To Give or Not to Give? The Impacts of Strategically Withheld Recourse

TL;DR

This work reveals a competition between providing algorithmic recourse and preventing strategic manipulation of publicly revealed information. By modeling a fixed classifier and a public reveal set that expands via recourse actions, the authors show that a utility-maximizing system may withhold recourse to curb manipulation, thereby increasing social costs and widening fairness gaps. They show subsidies can counteract these effects by lowering recourse costs, raising recourse uptake, reducing social costs, and mitigating group disparities. The findings highlight policy implications for regulating recourse provisions and designing subsidy-based interventions to promote fairer, more efficient outcomes in automated decision systems.

Abstract

Individuals often aim to reverse undesired outcomes in interactions with automated systems, like loan denials, by either implementing system-recommended actions (recourse), or manipulating their features. While providing recourse benefits users and enhances system utility, it also provides information about the decision process that can be used for more effective strategic manipulation, especially when the individuals collectively share such information with each other. We show that this tension leads rational utility-maximizing systems to frequently withhold recourse, resulting in decreased population utility, particularly impacting sensitive groups. To mitigate these effects, we explore the role of recourse subsidies, finding them effective in increasing the provision of recourse actions by rational systems, as well as lowering the potential social cost and mitigating unfairness caused by recourse withholding.

Figures (11)

• Figure 1: Demonstration of our modeling framework. Agents arrive simultaneously, and the system trains a classifier $f: \pazocal{X} \rightarrow \pazocal{Y}$ for maximum prediction accuracy. Negatively classified agents request recourse, and the system selects agents for recourse provision to maximize utility (\ref{['eq:sys_obj']}). Positively classified agents and those provided recourse have a probability $p \in [0, 1]$ to reveal features, contributing to the publicly revealed set $\textbf{Z} \subseteq \pazocal{X}_+$. Upon observing $\textbf{Z}$, agents execute final actions based on \ref{['eqn:final-action']}.
• Figure 2: Fraction of the population performing recourse (top row) or manipulation (bottom row). Each line corresponds to a different subsidy ratio "sub", i.e., the cost reduction applied to recourse.
• Figure 3: Difference in recourse rate (top row) and social cost (bottom row) between different sensitive attribute groups. Each line corresponds to a different subsidy ratio "subs", i.e., the cost reduction applied to recourse.
• Figure 4: Recourse rate difference as a function of subsidy with 95% confidence intervals. Each line corresponds to a different percentage of the population with provided recourse actions.
• Figure 5: Fraction of the population performing recourse, with 95% confidence intervals. Each line corresponds to a different subsidy ratio "subs", i.e., the cost reduction applied to recourse.

Theorems & Definitions (24)

• Definition 1
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