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Social Choice for Social Good

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Social Choice for Social Good Social Choice for Social Good Paul Gölz In this thesis, we study ways in which computational social choice can contribute to social good, by providing better democratic representation and by allocating scarce goods. On the side of political representation, we study multiple emerging innovations to the democratic process. If legislative elections with proportional representation allow for approval-based ballots rather than the choice of a single party, we give voting rules that satisfy attractive axioms of proportionality. For liquid democracy, a kind of transitive proxy voting, we show how an extension to multiple delegation options can decrease the concentration of power in few hands. Finally, for sortition, a system in which representatives are randomly selected citizens, we develop sampling algorithms, both for the case where all citizens participate if sampled and for the case in which participants self select. Concerning the allocation of scarce goods, we investigate the applications of refugee resettlement and kidney exchange. For refugee resettlement, we show how submodular optimization can lead to more diverse matchings that might increase employment by reducing competition for jobs between similar refugees. In kidney exchange, we give approximately incentive-compatible mechanisms for transplant chains in a semi-random model of compatibilities. Finally, we present three directions for future research, revisiting the topics of sortition, refugee resettlement, and semi-random models. 1 Contents 1 Introduction 3 1.1 Improving Democratic Representation.......................3 1.2 Allocating Scarce Goods...............................5 2 Approval-Based Legislative Apportionment6 2.1 Related Work.....................................8 2.2 Voting Rules with Strong Proportionality Guarantees...............8 3 Liquid Democracy 10 3.1 Related Work..................................... 11 3.2 Minimizing Supervoter Weight in Liquid Democracy............... 12 4 Sortition 14 4.1 Related Work..................................... 15 4.2 The Case of Full Participation........................... 16 4.3 Limited Participation................................ 19 5 Refugee Resettlement 21 5.1 Related Work..................................... 22 5.2 Migration as Submodular Optimization...................... 23 6 Kidney Exchange 24 6.1 Related Work..................................... 26 6.2 Mechanism Design for Kidney Exchange in a Semi-Random Model....... 27 7 Future Directions 30 7.1 Sortition with Fairness to the Pool......................... 30 7.2 Online Refugee Matching.............................. 31 7.3 Semi-Random Models in Fair Division....................... 32 2 1 Introduction In advising young students of science, Thomas Jefferson hoped to “keep their attention fixed on the main objects of all science, the freedom & happiness of man” [65]. How can computer science — which was certainly not on Jefferson’s mind — further the same goals? There is reason to believe that computer science can have a positive impact on society. Quite obviously, what computers can do has increased tremendously over the recent past, and computation has already deeply impacted many areas of society. However, technology need not be the only way in which computer science can contribute to the social good. Indeed, in the field of computational social choice, computational techniques have proved to bring new perspectives and solutions to theoretical social questions that once were the sole domain of political scientists, economists, and some mathematicians [26]. The two parts of this thesis loosely correspond to Jefferson’s ideals of freedom and happiness. In the first part (“freedom”), we study three democratic innovations: liquid democracy, approval-based legislative voting, and sortition. These innovations have in common that they identify new ways of selecting democratic representatives, hopefully in a way that gives citizens more freedom to have their voices impact the decisions of society. By informing the development of these nascent paradigms of democratic participation, we hope to strengthen the effectiveness and legitimacy of liberal democracy. The second part (“happiness”) studies two allocation problems that deeply impact people’s lifes: the allocation of resettled refugees to cities and the allocation of kidney transplants in a paired-donation system. By placing refugees where they can thrive best, and by encouraging hospitals to pool their patients and allow for more kidney transplants, the welfare of affected people can increase. General Background The field of computational social choice is concerned with the algorith- mic aspects of group decision making. In the first part of the thesis, the decision being studied is not an individual policy decision, but a decision on a set of representatives. This line of work has its roots in the area of multi-winner elections, in which a committee of candidates has to be selected [75]. However, our problems deviate from the classical setup in terms of the ballot format considered and in terms of the committees produced (whether a single entity can be chosen multiple times). The problems in the second part (in a very general sense) produce matchings in a graph, and borrow tools from matching and mechanism design. 1.1 Improving Democratic Representation The first part of this thesis studies three extensions to the current practice of democracy. On a high level, the history of democracy is a story of great success. Over the span of just 70 years, the share of the world population living in democratic systems increased from 11% in 1945 to 55% in 2015.1 While democracy proper only refers to the form of governance, political freedom and other civil liberties are often closely linked, with Mulligan, Gil, and Sala-i-Martin [87] finding that democracies are less “likely to torture, execute, regulate religion, censor the press and spend a lot of money on the military,” as compared to authoritarian countries. 1https://ourworldindata.org/grapher/world-pop-by-political-regime?stackMode=relative 3 Despite encouraging long-term trends, recent signs show that democracy’s success cannot be taken as granted in the future. Not only have multiple political systems become more authoritarian in the past decade, but support for democracy has dwindled even in supposedly consolidated democracies such as France and the United States [52]. It remains to hope that this dissatisfaction is not directed against the values of democracy itself but against the current implementation of this idea. For instance, in the median over 34 countries across the globe,2 64% diagree with the statement that “[m]ost elected officials care what people like me think,” and this view is highly correlated with low satisfaction with democracy. If, as Churchill said, “democracy is the worst form of Government except for all those other forms that have been tried,” it is worth investigating alternative ways of democratic decision making, in which citizens have a more ways of making their voices heard. We study three such systems, ordered from least disruptive to most disruptive: First, we study approval-based legislative apportionment, which extend legislative elections in systems of proportional representation. In the status quo, voters can vote for a single party and a fixed number of seats in the legislature is apportioned to the parties in a way that aims to represent parties proportionally to their number of votes. The restriction to indicating a single party can lead to coordination problem, where different voter groups could profit from voting for a consensus candidate, but fail to do so without coordination. Approval-based apportionment lifts the restriction of indicating a single party and instead allows voters to support any subset of the parties. We propose apportionment rules for this setting that guarantee attractive axioms of representation [30]. Liquid democracy goes even further by no longer requiring that political influence be mediated by parties and professional politicians. Instead, direct democracy is extended by allowing citizens to (transitively) delegate their voting power to any other citizen of their choice. In the largest liquid-democracy experiment so far, observers were concerned that too much power ended up being concentrated in the hands of few voters. We suggest an extension to liquid democracy in which agents can indicate multiple possible delegations that they are indifferent between, and in which a centralized algorithm chooses one of these delegations per agent such that the maximum power of any voter is minimized. In a stochastic model of delegation network formation, we observe a “power of two choices” effect, which suggests that this extension could drastically reduce the concentration of power in liquid democracy [55]. Finally, the system of sortition uses randomization to overcome the requirement that every member of the population must make a decision. Once a representative panel is selected from the population, it is possible to spend resources on informing the panel on the topic (which allows the panel to make an informed choice) and to have the panel deliberate (which allows the panel to take into account perspectives from all across the population). The democratic legitimacy of such a panel rests on the properties of sampling process, which ensure equal access to individuals and groups. If everybody in the population participates when sampled,3 we design a variant of stratified sampling that selects every member of the population
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