## 4 Recommender Systems
### Fairness for Users and Groups of Users  
These methods are aimed at ensuring fairness for individual or a group of users. Similar to the classification or statistical parity discussed in Section 3.1, fairness for users consider group fairness in which protected group incurs rating prediction errors in parity with the nonprotected group. [PERSON] and [PERSON] (2018) studied fairness in collaborative-filtering settings and identify new fairness metrics that can be optimized by adding fairness terms to the learning objective. They also show via experiments that their new metrics can better measure fairness than the baseline and are effectively useful in reducing bias. In another paper, [PERSON] and [PERSON] (2019) aimed to achieve the same notion of user fairness by adding a regularization term to the collaborative filtering objective function that measures the deviation with respect to the total weight assigned to the protected and nonprotected group member. A related but separate line of work looks at individual fairness in group recommendation, where the goal is to design systems that recommend to a group of users while respecting the individual preferences of the group members. In such a setting, the objective is not only to maximize the overall satisfaction among group members but also to ensure that the recommendations are fair in terms of minimizing the feeling of dissatisfaction among group members. Earlier work in this line mainly view fairness issues from the perspective of game theory and voting theory by treating the group decision process either as non-cooperative game or as a voting campaign without clearly modeling the trade-off between overall satisfaction and fairness of users ([PERSON] and [PERSON], 2010; [PERSON] and [PERSON], 2011; [PERSON] and [PERSON], 2012). In a more recent work, [PERSON] et al. (2018) investigated the group recommendation problem from a computational lens. Their method tries to maximize the satisfaction of each group member while minimizing the unfairness between them. The authors conceptualize such fairness-aware group recommendation as a multiobjective optimization problem consisting of two independent objectives: individual fairness and social welfare. In a similar line of research, user fairness is modeled in terms of satisfaction of the user with the group recommendation. [PERSON] et al. (2018) propose probabilistic models that capture the preference of a group towards a recommended package, and incorporate fairness into it by ensuring further devouring so that no user is consistently slighted by the item selection in the package. This idea has been further developed in subsequent papers ([PERSON] and [PERSON], 2011; [PERSON] and [PERSON], 2012). For example, in ([PERSON] and [PERSON], 2011), [PERSON] et al. develop fairness measures for package recommendation based on \"proportionality\" and \"envy-fairness\". **Proportionality. ** Given a package, \(P\), and a parameter, \(\triangle\), we say that a user \(u\) likes an item \(i\in P\) if \(i\) is ranked in the top-\(\triangle\)% of the preferences of \(u\) over all items. Consequently, for a user, \(u\), and a package, \(P\), we say that \(P\) is \(m\)-proportional for \(u\), for \(m\geq 1\), if there exists at least \(m\) items in \(P\), which are liked by \(u\). \begin{table}
\begin{tabular}{l l l} \hline \hline
**Type of RecSys Fairness** & **Focus** & **References** \\ \hline User \& Group & Ensure fairness for individual or a group of & [PERSON] and [PERSON] (2018) \\ Fairness & individuals, protected group incurs rating prediction & [PERSON] and [PERSON] (2019) \\  & errors in parity with the nonprotected group. & \\ \hline Item Fairness & Fairness among item categories when & [PERSON] (2019) \\  & recommended to users & [PERSON] et al. (2019) \\ \hline Multiple Stakeholder & Fairness for multiple & [PERSON] (2018) \\ Fairness & parties involved & [PERSON] et al. (2018) \\  & [PERSON] et al. (2018) \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Different types of fairness in recommender systems.