Policy Design in Long-run Welfare Dynamics

Jiduan Wu, Rediet Abebe, Moritz Hardt, Ana-Andreea Stoica

Keywords: Long-run welfare, policy design, Rawlsian policy and utilitarianism

Abstract: We study a stochastic dynamic model of long-term welfare in a population. Individuals in our model have welfare that improves with intervention and deteriorates in the absence of treatment. The planner can treat one individual at each time step. We contrast two fundamental policies in our model. The utilitarian policy greedily maximizes welfare improvement at each step. The Rawlsian policy intervenes on the individual of lowest welfare. Although hugely influential as a normative proposal, Rawlsian policies have been criticized for failing to optimize social welfare. We prove that, surprisingly, in a meaningful range of parameters Rawlsian policy has greater long-run utility than the utilitarian policy even though it is inferior on short time horizons. Specifically, this is true provided that treatment effects satisfy a weak homogeneity assumption, and the welfare dynamics satisfy a rich-get-richer and poor-get-poorer condition. We extend our results with a comprehensive comparison of different policies under different parameter regimes. Through semi-synthetic simulation studies, we evaluate various policies in cases where the assumptions of our theorems do not hold. Our results illustrate that comparing policies based on short-term evaluations can lead to misleading conclusions.

Primary Area: alignment, fairness, safety, privacy, and societal considerations

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Submission Number: 11925