# Discovering Optimal Scoring Mechanisms in Causal Strategic Prediction

arXiv: https://arxiv.org/abs/2302.06804 · HTML: https://mlsanity.com/paper/2302.06804/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 25 of its 52 references that are in the map.
- First posted on arXiv 14 Feb 2023.

## Builds on (most cited first, 25 of 25)

- [Invariant Risk Minimization](https://mlsanity.com/paper/1907.02893/) (2019)
- [Causal inference using invariant prediction: identification and confidence intervals](https://mlsanity.com/paper/1501.01332/) (2015)
- [Detecting and Correcting for Label Shift with Black Box Predictors](https://mlsanity.com/paper/1802.03916/) (2018)
- [Performative Prediction](https://mlsanity.com/paper/2002.06673/) (2020)
- [Strategic Classification](https://mlsanity.com/paper/1506.06980/) (2015)
- [Causal Discovery with Continuous Additive Noise Models](https://mlsanity.com/paper/1309.6779/) (2013)
- [Algorithmic Recourse: from Counterfactual Explanations to Interventions](https://mlsanity.com/paper/2002.06278/) (2020)
- [Algorithmic recourse under imperfect causal knowledge: a probabilistic approach](https://mlsanity.com/paper/2006.06831/) (2020)
- [Strategic Classification from Revealed Preferences](https://mlsanity.com/paper/1710.07887/) (2017)
- [Domain Adaptation by Using Causal Inference to Predict Invariant Conditional Distributions](https://mlsanity.com/paper/1707.06422/) (2017)
- [Strategic Classification is Causal Modeling in Disguise](https://mlsanity.com/paper/1910.10362/) (2019)
- [Performative Prediction in a Stateful World](https://mlsanity.com/paper/2011.03885/) (2020)
- [How Do Classifiers Induce Agents To Invest Effort Strategically?](https://mlsanity.com/paper/1807.05307/) (2018)
- [Characterizing and Learning Equivalence Classes of Causal DAGs under Interventions](https://mlsanity.com/paper/1802.06310/) (2018)
- [Permutation-Based Causal Structure Learning with Unknown Intervention Targets](https://mlsanity.com/paper/1910.09007/) (2019)
- [Strategic Classification in the Dark](https://mlsanity.com/paper/2102.11592/) (2021)
- [Causal Strategic Linear Regression](https://mlsanity.com/paper/2002.10066/) (2020)
- [PAC-Learning for Strategic Classification](https://mlsanity.com/paper/2012.03310/) (2020)
- [The Strategic Perceptron](https://mlsanity.com/paper/2008.01710/) (2020)
- [Anticipating Performativity by Predicting from Predictions](https://mlsanity.com/paper/2208.07331/) (2022)
- [Generalized Strategic Classification and the Case of Aligned Incentives](https://mlsanity.com/paper/2202.04357/) (2022)
- [Strategic Instrumental Variable Regression: Recovering Causal Relationships From Strategic Responses](https://mlsanity.com/paper/2107.05762/) (2021)
- [Matching a Desired Causal State via Shift Interventions](https://mlsanity.com/paper/2107.01850/) (2021)
- [Gaming Helps! Learning from Strategic Interactions in Natural Dynamics](https://mlsanity.com/paper/2002.07024/) (2020)
- [Margin-distancing for safe model explanation](https://mlsanity.com/paper/2202.11266/) (2022)

## Built on by (most cited first, 2 of 2)

- [Evaluating and Correcting Performative Effects of Decision Support Systems via Causal Domain Shift](https://mlsanity.com/paper/2403.00886/) (2024)
- [Prediction-Intervention Games and Invariant Sets](https://mlsanity.com/paper/2605.16828/) (2026)

## Abstract (arXiv)

Faced with data-driven policies, individuals will manipulate their features to obtain favorable decisions. While earlier works cast these manipulations as undesirable gaming, recent works have adopted a more nuanced causal framing in which manipulations can improve outcomes of interest, and setting coherent mechanisms requires accounting for both predictive accuracy and improvement of the outcome. Typically, these works focus on known causal graphs, consisting only of an outcome and its parents. In this paper, we introduce a general framework in which an outcome and n observed features are related by an arbitrary unknown graph and manipulations are restricted by a fixed budget and cost structure. We develop algorithms that leverage strategic responses to discover the causal graph in a finite number of steps. Given this graph structure, we can then derive mechanisms that trade off between accuracy and improvement. Altogether, our work deepens links between causal discovery and incentive design and provides a more nuanced view of learning under causal strategic prediction.