Collective Good and Optimization in Socioeconomic Systems

Abstract

Optimization is fundamentally grounded in perspective -- one party's desired outcome may induce unintended harm on another. Such cases of misalignment between designers' incentives and collective good therefore demand attention, especially when consequences are meaningful for society. To this end, we study three settings in which individualistic optimization and social good can conflict. First, we study how a centralized planner can modify the structure of a social or information network to reduce polarization. By formulating and analyzing a greedy approach to the planner's problem, we motivate two practical heuristics: coordinate descent and disagreement-seeking. We also introduce a setting where the population's innate opinions are adversarially chosen, which reduces to maximization of the Laplacian's spectral gap. We motivate a heuristic that adds edges spanning the cut induced by the spectral gap's eigenvector. These three heuristics are evaluated on real-world and synthetic networks. We observe that connecting disagreeing users is consistently effective, suggesting that the incentives of individuals and recommender systems may reinforce polarization.

Second, we build a model of the financial system in which banks control both their supply of liquidity, through cash holdings, and their exposures to risky interbank loans. The value of interbank loans drops when borrowing banks suffers liquidity shortages -- caused by the arrival of liquidity shocks that exceeds supply. In the decentralized setting, we study banks' optimal capital allocation under pure self-interest. The second centralized setting tasks a planner with maximizing collective welfare, i.e. sum of banks' utilities. We find that the decentralized equilibrium carries higher risk of liquidity shortages. As the number of banks grows, the relative gap in welfare is of constant order. We derive capitalization requirements for which decentralized banks hold the welfare-maximizing level of liquidity, and find that systemically important banks must face the greatest losses when suffering liquidity crises -- suggesting that bailouts can yield perverse incentives.

Finally, we study algorithmic fairness through the ethical frameworks of utilitarianism and John Rawls. Informally, these two theories of distributive justice measure the `good' as either a population's sum of utility, or worst-off outcomes, respectively. We present a parameterized class of objective functions that interpolates between these two conflicting notions of the `good'. By implementing this class of objectives on real-world datasets, we construct the tradeoff between utilitarian and Rawlsian notions of the `good'. Empirically, we see that increasing model complexity can manifest strict improvements to both measures of the `good'. This work suggests that model selection can be informed by a designer's preferences over the space of induced utilitarian and Rawlsian `good'.