Algorithmic Processes And Social Values

In this thesis, we study several problems at the interface of algorithmic decision-making and society, focusing on the tensions that arise between these processes and social values like fairness and privacy. In the first chapter, we examine the design of financial portfolios which adequately serve all segments of the population. In the second, we examine an allocation setting where the allocator wishes to distribute a scarce resource across many groups fairly, but does not know ahead of time which groups have a need for the resource. In the third, we study a game-theoretic model of information aggregation and the effects of individuals acting to preserve the privacy of their personal beliefs on the collective welfare of the population. Finally, we look at some of the issues that arise from the desire to apply automated techniques to problems in redistricting, including fundamental flaws in the definitions and frameworks typically used

Algorithmic Processes and Social Values

In this thesis, we study several problems at the interface of algorithmic decision-making and society, focusing on the tensions that arise between these processes and social values like fairness and privacy. In the first chapter, we examine the design of financial portfolios which adequately serve all segments of the population. In the second, we examine an allocation setting where the allocator wishes to distribute a scarce resource across many groups fairly, but does not know ahead of time which groups have a need for the resource. In the third, we study a game-theoretic model of information aggregation and the effects of individuals acting to preserve the privacy of their personal beliefs on the collective welfare of the population. Finally, we look at some of the issues that arise from the desire to apply automated techniques to problems in redistricting, including fundamental flaws in the definitions and frameworks typically used

Total Variation Isoperimetric Profiles

© 2019 Society for Industrial and Applied Mathematics Publications. All rights reserved. Applications such as political redistricting demand quantitative measures of geometric compactness to distinguish between simple and contorted shapes. While the isoperimetric quotient, or ratio of area to perimeter squared, is commonly used in practice, it is sensitive to noisy data and irrelevant geographic features like coastline. These issues are addressed in theory by the isoperimetric profile, which plots the minimum perimeter needed to inscribe regions of different prescribed areas within the boundary of a shape. Efficient algorithms for computing this profile, however, are not known in practice. Hence, in this paper, we propose a convex Eulerian relaxation of the isoperimetric profile using total variation. We prove theoretical properties of our relaxation, showing that it still satisfies an isoperimetric inequality and yields a convex function of the prescribed area. Furthermore, we provide a discretization of the problem, an optimization technique, and experiments demonstrating the value of our relaxation

Total variation isoperimetric profiles

Applications such as political redistricting demand quantitative measures of geometric compactness to distinguish between simple and contorted shapes. While the isoperimetric quotient, or ratio of area to perimeter squared, is commonly used in practice, it is sensitive to noisy data and irrelevant geographic features like coastline. These issues are addressed in theory by the isoperimetric profile, which plots the minimum perimeter needed to inscribe regions of different prescribed areas within the boundary of a shape. Efficient algorithms for computing this profile, however, are not known in practice. Hence, in this paper, we propose a convex Eulerian relaxation of the isoperimetric profile using total variation. We prove theoretical properties of our relaxation, showing that it still satisfies an isoperimetric inequality and yields a convex function of the prescribed area. Furthermore, we provide a discretization of the problem, an optimization technique, and experiments demonstrating the value of our relaxation