# Allocating Opportunities in a Dynamic Model of Intergenerational Mobility

arXiv: https://arxiv.org/abs/2101.08451 · HTML: https://mlsanity.com/paper/2101.08451/

## Key facts

- Cited by 12 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 21 Jan 2021.

## Built on by (most cited first, 12 of 12)

- [What-is and How-to for Fairness in Machine Learning: A Survey, Reflection, and Perspective](https://mlsanity.com/paper/2206.04101/) (2022)
- [The Long Arc of Fairness: Formalisations and Ethical Discourse](https://mlsanity.com/paper/2203.06038/) (2022)
- [Towards Substantive Conceptions of Algorithmic Fairness: Normative Guidance from Equal Opportunity Doctrines](https://mlsanity.com/paper/2207.02912/) (2022)
- [Fairness and Sequential Decision Making: Limits, Lessons, and Opportunities](https://mlsanity.com/paper/2301.05753/) (2023)
- [Maximizing Submodular Functions for Recommendation in the Presence of Biases](https://mlsanity.com/paper/2305.02806/) (2023)
- [Minimum Levels of Interpretability for Artificial Moral Agents](https://mlsanity.com/paper/2307.00660/) (2023)
- [Interpolating Item and User Fairness in Multi-Sided Recommendations](https://mlsanity.com/paper/2306.10050/) (2023)
- [Subset Selection Based On Multiple Rankings in the Presence of Bias: Effectiveness of Fairness Constraints for Multiwinner Voting Score Functions](https://mlsanity.com/paper/2306.09835/) (2023)
- [The Hidden Cost of Waiting for Accurate Predictions](https://mlsanity.com/paper/2503.00650/) (2025)
- [Achievement and Fragility of Long-term Equitability](https://mlsanity.com/paper/2206.12333/) (2022)
- [Centralized Selection with Preferences in the Presence of Biases](https://mlsanity.com/paper/2409.04897/) (2024)
- [Price of Fairness in Short-Term and Long-Term Algorithmic Selections](https://mlsanity.com/paper/2605.06227/) (2026)

## Abstract (arXiv)

Opportunities such as higher education can promote intergenerational mobility, leading individuals to achieve levels of socioeconomic status above that of their parents. We develop a dynamic model for allocating such opportunities in a society that exhibits bottlenecks in mobility; the problem of optimal allocation reflects a trade-off between the benefits conferred by the opportunities in the current generation and the potential to elevate the socioeconomic status of recipients, shaping the composition of future generations in ways that can benefit further from the opportunities. We show how optimal allocations in our model arise as solutions to continuous optimization problems over multiple generations, and we find in general that these optimal solutions can favor recipients of low socioeconomic status over slightly higher-performing individuals of high socioeconomic status -- a form of socioeconomic affirmative action that the society in our model discovers in the pursuit of purely payoff-maximizing goals. We characterize how the structure of the model can lead to either temporary or persistent affirmative action, and we consider extensions of the model with more complex processes modulating the movement between different levels of socioeconomic status.