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Computational Perspectives on Democracy

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Computational Perspectives on Democracy Computational Perspectives on Democracy Anson Kahng CMU-CS-21-126 August 2021 Computer Science Department School of Computer Science Carnegie Mellon University Pittsburgh, PA 15213 Thesis Committee: Ariel Procaccia (Chair) Chinmay Kulkarni Nihar Shah Vincent Conitzer (Duke University) David Pennock (Rutgers University) Submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy. Copyright c 2021 Anson Kahng This research was sponsored by the National Science Foundation under grant numbers IIS-1350598, CCF- 1525932, and IIS-1714140, the Department of Defense under grant number W911NF1320045, the Office of Naval Research under grant number N000141712428, and the JP Morgan Research grant. The views and conclusions contained in this document are those of the author and should not be interpreted as representing the official policies, either expressed or implied, of any sponsoring institution, the U.S. government or any other entity. Keywords: Computational Social Choice, Theoretical Computer Science, Artificial Intelligence For Grandpa and Harabeoji. iv Abstract Democracy is a natural approach to large-scale decision-making that allows people affected by a potential decision to provide input about the outcome. However, modern implementations of democracy are based on outdated infor- mation technology and must adapt to the changing technological landscape. This thesis explores the relationship between computer science and democracy, which is, crucially, a two-way street—just as principles from computer science can be used to analyze and design democratic paradigms, ideas from democracy can be used to solve hard problems in computer science. Question 1: What can computer science do for democracy? To explore this first question, we examine the theoretical foundations of three democratic paradigms: liquid democracy, participatory budgeting, and multiwinner elections. Each of these paradigms broadly redistributes power from the few to the many: For instance, liquid democracy allows people to choose delegates more flexibly and participatory budgeting enables citizens to directly influence government spending toward public projects. However, be- cause these paradigms are relatively new, their theoretical properties are rel- atively unexplored. We analyze each of these three settings from the point of view of computational social choice, which is a mathematical framework for collective decision-making. In particular, we focus on a combination of robust- ness, fairness, and efficiency with the end goal of providing actionable advice for future iterations of these paradigms. Question 2: What can democracy do for computer science? Toward this end, we explore two settings in which democratic principles can be used to augment approaches to making difficult decisions—in our case, automating ethical decision-making and hiring in online labor markets. Both of these problems are difficult in the sense that there is no universally agreed- upon function to optimize, making them a poor fit for traditional approaches in computer science. Instead, we try to emulate a world in which we can get input from people in order to arrive at a “societal” decision. In each of these settings, we first propose and analyze a theoretical approach that leads a single decision, and then, in collaboration with HCI researchers, run experiments in the real world to test the efficacy and practicability of our approaches in the real world. vi Acknowledgments First and foremost, I must thank Ariel Procaccia, my advisor, for being the best advisor anyone could hope for. You have taught me so much, not only technically, but also with respect to writing effective papers, giving better talks, mentoring junior students, and providing me with a sustainable example of healthy (and productive!) work-life balance. I will strive to learn from and emulate your unrivaled blend of brilliance, eloquence, and patience. Thank you for everything. To my thesis committee, Vince Conitzer, Chinmay Kulkarni, David Pen- nock, and Nihar Shah, thank you for your insightful comments and wonderful questions that have helped me structure and present my work. I truly appre- ciate all the comments and questions, even if I may not have all the answers yet! To the professors at Harvard that led me down the grad school path: David and Yiling. Thank you for opening my eyes to the wonders of Econ-CS (or CS- Econ here at CMU), for supervising my first attempt at independent research (David), and for your continued support and guidance over the years. To my collaborators: Gerdus Benadè, Allissa Chan, Rupert Freeman, Paul Gölz, Bernhard Haeupler, Ellis Hershkowitz, Gregory Kehne, Ji Tae Kim, Yas- mine Kotturi, Chinmay Kulkarni, David