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When In Doubt, Abstain: The Impact of Abstention on Strategic Classification

Lina Alkarmi, Ziyuan Huang, Mingyan Liu

TL;DR

The study addresses the challenge of strategic manipulation in automated decision systems by introducing abstention as a controllable action. It frames the interaction as a Stackelberg game in which the principal commits to a classifier and an abstention policy, and agents respond by manipulating observable features at a cost. Theoretical results show that optimal abstention cannot worsen the principal’s loss and can increase resistance to manipulation, particularly when manipulation costs are nontrivial; a key insight is that constrained abstention is typically more cautious than unconstrained abstention, leading to higher abstention thresholds. A detailed one-dimensional uniform-distribution case and simulations illustrate how the optimal threshold depends on manipulation cost $\gamma$ and abstention cost $c$, and demonstrate conditions under which abstention meaningfully reduces strategic harm. Overall, abstention emerges as a valuable tool for mitigating strategic manipulation in algorithmic decision-making, with practical policy implications for deploying abstention mechanisms in risk-sensitive settings.

Abstract

Algorithmic decision making is increasingly prevalent, but often vulnerable to strategic manipulation by agents seeking a favorable outcome. Prior research has shown that classifier abstention (allowing a classifier to decline making a decision due to insufficient confidence) can significantly increase classifier accuracy. This paper studies abstention within a strategic classification context, exploring how its introduction impacts strategic agents' responses and how principals should optimally leverage it. We model this interaction as a Stackelberg game where a principal, acting as the classifier, first announces its decision policy, and then strategic agents, acting as followers, manipulate their features to receive a desired outcome. Here, we focus on binary classifiers where agents manipulate observable features rather than their true features, and show that optimal abstention ensures that the principal's utility (or loss) is no worse than in a non-abstention setting, even in the presence of strategic agents. We also show that beyond improving accuracy, abstention can also serve as a deterrent to manipulation, making it costlier for agents, especially those less qualified, to manipulate to achieve a positive outcome when manipulation costs are significant enough to affect agent behavior. These results highlight abstention as a valuable tool for reducing the negative effects of strategic behavior in algorithmic decision making systems.

When In Doubt, Abstain: The Impact of Abstention on Strategic Classification

TL;DR

The study addresses the challenge of strategic manipulation in automated decision systems by introducing abstention as a controllable action. It frames the interaction as a Stackelberg game in which the principal commits to a classifier and an abstention policy, and agents respond by manipulating observable features at a cost. Theoretical results show that optimal abstention cannot worsen the principal’s loss and can increase resistance to manipulation, particularly when manipulation costs are nontrivial; a key insight is that constrained abstention is typically more cautious than unconstrained abstention, leading to higher abstention thresholds. A detailed one-dimensional uniform-distribution case and simulations illustrate how the optimal threshold depends on manipulation cost and abstention cost , and demonstrate conditions under which abstention meaningfully reduces strategic harm. Overall, abstention emerges as a valuable tool for mitigating strategic manipulation in algorithmic decision-making, with practical policy implications for deploying abstention mechanisms in risk-sensitive settings.

Abstract

Algorithmic decision making is increasingly prevalent, but often vulnerable to strategic manipulation by agents seeking a favorable outcome. Prior research has shown that classifier abstention (allowing a classifier to decline making a decision due to insufficient confidence) can significantly increase classifier accuracy. This paper studies abstention within a strategic classification context, exploring how its introduction impacts strategic agents' responses and how principals should optimally leverage it. We model this interaction as a Stackelberg game where a principal, acting as the classifier, first announces its decision policy, and then strategic agents, acting as followers, manipulate their features to receive a desired outcome. Here, we focus on binary classifiers where agents manipulate observable features rather than their true features, and show that optimal abstention ensures that the principal's utility (or loss) is no worse than in a non-abstention setting, even in the presence of strategic agents. We also show that beyond improving accuracy, abstention can also serve as a deterrent to manipulation, making it costlier for agents, especially those less qualified, to manipulate to achieve a positive outcome when manipulation costs are significant enough to affect agent behavior. These results highlight abstention as a valuable tool for reducing the negative effects of strategic behavior in algorithmic decision making systems.
Paper Structure (39 sections, 6 theorems, 41 equations, 4 figures)

This paper contains 39 sections, 6 theorems, 41 equations, 4 figures.

Table of Contents

  1. Introduction
  2. Problem Formulation
  3. Optimal Abstention for a Fixed Classifier
  4. Agent's Best Response
  5. Principal's Expected Loss and the Advantage of Abstention
  6. Comparison of Optimal Abstention: Strategic vs. Non-Strategic
  7. Case Study: One-Dimensional Uniform Distribution
  8. The Principal's Optimal Abstention Threshold
  9. The Equilibrium Without Abstention
  10. Expected Manipulation of Unqualified Agents
  11. Expected Manipulation Without Abstention:
  12. Expected Manipulation With Abstention:
  13. Comparing $E_{\text{no\_abstention}}$ and $E_{\text{with\_abstention}}$:
  14. Simulation Results
  15. Simulation Setup and Impact of System Parameters
  16. ...and 24 more sections

Key Result

theorem 1

For any fixed classifier $f$, any data distribution $\mathcal{D}$, and any principal's cost of abstention $c$, the minimum expected loss achievable with an optimal abstention function $\bar{r}^*$ is less than or equal to the expected loss without abstention. That is: where $L_{\textrm{no\_abstention}}(f)$ is the expected loss under $f$ with no abstention applied.

Figures (4)

  • Figure 1: Illustration of expected loss contributions for the uniform distribution case study when $c < 0.5$ and $0 < K < 2$.
  • Figure 2: Illustration of expected loss contributions when $c = 0.5$ and $0 < K < 2$. In this scenario, the optimal threshold $\bar{T}^*$ is a range $[\frac{K}{2}, K]$.
  • Figure 3: Optimal thresholds $\bar{T}^*$ and $T^*$ under varying parameters.
  • Figure 4: Harm reduction via optimal abstention across system parameters.

Theorems & Definitions (10)

  • theorem 1
  • proof
  • theorem 2
  • theorem 3
  • definition 1
  • proposition 1
  • proposition 2
  • proposition 3
  • proof
  • proof