Introduction -- Overview of the Book

PART I THEORETICAL FOUNDATIONS FOR FAIRNESS IN ALGORITHMIC DECISION-MAKING -- Overview of Part I

1 Inherent Tradeoffs in the Fair Determination of Risk Scores -- 1.1 A Formal Model of Risk Assessment -- 1.2 The Characterization Theorems -- 1.3 The Approximate Theorem -- 1.4 Reducing Loss with Equal Base Rates -- 1.5 Conclusion

2 On Fairness and Calibration -- 2.1 Problem Setup -- 2.2 Relaxing Equalized Odds to Preserve Calibration -- 2.3 Experiments -- 2.4 Discussion and Conclusion

3 The Externalities of Exploration and How Data Diversity Helps Exploitation -- 3.1 Preliminaries --3.2 Group Externality of Exploration -- 3.3 Greedy Algorithms and LinUCB with Perturbed Contexts -- 3.4 Analysis: LinUCB with Perturbed Contexts -- 3.5 Analysis: Greedy Algorithms with Perturbed Contexts

PART II MODELS OF BEHAVIOR -- Overview of Part II

4 Selection Problems in the Presence of Implicit Bias -- 4.1 Overview and Summary of Results -- 4.2 Biased Selection with Power Law Distributions -- 4.3 Biased Selection with Bounded Distributions -- 4.4 Conclusion

5 How Do Classifiers Induce Agents to Behave Strategically? -- 5.1 Model and Overview of Results -- 5.2 Incentivizing Particular Effort Profiles -- 5.3 Optimizing Other Objectives -- 5.4 The Structure of the Space of Linear Mechanisms -- 5.5 Conclusion

6 Algorithmic Monoculture and Social Welfare -- 6.1 Algorithmic Hiring as a Case Study -- 6.2 Instantiating with Ranking Models -- 6.3 Models with Multiple Firms -- 6.4 Conclusion

PART III APPLICATION DOMAINS -- Overview of Part III

7 Mitigating Bias in Algorithmic Hiring: Evaluating Claims and Practices -- 7.1 Background -- 7.2 Empirical Findings -- 7.3 Analysis of Technical Concerns -- 7.4 Algorithmic De-biasing -- 7.5 Discussion and Recommendations

8 The Hidden Assumptions Behind Counterfactual Explanations and Principal Reasons -- 8.1 What Are Feature-highlighting Explanations? -- 8.2 Feature-highlighting Explanations in Practice -- 8.3 Unavoidable Tensions -- 8.4 Conclusion

PART IV CONCLUSION AND FUTURE WORK

9 Future Directions -- 9.1 Fairness in Machine Learning and Mechanism Design -- 9.2 Algorithmic Discrimination -- 9.3 Transparent and Meaningful Explanations

PART V APPENDICES

10 Appendix A Inherent Tradeoffs in the Fair Determination of Risk Scores -- A.1 NP-completeness of Non-trivial Integral Fair Risk Assignments

11 Appendix B On Fairness and Calibration -- B.1 Linearity of Calibrated Classifiers -- B.2 Cost Functions -- B.3 Relationship Between Cost and Error -- B.4 Proof of Algorithm 2.1 Optimality and Approximate Optimality -- B.5 Proof of Impossibility and Approximate Impossibility -- B.6 Details on Experiments

12 Appendix C The Externalities of Exploration and How Data Diversity Helps Exploitation -- C.1 (Sub)gaussians and Concentration -- C.2 KL-divergence -- C.3 Linear Algebra -- C.4 Logarithms

13 Appendix D Selection Problems in the Presence of Implicit Bias -- D.1 Missing Proofs for Section 4.2 -- D.2 Additional Theorems for Power Laws --D.3 Lemmas for the Equivalence Definition -- D.4 Lemmas for Section D.2 -- D.5 Lemmas and Proofs for Section 4.3

14 Appendix E How Do Classifiers Induce Agents to Behave Strategically? -- E.1 Characterizing the Agent's Response to a Linear Mechanism

15 Appendix F Algorithmic Monoculture and Social Welfare -- F.1 Random Utility Models Satisfying Definition 6.1 -- F.2 3-candidate RUM Counterexamples -- F.3 Proof of Theorem 6.2 -- F.4 Verifying that the Mallows Model Satisfies Definition 6.1 -- F.5 Proof of Theorem 6.3 -- F.6 Supplementary Lemmas for the Mallows Model

16 Appendix G Mitigating Bias in Algorithmic Decision-making: Evaluating Claims and Practices -- G.1 Administrative Information on Vendors

Bibliography

Authors' Biographies

Index

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