Kurokawa, Daniel Kusbit, Min Kyung Lee, Siheon Lee, Simon Mackenzie, Ritesh Noothigattu, David Pennock, Do- minik Peters, Ariel Procaccia, Alex Psomas, Daniel See, and Xinran Yuan. I truly enjoyed collaborating with each and every one of you, and thank you for bringing your expertise and hard work to the projects we worked on together. To my friends: Ellis, Alex, Greg, Roie, Mark, Kevin, Paul, Bailey, Jalani, Ellen, Ryan, Costin, Sidu, Ved, Kevin, Carl, Lisa, Amna, Michelle, Ramya, Chara, Robi, Andrew, Justin, and all others. Thank you for your continued support and companionship through this journey. Grad school would have been an altogether different and darker time without you. To my family: Dad, Mom, Alex, Aidan, Aunt Lyn Sue, Grandma, Halmoni, and everyone else. Thank you for loving and supporting me since the very beginning, and for instilling in me an innate curiosity and love of learning. I owe you everything, and hope to make you proud. To Soyeun. Last but certainly not least, thank you for your unwavering support through the highs and lows of grad school. I truly could not have done it without your invariably sage advice, spot-on presentation notes, and emotional and moral support. viii Contents 0 Introduction1 0.1 Structure....................................3 1 Liquid Democracy7 1.1 An Algorithmic Perspective on Liquid Democracy..............7 1.1.1 Overview of the Model and Results..................8 1.1.2 Related Work..............................9 1.1.3 The Model................................ 10 1.1.4 Impossibility for Local Mechanisms.................. 12 1.1.5 Possibility for Non-Local Mechanisms................. 20 1.2 Minimizing the Maximum Weight of Voters in Liquid Democracy..... 29 1.2.1 Our Approach and Results....................... 30 1.2.2 Related Work.............................. 31 1.2.3 Algorithmic Model and Results.................... 32 1.2.4 Probabilistic Model and Results.................... 38 1.2.5 Simulations............................... 46 1.3 Conclusions................................... 51 1.3.1 An Algorithmic Perspective on Liquid Democracy.......... 51 1.3.2 Minimizing the Maximum Weight of Voters............. 52 2 District-Fair Participatory Budgeting 55 2.1 Introduction................................... 55 2.2 Related Work.................................. 57 2.3 Formal Problem, Notation and Definitions.................. 58 2.3.1 NP-Hardness.............................. 59 2.4 Optimal District-Fair Lottery......................... 60 2.5 Optimal DF1 Outcome with Extra Budget.................. 63 2.6 Conclusions................................... 66 3 Representation in Multiwinner Elections 69 3.1 Introduction................................... 69 3.2 Related Work.................................. 70 3.3 Preliminaries.................................. 71 3.4 Justified Representation in VNW Elections.................. 74 ix 3.5 Deterministic Rules............................... 75 3.6 Randomized Rules............................... 76 3.7 Conclusions................................... 79 4 Virtual Democracy 81 4.1 Virtual Democracy in Theory......................... 81 4.1.1 Related Work.............................. 83 4.1.2 Preliminaries.............................. 84 4.1.3 From Predictions to Mallows...................... 85 4.1.4 Robustness of Borda Count...................... 87 4.1.5 Non-Robustness of PMC Rules.................... 90 4.1.6 Empirical Results............................ 91 4.2 Virtual Democracy in Practice: 412 Food Rescue.............. 93 4.2.1 Introduction............................... 93 4.2.2 Governing Algorithm Design and Participation............ 95 4.2.3 The WeBuildAI Framework...................... 98 4.2.4 Case study: Matching algorithm for donation allocation....... 100 4.2.5 Individual Belief Model Building................... 104 4.2.6 Collective aggregation......................... 108 4.2.7 Explanation and decision support................... 109 4.2.8 Findings: the impact of participatory algorithm design....... 110 4.2.9 Evaluation of Algorithmic Outcomes................. 115 4.2.10 Discussion................................ 118 4.3 Conclusions................................... 122 4.3.1 Virtual Democracy, in Theory..................... 122 4.3.2 Virtual Democracy, in Practice: WeBuildAI............. 122 5 Impartial Ranking 125 5.1 Impartial Ranking, in Theory......................... 125 5.1.1 Our Approach and Results....................... 126 5.1.2 Related Work.............................. 127 5.1.3 Preliminaries.............................. 127 5.1.4 Measures of Error............................ 128 5.1.5 The k-Partite Algorithm....................... 130 5.1.6 The Committee Algorithm...................... 133 5.1.7 Experiments............................... 134 5.2 Impartial
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