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| \textit{resource}, which we will define simply as an element which may be | ||
| distributed among agents. Traditional examples include money and admissions, | ||
| but we will also consider more abstract resources such as representation or | ||
| influence. Following \cite{Kuppler_2021}, we will define a \textit{distribution |
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May be good to include the contrast here: So while admissions or loan decisions fit your account, it would seem like granting parole would not, since that is not a "finite resource" in the same sense. Is that the right way of thinking about the set-up here?
| in terms of resource allocation, but the reader may still be concerned with the | ||
| perpetuation of social biases through the decisions it makes in translation. | ||
| While these cases are significant, they do not fall simply within the domain of | ||
| distributive justice, and so we will not consider them here. |
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ok, good -- there are many more general AI issues that may contain bias but not fit the bill (e.g. image classification), but I think the distinction from the parole case (see above) may be more relevant here as it seems much closer than AI translation.
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Also, maybe it would be good to start developing a specific running example that you can work with -- explain the sorts of issues that your running example may give rise to.
| \subsection{Algorithmic Fairness Measures}\label{sec:fairness-measures} | ||
| In the canonical presentation of algorithmic fairness, we are given a population | ||
| of agents $A = \{a_1, a_2, \ldots, a_n\}$ with observed covariates $X$ drawn | ||
| from some distribution $P(X)$. We are told that some set $A$ of protected |
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disentangle your symbols: agents and protected attributes are A for you; also X was the resource that is being allocated, not the attributes.
| from some distribution $P(X)$. We are told that some set $A$ of protected | ||
| attributes may be derived from $X$. Each agent $a_n$ in the population is | ||
| subjected to a binary decision according to some decision rule | ||
| $d: X \to \{0, 1\}$~\cite{CorbettDavies_2023}. |
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ok, this is correct as a description for the fairness literature, but right now it seems a bit odd given your zero-sum resource allocation problem in the previous section. I assume you will clarify in the following how one maps to the other
| straightforward, and we are unlikely to be able to predict it perfectly from the | ||
| information delivered by $x_n$. The decision rule $d$ is then a function which | ||
| imperfectly approximates the desired distribution rule, making errors at some | ||
| frequency. Algorithmic fairness measures presented in the literature thus may |
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the sentences preceding this comment are an attempt to address my previous comment, but I am not quite clear what the proposal is here. Are you simply turning the standard decision problem into one that has continuous outcomes that represent the resource? Or is there something else going on, e.g. that it is a binary decision about the allocation rule?
| \begin{itemize} | ||
| \item The relationship of the attribute $y$ to the set of protected | ||
| characteristics $A$ | ||
| \item The method of detection of errors made by a decision rule $d$ |
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I am not sure I fully understand how this second point is different from the first. Isn't it one way of characterizing the relationship alluded to in the first bullet?
| \begin{definition} Demographic Parity — A decision rule $d$ is said to satisfy | ||
| demographic parity if the probability of receiving a positive decision is | ||
| independent of the protected attributes $A$~\cite{Dwork_2012}. \end{definition} | ||
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provide a formal definition in terms of the notation you have introduced
| When using demographic parity as a fairness measure, therefore we measure | ||
| errors made by the decision rule $d$ by the extent to which the probability of | ||
| receiving a positive decision depends on the protected attributes in $A$. | ||
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before criticizing the standard, maybe provide a couple of sentences of positive motivation first
| Equalized Odds — A decision rule $d$ satisfies equalized odds if the | ||
| true positive rate and false positive rate do not vary with respect to | ||
| $A$~\cite{Hardt_2016}. | ||
| \end{definition} |
| \end{definition} | ||
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| Equalized odds may be thought of as again positing that attribute $y$ may not | ||
| depend on $A$, but it goes further to say that errors in our prediction of $y$ |
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in what sense does it go further? it does not ensure demographic parity, it only cares about the error rates
| white defendants~\cite{CrimeJustice_2023}. As a result, allocating a parole to | ||
| a white prisoner has a base line lower likelihood of being a false positive. | ||
| Therefore, when we perform post-processing of our data to balance false positive | ||
| rates, we may actually \textit{add} false positives to the white portion of the |
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wording: one could achieve equal false positive rates by adding...
