With algorithms becoming ubiquitous in our society, it is important to ensure that they are compatible with our social values. In this thesis, we study some of the social aspects of algorithms including fairness, diversity, and resilience to strategic behavior of individuals.

Lack of diversity has a potential impact on discrimination against marginalized groups. Inspired by this issue, in the first part of this thesis, we study a notion of diversity in bipartite matching problems. Bipartite matching where agents on one side of a market are matched to one or more agents or items on the other side, is a classical model that is used in myriad application areas such as healthcare, advertising, education, and general resource allocation. In particular, we consider an application of matchings where a firm wants to hire, i.e. match, some workers for a number of teams. Each team has a demand that needs to be satisfied, and each worker has multiple features (e.g., country of origin, gender). We ask the question of how to assign workers to the teams in an efficient way, i.e. low-cost matching, while forming diverse teams with respect to all the features. Inspired by previous work, we balance whole-match diversity and economic efficiency by optimizing a supermodular function over the matching. Particularly, we show when the number of features is given as part of the input, this problem is NP-hard, and design a pseudo-polynomial time algorithm to solve this problem.

Next, we focus on studying fairness in optimization problems. Particularly, in this thesis, we study two notions of fairness in an optimization problem called correlation clustering. In correlation clustering, given an edge-weighted graph, each edge in addition to a weight has a positive or negative label. The goal is to obtain a clustering of the vertices into an arbitrary number of clusters that minimizes disagreements which is defined as the total weight of negative edges trapped inside a cluster plus the sum of weights of positive edges between different clusters. In the first fairness notion, assuming each node has a color, i.e. feature, our aim is to generate clusters with minimum disagreements, where the distribution of colors in each cluster is the same as the global distribution. Next, we switch our attention to a min-max notion of fairness in correlation clustering. In this notion of fairness, we consider a cluster-wise objective function that asks to minimize the maximum number of disagreements of each cluster. In this notion, the goal is to respect the quality of each cluster. We focus on designing approximation algorithms for both of these notions.

In the last part of this thesis, we take into consideration, the vulnerability of algorithms to manipulation and gaming. We study the problem of how to learn a linear classifier in presence of strategic agents that desire to be classified as positive and that are able to modify their position by a limited amount, making the classifier not be able to observe the true position of agents but rather a position where the agent pretends to be. We focus on designing algorithms with a bounded number of mistakes for a few different variations of this problem.