Further Reading: Fairness — Definitions, Tensions, and Trade-offs

The sources below provide deeper engagement with the themes introduced in Chapter 15. They are organized by topic and include the original technical papers that defined the field, accessible introductions, and critical analyses of the fairness landscape.

The Original Impossibility Results

Chouldechova, Alexandra. "Fair Prediction with Disparate Impact: A Study of Bias in Recidivism Prediction Instruments." Big Data 5, no. 2 (2017): 153-163. The formal proof that when base rates differ across groups, a classifier cannot simultaneously achieve equal false positive rates, equal false negative rates, and equal positive predictive values. Chouldechova's proof is remarkably concise and is accessible to readers with basic statistical knowledge. This paper is the foundational reference for the impossibility theorem as applied to risk assessment tools like COMPAS.

Kleinberg, Jon, Sendhil Mullainathan, and Manish Raghavan. "Inherent Trade-Offs in the Fair Determination of Risk Scores." Proceedings of Innovations in Theoretical Computer Science (ITCS), 2017. An independently derived impossibility result proving that calibration, balance for the positive class, and balance for the negative class cannot be simultaneously achieved (except in trivial cases). Kleinberg et al.'s framing is more general than Chouldechova's and provides a complementary perspective on the mathematical constraints that fairness-constrained systems face.

Surveys and Frameworks

Narayanan, Arvind. "21 Fairness Definitions and Their Politics." Tutorial at Conference on Fairness, Accountability, and Transparency (FAT)*, February 2018. Available at: https://www.youtube.com/watch?v=jIXIuYdnyyk A widely viewed tutorial that catalogs 21 distinct mathematical definitions of fairness and explains the political assumptions behind each. Narayanan's presentation is accessible, engaging, and essential for understanding the breadth of the fairness landscape. The tutorial's central message — that choosing a fairness definition is choosing a set of values — aligns directly with this chapter's argument.

Corbett-Davies, Sam, and Sharad Goel. "The Measure and Mismeasure of Fairness: A Critical Review of Fair Machine Learning." arXiv preprint arXiv:1808.00023, 2018. The most comprehensive survey of fairness definitions, their relationships, and their limitations. Corbett-Davies and Goel organize the landscape into three traditions: anti-classification (excluding protected attributes), classification parity (equalizing metrics across groups), and calibration (equalizing predictive accuracy). Their critical assessment of each tradition provides invaluable perspective for students navigating the fairness debate.

Berk, Richard, Hoda Heidari, Shahin Jabbari, Michael Kearns, and Aaron Roth. "Fairness in Criminal Justice Risk Assessments: The State of the Art." Sociological Methods & Research 50, no. 1 (2021): 3-44. A comprehensive review of how fairness definitions apply specifically to criminal justice risk assessment. Berk et al. evaluate multiple fairness criteria in the context of bail, sentencing, and parole decisions, discussing practical implementation challenges and institutional constraints. Essential for students interested in the criminal justice applications of the chapter's framework.

Foundational Technical Papers

Hardt, Moritz, Eric Price, and Nati Srebro. "Equality of Opportunity in Supervised Learning." Proceedings of the 30th International Conference on Neural Information Processing Systems (NeurIPS), 3315-3323. 2016. The paper that formalized equalized odds and equal opportunity as fairness criteria for supervised learning. Hardt et al. also propose a post-processing method for achieving equalized odds by adjusting classifier thresholds. The paper is technically rigorous but accessible to readers familiar with basic machine learning concepts.

Dwork, Cynthia, Moritz Hardt, Toniann Pitassi, Omer Reingold, and Richard Zemel. "Fairness through Awareness." Proceedings of the 3rd Innovations in Theoretical Computer Science Conference, 214-226. ACM, 2012. The foundational paper on individual fairness, proposing the principle that "similar individuals should be treated similarly." Dwork et al. formalize this intuition using a metric space framework. The paper highlights the key challenge: defining the similarity metric. This is the paper that first demonstrated that individual fairness, while appealing, requires value-laden decisions about what "similarity" means.

Corbett-Davies, Sam, Emma Pierson, Avi Feller, Sharad Goel, and Aziz Huq. "Algorithmic Decision Making and the Cost of Fairness." Proceedings of the 23rd ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, 797-806. ACM, 2017. This paper proposes a cost-based framework for navigating the impossibility theorem. Rather than choosing one fairness definition, the authors argue that the fairness choice should be framed as an optimization problem in which different types of errors have explicit costs. The framework does not eliminate the value judgment but makes it transparent and quantifiable.

