# The Role of Randomness and Noise in Strategic Classification

arXiv: https://arxiv.org/abs/2005.08377 · HTML: https://mlsanity.com/paper/2005.08377/

## Key facts

- Cited by 40 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 17 May 2020.

## Built on by (most cited first, 30 of 40)

- [Strategic Classification in the Dark](https://mlsanity.com/paper/2102.11592/) (2021)
- [Who Leads and Who Follows in Strategic Classification?](https://mlsanity.com/paper/2106.12529/) (2021)
- [Information Discrepancy in Strategic Learning](https://mlsanity.com/paper/2103.01028/) (2021)
- [Alternative Microfoundations for Strategic Classification](https://mlsanity.com/paper/2106.12705/) (2021)
- [Performative Power](https://mlsanity.com/paper/2203.17232/) (2022)
- [On classification of strategic agents who can both game and improve](https://mlsanity.com/paper/2203.00124/) (2022)
- [Strategic Ranking](https://mlsanity.com/paper/2109.08240/) (2021)
- [Fundamental Bounds on Online Strategic Classification](https://mlsanity.com/paper/2302.12355/) (2023)
- [Learnability Gaps of Strategic Classification](https://mlsanity.com/paper/2402.19303/) (2024)
- [Performative Federated Learning: A Solution to Model-Dependent and Heterogeneous Distribution Shifts](https://mlsanity.com/paper/2305.05090/) (2023)
- [Bayesian Strategic Classification](https://mlsanity.com/paper/2402.08758/) (2024)
- [Non-linear Welfare-Aware Strategic Learning](https://mlsanity.com/paper/2405.01810/) (2024)
- [Automating Data Annotation under Strategic Human Agents: Risks and Potential Solutions](https://mlsanity.com/paper/2405.08027/) (2024)
- [Addressing Strategic Manipulation Disparities in Fair Classification](https://mlsanity.com/paper/2205.10842/) (2022)
- [Sequential Strategic Screening](https://mlsanity.com/paper/2301.13397/) (2023)
- [Learning under Imitative Strategic Behavior with Unforeseeable Outcomes](https://mlsanity.com/paper/2405.01797/) (2024)
- [Incentivizing Desirable Effort Profiles in Strategic Classification: The Role of Causality and Uncertainty](https://mlsanity.com/paper/2502.06749/) (2025)
- [Setting Fair Incentives to Maximize Improvement](https://mlsanity.com/paper/2203.00134/) (2022)
- [Choosing the Right Weights: Balancing Value, Strategy, and Noise in Recommender Systems](https://mlsanity.com/paper/2305.17428/) (2023)
- [Algorithmic Decision-Making under Agents with Persistent Improvement](https://mlsanity.com/paper/2405.01807/) (2024)
- [PAC Learning with Improvements](https://mlsanity.com/paper/2503.03184/) (2025)
- [How Strategic Agents Respond: Comparing Analytical Models with LLM-Generated Responses in Strategic Classification](https://mlsanity.com/paper/2501.16355/) (2025)
- [Incentive-Aware Machine Learning; Robustness, Fairness, Improvement & Causality](https://mlsanity.com/paper/2505.05211/) (2025)
- [Should Decision-Makers Reveal Classifiers in Online Strategic Classification?](https://mlsanity.com/paper/2506.01936/) (2025)
- [Minimax Group Fairness in Strategic Classification](https://mlsanity.com/paper/2410.02513/) (2024)
- [Strategic Classification with Randomised Classifiers](https://mlsanity.com/paper/2502.01313/) (2025)
- [When In Doubt, Abstain: The Impact of Abstention on Strategic Classification](https://mlsanity.com/paper/2510.13327/) (2025)
- [Policy Learning with Competing Agents](https://mlsanity.com/paper/2204.01884/) (2022)
- [Metric-Fair Classifier Derandomization](https://mlsanity.com/paper/2206.07826/) (2022)
- [Anticipating Gaming to Incentivize Improvement: Guiding Agents in (Fair) Strategic Classification](https://mlsanity.com/paper/2505.05594/) (2025)

## Abstract (arXiv)

We investigate the problem of designing optimal classifiers in the strategic classification setting, where the classification is part of a game in which players can modify their features to attain a favorable classification outcome (while incurring some cost). Previously, the problem has been considered from a learning-theoretic perspective and from the algorithmic fairness perspective. Our main contributions include 1. Showing that if the objective is to maximize the efficiency of the classification process (defined as the accuracy of the outcome minus the sunk cost of the qualified players manipulating their features to gain a better outcome), then using randomized classifiers (that is, ones where the probability of a given feature vector to be accepted by the classifier is strictly between 0 and 1) is necessary. 2. Showing that in many natural cases, the imposed optimal solution (in terms of efficiency) has the structure where players never change their feature vectors (the randomized classifier is structured in a way, such that the gain in the probability of being classified as a 1 does not justify the expense of changing one's features). 3. Observing that the randomized classification is not a stable best-response from the classifier's viewpoint, and that the classifier doesn't benefit from randomized classifiers without creating instability in the system. 4. Showing that in some cases, a noisier signal leads to better equilibria outcomes -- improving both accuracy and fairness when more than one subpopulation with different feature adjustment costs are involved. This is interesting from a policy perspective, since it is hard to force institutions to stick to a particular randomized classification strategy (especially in a context of a market with multiple classifiers), but it is possible to alter the information environment to make the feature signals inherently noisier.