## 3 Machine Learning Algorithms
### Fairness Notions
Nevertheless, in our review, we aim to cluster fairness in machine learning algorithms studied in the extant literature into three main categories, namely, anticlassification, statistical parity, and calibration. 1. Anticlassification, also known as unawareness, seeks to achieve fairness in ML outcomes by excluding the use of protected features such as race, gender, or ethnicity from the statistical model. This notion is consistent with disparate treatment. Despite being intuitive, easy-to-use and having legal support, a crucial difficulty of this approach is that a protected feature might be correlated with many other unprotected features, and it is practically infeasible to identify all such covariate \"proxies\" and remove them from the statistical model. For example, protected class _race_ might be correlated with various other features, such as education level, salary, life-expectancy, etc., and removing all these proxies from the statistical model could have detrimental effects in predictive performance. Consider we have a vector \(x_{i}\in\mathbb{R}^{t}\) that represents the visible attributes of individual \(i\) such as race, gender, education level, age, etc. An algorithmic decision can be represented as a function \(d:\mathbb{R}^{t}\mapsto\{0,1\}\), where \(d(x)=k\), \(k\in\{0,1\}\), means that action \(a_{k}\) is taken. Suppose that \(x\) can be partitioned into protected and unprotected features: \(x=(x_{p},x_{u})\). Let \(X_{p}\) denote the set of all protected features. Then, anticlassification requires that decisions do not consider protected attributes, more formally, \[d(x)=d(x^{\prime})\text{ for all }x,x^{\prime}\text{ such that }x_{u}=x^{\prime}.\] Several other variants of anticlassification are also proposed in the literature [53; 54]. 2. Statistical parity (also known by the names of demographic parity, independence, statistical parity, and classification parity) requires that common measures of predictive accuracy and performance errors remain uniform across various groups segmented by the protected features. This includes notions such as statistical parity, equality of accuracy, equality of false positive/false negative rates, and equality of positive/negative predictive values [55; 56; 57]. The main idea of this notion is to quantify and equate benefit and harm of the impact of the ML prediction to groups segmented by protected attributes equally and to distribute the errors among different stakeholders equally [55]. This notion of fairness has recently found application in criminal justice [58] and is consistent with disparate impact. The measure of classification parity based on false positive rate and the proportion of decisions that are positive have received considerable attention in machine learning domain [55; 59; 60]. For formal definition, please refer to Table 5. Recent research by [PERSON] and [PERSON] [61] suggests that the enforcement of statistical parity criteria in the short-term benefits building up the reputation of the disadvantageous minority in labor market in the long run. Note that, a critical flaw of notion of statistical parity is that it is easy to satisfy it by some arbitrary configuration, for example selecting best and qualified candidates from one group and random alternatives from the other group can still satisfy statistical parity. Moreover, the definition also ignores any possible correlation between positive outcome and protected attributes. 3. Calibration requires that ML outcomes remain independent of protected features after controlling for estimated risk. Calibration relates to the fairness of risk scores and requires that for a given risk score, the proportion of individuals re-offending remains uniform across protected groups. Calibration is beneficial as a fairness condition as it does not require much intervention in the existing decision-making process [62]. A major disadvantage of calibration is that it has been shown that risk score can be manipulated to appear calibrated by ignoring information about the favored group [63].