Some authors call these trivial or degenerate cases, but we could just as well call them utopian cases. Each of these situations can be regarded either as an unrealistic edge cases or as a political goal.
We observe that the political translation of these conditions seem to be very different. Redlining wiki: Redlining is defined as the denial of services to residents of certain areas based on the racial makeup of these areas. But what do we mean by based on? In cases of interest, this effect can occur both intentionally and unintentionally. For example, a discriminatory lender could deny housing loans to residents of a neighborhood which is known to be majority black, and could in a sense hide their anti-black racism behind a ZIP code.
But one could produce similar effects unintentionally, for example by including average neighborhood income as a factor in a model of loan default, in a situation where black applicants mostly live in black neighborhoods that are on average economically depressed, while white applicants live in wealthier neighborhoods. In this situation, a wealthy black person may be harmed by the choice to use the neighborhood income information, while a poorer white person may be helped by the choice to include it. So we see that the decision to include these variables in our model is not politically neutral, and that it is not necessarily clear that considering more variables produces a fairer outcome.
It depends substantially on our notion of fairness. Between arrest and trial, US criminal law leaves a lot of latitude to interpretation of whether accused individuals should be incarcerated, in what kind of facility, and for how long.
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These scores are then used in an unspecified way to make decisions of jail, bail, home arrest, release, etc. Ideally in this situation one should ask for end-to-end transparency. We raise a number of questions:. In , Angwin et al. Two of their findings can be phrased in our language as follows:. Much of the subsequent conversation consisted of either trying to harmonize these definitions of fairness or asserting that one or the other is correct.
A risk score of seven for black defendants should mean the same thing as a score of seven for white defendants. We would consider that a violation of the fundamental tenet of equal treatment. To the contrary, since classification errors here disproportionately affect black defendants, we have an obligation to explore alternative policies.
For example, rather than using risk scores to determine which defendants must pay money bail, jurisdictions might consider ending bail requirements altogether — shifting to, say, electronic monitoring so that no one is unnecessarily jailed. Chouldechova has written on the trade-offs among equal false negative rates , equal false positive rates , and equal positive predictive values. We mentioned this work above in our chapter on Ensembles and Impossibility.
Why is this work so difficult to do? The authors venture an unguarded opinion: this situation is a travesty.
We need end-to-end transparency here at a minimum, and until we have it, skepticism of these tools is more than warranted. This is unlikely to be the last legislation of its kind and it would be useful for the field to think a bit beyond the currently available datasets, public records laws, and avenues of accountability.
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In the past several years there has been an increasing interest in the mathematics of gerrymandering and other forms of election manipulation. In addition to the mathematical conversation , there are several active court cases. Whether or not these conversations connect for now at a theoretical level to those on quantitative fairness, they are likely to meet similar challenges in the policy sphere.
In other words, in race discrimination cases, discrimination tends to be viewed in terms of sex- or class-privileged Blacks; in sex discrimination cases, the focus is on race- and class-privileged women. Crenshaw analyzes a series of failed Title VII cases, each involving black women who must pursue recourse against discrimination as black women which they are unable to establish simply as sex discrimination since it does not apply to white women or as race discrimination since it does not apply to black men , and whose cases therefore failed.
Crenshaw quotes the court in deGraffenreid vs General Motors :. Plaintiffs have failed to cite any decisions which have stated that Black women are a special class to be protected from discrimination. The plaintiffs are clearly entitled to a remedy if they have been discriminated against. Thus, this lawsuit must be examined to see if it states a cause of action for race discrimination, sex discrimination, or alternatively either, but not a combination of both.
In spite of the uphill legal battle, this line of thought has proved extremely productive in and beyond the legal sphere. It is possible to mislead with an overly simplified framework which becomes cumbersome or conceals issues when we reach the level of complexity which is relevant. From the quantitative fairness literature, see Kearns et al.
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From the epidemiology literature, see Jackson et al. Even within a legal framework of protected classes, such analyses may be helpful in clarifying the edges of those classes, where interpretations frequently shift as to who is included. Evidently protected classes are somewhat rickety and unstable political constructions, and it is the opinion of the authors that we need to pursue legal reforms that go a bit deeper than politically reversible guidance in the interpretation of a statute.
Those of us in the quantitative fairness conversation need to think about going beyond quantification of the principles which are already explicit in Title VII and instead push for new political solutions which are intersectional from the jump. That means among other things, catching up to the jurisprudential, theoretical, and activist conversations which continue to this day.
The recent focus on quantitative fairness has been motivated by the increased use of automated procedures. Many researchers in this area come from machine learning, because of its development of such automated procedures. However, this article has also considered the definitions of fairness in examples of mostly human procedures, e.
Here we connect to the public health study of disparities to bring in insights from this field. Bailey et al. Focusing on the second, we can consider health care utilization as the output from a complex mostly human procedure, our health care system. How can we evaluate its fairness along racial lines? LeCook et al. Each disparity definition corresponds violating a version of conditional statistical parity.
Institute of Medicine [ IOM ]:. Requiring this be 0 is conditional statistical parity , conditioned on more data. These three definitions are genuinely different. The Institute of Medicine IOM definition allows for utilization differences between racial groups that are explained by health care needs, but not by socioeconomic status.
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Connecting to our discussion of causal pathways above, we can consider current socioeconomic status a mediating variable between race and health care utilization. Though these disparity definitions are observational and not causal, in a somewhat vague sense, the IOM definition expresses that a path from race to utilization through socioeconomic status is unfair. We believe it is valuable to highlight some of the confusion that exists in the definition of fairness and that this confusion has consequences.
Returning to some of the questions of the introduction it is by no means clear that any formalization of fairness exhausts the moral and political sense of fairness. Which notions deserve to be animated with the normativity of moral judgments or the force of law?
Which are to be pursued politically? Much communication consists of taking one or another of these fairness concepts as obvious or axiomatic and asserting the violation of that principle as a political or moral gotcha. Formalization should not be regarded as a panacea in these debates but perhaps it can help to cement the points that:. For more than fifty years, understandings of fairness have been shaped by the language of protected classes, disparate treatment and disparate impact. As new understandings of fairness emerge from the quantitative conversation, we ought to consider:.
Knowing that each definition of fairness has its trade-offs increases the interest in auditing decision procedures, possibly automatically, for various forms of unfairness.
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It is easy to imagine tools for pre-registration of decision procedures, which can then be measured by various fairness criteria in a responsive manner, enabling new kinds of intervention. It is not even necessary to resolve conflicts between formalizations before building such a tool, since nothing in principle prevents checking all of these conditions at once. But we ought to beware, we urge anyone to consider as a thought experiment the explicit regulatory codification of fairness if it had happened five years before your favorite articles in the subject.
We may have more reason to fear success than failure in this enterprise. It is possible and a hope of the authors that widespread awareness of the trade-offs and inconsistencies in the definitions of fairness may reduce the secrecy and publication bias in this field. This can proceed in a number of ways:. Pointedly, the existence of many plausible metrics of fairness allows us to pose explicitly the question of whether organizations are deliberately only publishing those metrics which reflect favorably on them, or whether they are suppressing any inquiry whatsoever to avoid a paper trail.
In this article we have not taken a particularly adversarial analysis of the fairness landscape, but we encourage the reader to think through the way each definition of fairness can be gamed by malicious actors.