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Decision Making with Differential Privacy under a Fairness Lens

Ferdinando Fioretto, Cuong Tran, Pascal Van Hentenryck

TL;DR

It is shown that, when the decisions take as input differentially private data, the noise added to achieve privacy disproportionately impacts some groups over others.

Abstract

Agencies, such as the U.S. Census Bureau, release data sets and statistics about groups of individuals that are used as input to a number of critical decision processes. To conform to privacy and confidentiality requirements, these agencies are often required to release privacy-preserving versions of the data. This paper studies the release of differentially private data sets and analyzes their impact on some critical resource allocation tasks under a fairness perspective. {The paper shows that, when the decisions take as input differentially private data}, the noise added to achieve privacy disproportionately impacts some groups over others. The paper analyzes the reasons for these disproportionate impacts and proposes guidelines to mitigate these effects. The proposed approaches are evaluated on critical decision problems that use differentially private census data.

Decision Making with Differential Privacy under a Fairness Lens

TL;DR

It is shown that, when the decisions take as input differentially private data, the noise added to achieve privacy disproportionately impacts some groups over others.

Abstract

Agencies, such as the U.S. Census Bureau, release data sets and statistics about groups of individuals that are used as input to a number of critical decision processes. To conform to privacy and confidentiality requirements, these agencies are often required to release privacy-preserving versions of the data. This paper studies the release of differentially private data sets and analyzes their impact on some critical resource allocation tasks under a fairness perspective. {The paper shows that, when the decisions take as input differentially private data}, the noise added to achieve privacy disproportionately impacts some groups over others. The paper analyzes the reasons for these disproportionate impacts and proposes guidelines to mitigate these effects. The proposed approaches are evaluated on critical decision problems that use differentially private census data.

Paper Structure

This paper contains 35 sections, 20 theorems, 54 equations, 10 figures.

Table of Contents

  1. Introduction
  2. Preliminaries: Differential Privacy
  3. Problem Setting and Goals
  4. Motivating Problems
  5. Allotment problems
  6. Decision Rules
  7. Fair Allotments and Decision Rules
  8. Fair Allotments: Characterization
  9. Fair Decision Rules: Characterization
  10. The Nature of Bias
  11. The Problem Structure
  12. Ratio Functions
  13. Thresholding Functions
  14. Predicates Composition
  15. Post-Processing
  16. ...and 20 more sections

Key Result

Theorem 1

The composition $(\mathcal{M}_1(\bm{x}), \ldots, \mathcal{M}_k(\bm{x}))$ of a collection $\{\mathcal{M}_i\}_{i=1}^k$ of $\epsilon_i$-differentially private mechanisms satisfies $(\epsilon=\sum_{i=1}^{k} \epsilon_i)$-differential privacy.

Figures (10)

  • Figure 1: Diagram of the private allocation problem.
  • Figure 2: Disproportionate Title 1 funds allotment in NY school districts.
  • Figure 3: Disproportionate Minority Language Voting Benefits.
  • Figure 4: Unfairness effect in ratios (left), thresholding (middle) and predicates disjunction (right)
  • Figure 5: Absolute bias (decision errors) in the Minority Language Problem: The errors are shown for four different groups of data corresponding to predicates $P = P^1 \lor P^2$ (left) and $P = P^1 \land P^3$ (right)
  • ...and 5 more figures

Theorems & Definitions (38)

  • Definition 1
  • Theorem 1: Sequential Composition
  • Theorem 2: Post-Processing Immunity
  • Definition 2
  • Definition 3
  • Theorem 3
  • proof
  • Corollary 1
  • proof
  • Corollary 2
  • ...and 28 more