Philosophical and Ethical Foundations

Rawls, John. A Theory of Justice. Cambridge, MA: Harvard University Press, 1971. Rawls's theory of justice — particularly the difference principle (inequalities are justified only if they benefit the least advantaged members of society) and the veil of ignorance (just principles are those chosen without knowing one's position in society) — provides philosophical grounding for the demographic parity perspective. Understanding Rawls is essential for connecting algorithmic fairness to the broader tradition of political philosophy.

Sen, Amartya. The Idea of Justice. Cambridge, MA: Harvard University Press, 2009. Sen argues that justice does not require a single, unified theory but rather the ability to compare alternatives and reduce clearly identifiable injustices. His "capabilities approach" — evaluating fairness by what people are actually able to do and be — offers a lens for assessing algorithmic systems that goes beyond statistical metrics. Particularly relevant for students who find the impossibility theorem paralyzing: Sen's framework suggests that partial improvements in fairness are valuable even when perfect fairness is unachievable.

Binns, Reuben. "Fairness in Machine Learning: Lessons from Political Philosophy." Proceedings of the 1st Conference on Fairness, Accountability and Transparency, 149-159. PMLR, 2018. Binns maps the major fairness definitions in machine learning to corresponding positions in political philosophy: demographic parity to luck egalitarianism, equalized odds to procedural justice, calibration to meritocratic ideals. This paper is essential for students seeking to understand why different fairness definitions seem intuitively appealing to different people — the answer lies in the philosophical traditions those definitions embody.

Applied Fairness in Practice

Selbst, Andrew D., danah boyd, Sorelle A. Friedler, Suresh Venkatasubramanian, and Janet Vertesi. "Fairness and Abstraction in Sociotechnical Systems." Proceedings of the Conference on Fairness, Accountability, and Transparency (FAT)*, 59-68. ACM, 2019. This influential paper identifies five "traps" that arise when fairness is treated as a purely technical property divorced from social context. The Framing Trap (failing to model the full sociotechnical system), the Portability Trap (assuming fairness transfers across contexts), the Formalism Trap (conflating mathematical formalization with substantive fairness), the Ripple Effect Trap (ignoring downstream consequences), and the Solutionism Trap (assuming fairness is a problem technology can solve). Essential reading for any student who wants to apply fairness definitions in practice without falling into reductive thinking.

Mitchell, Shira, Eric Potash, Solon Barocas, Alexander D'Amour, and Kristian Lum. "Algorithmic Fairness: Choices, Assumptions, and Definitions." Annual Review of Statistics and Its Application 8 (2021): 141-163. A comprehensive review that contextualizes fairness definitions within the choices and assumptions that precede them. Mitchell et al. argue that many fairness debates are actually debates about upstream choices (how to define the target variable, what data to use, which populations to serve) rather than about the fairness metric itself. This reframing is valuable for students who find the fairness definition landscape overwhelming.

Raji, Inioluwa Deborah, Andrew Smart, Rebecca N. White, Margaret Mitchell, Timnit Gebru, Ben Hutchinson, Jamila Smith-Loud, Daniel Theron, and Parker Barnes. "Closing the AI Accountability Gap: Defining an End-to-End Framework for Internal Algorithmic Auditing." Proceedings of the 2020 Conference on Fairness, Accountability, and Transparency (FAT)*, 33-44. ACM, 2020. A practical framework for conducting internal fairness audits of AI systems. Raji et al. draw on Google's experience to propose a structured audit process that surfaces fairness concerns at every stage of development. This paper bridges the gap between theoretical fairness definitions and organizational practice — essential for students preparing to implement fairness in real-world settings.

The COMPAS Debate (Extended)

Flores, Anthony W., Kristin Bechtel, and Christopher T. Lowenkamp. "False Positives, False Negatives, and False Analyses: A Rejoinder to 'Machine Bias: There's Software Used Across the Country to Predict Future Criminals. And It's Biased Against Blacks.'" Federal Probation 80, no. 2 (2016): 38-46. A direct response to ProPublica's COMPAS analysis from criminal justice researchers who argue that ProPublica's framing was misleading and that the relevant fairness standard for risk assessment is calibration, not equalized odds. Reading this alongside the ProPublica investigation provides students with a complete picture of the debate — both positions, with their supporting evidence and reasoning.

These readings build directly on the impossibility theorem and the fairness definitions introduced in Chapter 15. As Chapter 16 turns to transparency and explainability, the question shifts from "is the system fair?" to "can we explain how it works?" — a question that connects fairness, accountability, and the right to understand the systems that govern our lives.