Collective Good and Optimization in Socioeconomic Systems

Daniel E. Rigobon’s May 2023 Princeton dissertation asks how optimization changes when a decision-maker accounts for effects on other people. Its three settings are social-network polarization, interbank lending and distributive objectives in supervised learning. Mathematical models and simulations make particular conflicts inspectable; they do not establish one objective that captures every meaning of the collective good.^[1]

Connections can change the collective outcome

The network chapter uses Friedkin–Johnsen opinion dynamics: people retain an innate opinion while being drawn toward their neighbors’ expressed opinions. Polarization measures dispersion around the population mean. A planner can modify connections to reduce that dispersion, rather than maximize each user’s satisfaction with a connection. Disagreement-seeking and coordinate-descent heuristics perform well on several real and synthetic networks. When innate opinions are instead chosen adversarially, reducing worst-case polarization becomes a problem of enlarging the graph’s spectral gap, which measures how strongly its structure resists separation into weakly connected communities (chapter 2).^[1]

The mechanism depends on attraction between connected opinions. The dissertation explicitly acknowledges that exposure to disagreement can have no effect or reinforce a position in real interactions. Its network simulations therefore support a conditional intervention in a specified model, rather than proving that recommending opposing views will depolarize actual users. Performance also varies across network structures.^[1]

The banking chapter exposes a different externality. Banks choose cash holdings and investments in one another’s projects. A liquidity shock exceeding a bank’s cash causes its project to lose value, harming its investors as well as itself. A self-interested bank does not fully internalize those creditor losses. The model compares decentralized choices with a planner maximizing the sum of banks’ utilities; the former carries greater liquidity-shortfall risk. Capitalization requirements are derived to align incentives under the model’s conditions. This is a formal financial-system analysis, not a measured effect of an implemented regulation (chapter 3).^[1]

Which predictive losses count most?

Chapter 4 assumes that a person’s predictive loss represents their disutility. Under that assumption, minimizing average loss is interpreted as utilitarian, while minimizing the largest individual loss is interpreted as Rawlsian. The latter is a simplified use of the difference principle. The chapter assumes basic liberties and fair opportunity are already satisfied, and acknowledges that real inequalities can violate those prerequisites. Optimizing a loss cannot establish that those conditions hold.^[1]

The proposed objective provides a smooth path between the two criteria. For losses ℓᵢ across n observations and a positive parameter λ, it minimizes:

L = (1/λ) log[(1/n) Σᵢ exp(λℓᵢ)]

As λ approaches zero, this objective approaches average loss; as it grows without bound, it approaches maximum loss. Its gradient gives more weight to observations with larger losses. The connection to a relaxed Veil of Ignorance assigns someone uniformly to one of the observed people and gives them an exponential utility function: λ then expresses constant absolute risk aversion. This is a specified ethical and utility model, rather than an empirical measurement of everyone’s preferences (§§4.2–4.3).^[1]

The family is closely related to existing tilted empirical risk minimization. The chapter’s contribution includes the distributive-justice interpretation, convergence analysis and examination of how model complexity changes the tradeoff. It does not introduce exponentiated-loss aggregation as an entirely new optimization idea.^[1]

What the experiments show

The experiments use COMPAS, Bank Marketing, Adult Income, Credit Card Default, and Communities & Crime data. They compute average and maximum individual loss within the training sample, also examining average loss within specified groups. Logistic regression displays the clearest average–maximum tradeoff on COMPAS and Communities & Crime: reducing the largest loss increases the average. Other datasets show much less worst-case improvement from changing λ (§4.4).^[1]

The COMPAS complexity comparison adds neural networks with one through four layers. Greater depth can reduce maximum individual loss at a similar average loss. This illustrates how enlarging the model class can improve the available choices; it does not show that deeper models always improve both criteria on unseen people. Training details are delegated to linked code, and the displayed measurements do not establish out-of-sample welfare effects.^[1]

Individual and group objectives also differ. A group’s loss here is its average, which can conceal variation among its members. In the COMPAS example, movement toward more equal group averages can increase both the average and maximum group loss. Equality of those averages is consequently distinct from improving the worst group or worst individual. The result is specific to the model, loss and data, not a general rejection of equality.^[1]

Choosing a frontier still requires values

For Social Alignment, the dissertation’s common point is that a useful optimizer inherits a choice about whose outcomes count and how they are combined. The fairness chapter makes that choice explicit instead of treating accuracy and fairness as self-defining opposites. It leaves other ethical theories, preprocessing and postprocessing, statistical generalization, and wider implementation effects for further work. Better optimization can expand the options while leaving the selection among them a substantive social decision.^[1]