On Meritocracy in Optimal Set Selection

We consider the problem of selecting a set of individuals from a candidate population in order to maximise utility. When the utility function is defined over sets, this raises the question of how to define meritocracy. We define and analyse an appropriate notion of meritocracy derived from the utility function. We introduce the notion of expected marginal contributions of individuals and analyse its links to the underlying optimisation problem, our notion of meritocracy, and other notions of fairness such as the Shapley value. We also experimentally analyse the effect of different policy structures on the utility and meritocracy in a simulated college admission setting including constraints on statistical parity

On Fair Selection in the Presence of Implicit Variance

Quota-based fairness mechanisms like the so-called Rooney rule or four-fifths rule are used in selection problems such as hiring or college admission to reduce inequalities based on sensitive demographic attributes. These mechanisms are often viewed as introducing a trade-off between selection fairness and utility. In recent work, however, Kleinberg and Raghavan showed that, in the presence of implicit bias in estimating candidates' quality, the Rooney rule can increase the utility of the selection process. We argue that even in the absence of implicit bias, the estimates of candidates' quality from different groups may differ in another fundamental way, namely, in their variance. We term this phenomenon implicit variance and we ask: can fairness mechanisms be beneficial to the utility of a selection process in the presence of implicit variance (even in the absence of implicit bias)? To answer this question, we propose a simple model in which candidates have a true latent quality that is drawn from a group-independent normal distribution. To make the selection, a decision maker receives an unbiased estimate of the quality of each candidate, with normal noise, but whose variance depends on the candidate's group. We then compare the utility obtained by imposing a fairness mechanism that we term $\gamma$-rule (it includes demographic parity and the four-fifths rule as special cases), to that of a group-oblivious selection algorithm that picks the candidates with the highest estimated quality independently of their group. Our main result shows that the demographic parity mechanism always increases the selection utility, while any $\gamma$-rule weakly increases it. We extend our model to a two-stage selection process where the true quality is observed at the second stage. We discuss multiple extensions of our results, in particular to different distributions of the true latent quality.Comment: 27 pages, 10 figures, Economics and Computation (EC'20

Dealing with Intransitivity, Non-Convexity, and Algorithmic Bias in Preference Learning

Rankings are ubiquitous since they are a natural way to present information to people who are making decisions. There are seemingly countless scenarios where rankings arise, such as deciding whom to hire at a company, determining what movies to watch, purchasing products, understanding human perception, judging science fair projects, voting for political candidates, and so on. In many of these scenarios, the number of items in consideration is prohibitively large, such that asking someone to rank all of the choices is essentially impossible. On the other hand, collecting preference data on a small subset of the items is feasible, e.g., collecting answers to ``Do you prefer item A or item B?" or ``Is item A closer to item B or item C?". Therefore, an important machine learning task is to learn a ranking of the items based on this preference data. This thesis theoretically and empirically addresses three key challenges of preference learning: intransitivity in preference data, non-convex optimization, and algorithmic bias. Chapter 2 addresses the challenge of learning a ranking given pairwise comparison data that violates rational choice such as intransitivity. Our key observation is that two items compared in isolation from other items may be compared based on only a salient subset of features. Formalizing this framework, we propose the salient feature preference model and prove a sample complexity result for learning the parameters of our model and the underlying ranking with maximum likelihood estimation. Chapter 3 addresses the non-convexity of an optimization problem inspired by ordinal embedding, which is a preference learning task. We aim to understand the landscape, that is local minimizers and global minimizers, of the non-convex objective, which corresponds to the hinge loss arising from quadratic constraints. Under certain assumptions, we give necessary conditions for non-global, local minimizers of our objective and additionally show that in two dimensions, every local minimizer is a global minimizer. Chapters 4 and 5 address the challenge of algorithmic bias. We consider training machine learning models that are fair in the sense that their performance is invariant under certain sensitive perturbations to the inputs. For example, the performance of a resume screening system should be invariant under changes to the gender and ethnicity of the applicant. We formalize this notion of algorithmic fairness as a variant of individual fairness. In Chapter 4, we consider classification and develop a distributionally robust optimization approach, SenSR, that enforces this notion of individual fairness during training and provably learns individually fair classifiers. Chapter 5 builds upon Chapter 4. We develop a related algorithm, SenSTIR, to train provably individually fair learning-to-rank (LTR) models. The proposed approach ensures items from minority groups appear alongside similar items from majority groups. This notion of fair ranking is based on the individual fairness definition considered in Chapter 4 for the supervised learning context and is more nuanced than prior fair LTR approaches that simply provide underrepresented items with a basic level of exposure. The crux of our method is an optimal transport-based regularizer that enforces individual fairness and an efficient algorithm for optimizing the regularizer.PHDApplied and Interdisciplinary MathematicsUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/166120/1/amandarg_1.pd