| distribution rule which says to allocate a parole to a prisoner if they are very | ||
| unlikely to recidivate. Due to a history of discriminatory practices and social | ||
| marginalization, black prisoners have a base rate of recidivism much higher than | ||
| white defendants~\cite{CrimeJustice_2023}. As a result, allocating a parole to |
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I think you should reference the ProPublica article on Machine Bias here, since much of the discussion of their analysis centered on the issue that they were complaining about unequal false positive rates when the method was actually well calibrated, but there were different base rates.
| Counterfactual Fairness — A decision rule $d$ satisfies counterfactual | ||
| fairness if protected attributes from $A$ do not play a causal role in its | ||
| output~\cite{Kusner_2018}. | ||
| \end{definition} |
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Not quite so easy to state formally, but I think it would again be good to do so.
| issues are set aside, the computational expense of causal discovery can create | ||
| issues of practicality. | ||
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| This discussion of dominant algorithmic fairness measures and their shortcomings |
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I think you should mention the "fairness through unawareness" measure as well. Not because it is good, but because the idea persists in discussions that really what one should do is just not let protected categories enter into the decision process. It is a terrible idea to try to keep them out, but people are still susceptible to that misconception
| distribution dictated by theories of algorithmic justice? Is it valid to say | ||
| that these measures enforce distributive justice in any way? And it is possible | ||
| to address or understand their shortcomings in terms of the philosophy of | ||
| distributive justice? |
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As noted above, I think it is important that you build a clearer translation between the standard fairness setting and your resource allocation setting, so that it is more obvious how we should think of applying these measures.
| distributive justice? | ||
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| \subsection{Theories of Distributive Justice} | ||
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A bit more motivation: You are turning towards theories of distributive justice because you think this work in political philosophy can be informative about how to determine appropriate fairness measures for your setting. In some sense, you want to use these theories as guiding lights to make the formal automated process precise.
| distribution that define fairness in society. Specification of these rules is | ||
| exactly the process of defining a $y$ in the formalism we have presented. | ||
| Several conventional theories of distributive justice have been proposed in the | ||
| literature, and we will discuss a few of them here. For a more exhaustive list |
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Maybe indicate why you have selected ones you did -- or do so below. Otherwise this is just a review of some random theories.
| amount $R$ of resource $X$ should be allocated to agent $a_n$ if and only if | ||
| the doing so minimizes the overall inequality across the population. Thus in | ||
| this case, $y$ is the property of \textit{lacking} good $X$ relative to the | ||
| population. |
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Well, it seems that your sentence after the definition is not consistent with the definition. The definition suggests that everyone gets R/n of the resource, but the sentence after that (following Rawls) does allow for inequality. Note, that Rawls's account has this ordering of his principles. So does egalitarianism in general allow for inequalities?
| \begin{definition} | ||
| Desert — Moral desert is the idea that individuals should receive resources | ||
| in proportion to their moral worth as measured by some metric of | ||
| merit~\cite{Pojman_1997}. |
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Clarification: moral worth is measured by a metric of merit? At least superficially it is not obvious why merit has anything to do with moral worth, unless you say something about what you mean by merit.
| merit~\cite{Pojman_1997}. | ||
| \end{definition} | ||
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| Theories of desert therefore set $y$ to be some form of moral merit, and the |
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ah, now you mix it to be "moral merit" -- try to get some clarity into this
| distribution of the decision rule is equal across protected groups. However, | ||
| this is a failure in two ways. Firstly, egalitarianism mandates that allocations | ||
| be balanced across all individuals, not across groups. Secondly, our measurement | ||
| of errors in the decision rule $d$ is based solely on the distribution enforced |
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I am actually unclear at the moment still how you are thinking about "errors" in the distribution of resources. What would it mean to have equal false positive errors in resource allocation?
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Feedback for the rough draft of the background section.
See the rendered PDF as it currently appears here
I feel it is very likely that both