Proportionally Representative Clustering

In recent years, there has been a surge in effort to formalize notions of fairness in machine learning. We focus on clustering -- one of the fundamental tasks in unsupervised machine learning. We propose a new axiom ``proportional representation fairness'' (PRF) that is designed for clustering problems where the selection of centroids reflects the distribution of data points and how tightly they are clustered together. Our fairness concept is not satisfied by existing fair clustering algorithms. We design efficient algorithms to achieve PRF both for unconstrained and discrete clustering problems. Our algorithm for the unconstrained setting is also the first known polynomial-time approximation algorithm for the well-studied Proportional Fairness (PF) axiom (Chen, Fain, Lyu, and Munagala, ICML, 2019). Our algorithm for the discrete setting also matches the best known approximation factor for PF.Comment: Revised version includes a new author (Jeremy Vollen) and new results: Our algorithm for the unconstrained setting is also the first known polynomial-time approximation algorithm for the well-studied Proportional Fairness (PF) axiom (Chen, Fain, Lyu, and Munagala, ICML, 2019). Our algorithm for the discrete setting also matches the best known approximation factor for P

Family life in lockdown

The lockdown imposed following the COVID-19 pandemic of spring 2020 dramatically changed the daily lives and routines of millions of people worldwide. We analyse how such changes contributed to patterns of activity within the household using a novel survey of Italian, British, and American families in lockdown. A high percentage report disruptions in the patterns of family life, manifesting in new work patterns, chore allocations, and household tensions. Though men have taken an increased share of childcare and grocery shopping duties, reallocations are not nearly as stark as disruptions to work patterns might suggest, and families having to reallocate duties report greater tensions. Our results highlight tightened constraints budging up against stable and gendered patterns of intra-household cooperation norms. While the long-run consequences of the COVID-19 lockdown on family life cannot be assessed at this stage, we point towards the likely opportunities and challenges

Family life in lockdown

The lockdown imposed following the COVID-19 pandemic of spring 2020 dramatically changed the daily lives and routines of millions of people worldwide. We analyse how such changes contributed to gender inequality within the household using a novel survey of Italian, British, and American families in lockdown. A high percentage report disruptions in the patterns of family life, manifesting in new work patterns, chore allocations, and household tensions. Though men have taken an increased share of childcare and grocery shopping duties, reallocations are not nearly as stark as disruptions to work patterns might suggest, and families having to reallocate duties report greater tensions. Our results paint a picture of tightened constraints budging up against stable and gendered patterns of intra-household cooperation. While the long-run consequences of the COVID-19 lockdown on family life cannot be assessed at this stage, we point towards the likely opportunities and challenges

Coordinating Monetary Contributions in Participatory Budgeting

We formalize a framework for coordinating the funding of projects and sharing the costs among agents with quasi-linear utility functions and individual budgets. Our model contains the classical discrete participatory budgeting model as a special case, while capturing other well-motivated problems. We propose several important axioms and objectives and study how well they can be simultaneously satisfied. One of our main results is that whereas welfare maximization admits an FPTAS, welfare maximization subject to a well-motivated and very weak participation requirement leads to a strong inapproximability result. We show that this result is bypassed if we consider some natural restricted valuations or when we take an average-case heuristic approach

Best-of-Both-Worlds Fairness in Committee Voting

The best-of-both-worlds paradigm advocates an approach that achieves desirable properties both ex-ante and ex-post. We launch a best-of-both-worlds fairness perspective for the important social choice setting of approval-based committee voting. To this end, we initiate work on ex-ante proportional representation properties in this domain and formalize a hierarchy of properties including Individual Fair Share (IFS), Unanimous Fair Share (UFS), Group Fair Share (GFS), and their stronger variants. We establish their compatibility with well-studied ex-post concepts such as extended justified representation (EJR) and fully justified representation (FJR). Our first main result is a polynomial-time algorithm that simultaneously satisfies ex-post EJR, ex-ante GFS and ex-ante Strong UFS. Subsequently, we strengthen our ex-post guarantee to FJR and present an algorithm that outputs a lottery which is ex-post FJR and ex-ante Strong UFS, but does not run in polynomial time.Comment: This version contains a new section on Fully Justified Representation (FJR) as well as additional results on stronger ex-ante fair share notion