[Paper Review] Performative Prediction: Past and Future

Moritz Hardt, Celestine Mendler-Dünner|arXiv (Cornell University)|Oct 25, 2023

Complex Systems and Time Series Analysis4 citations

TL;DR

This paper introduces performative prediction as a formal framework to study how machine learning predictions influence the very data they aim to predict, leading to feedback loops that alter outcomes. It establishes equilibrium concepts, distinguishes learning from steering, and introduces performative power as a measure of predictive influence, offering new optimization and governance insights for algorithmic systems in digital markets.

ABSTRACT

Predictions in the social world generally influence the target of prediction, a phenomenon known as performativity. Self-fulfilling and self-negating predictions are examples of performativity. Of fundamental importance to economics, finance, and the social sciences, the notion has been absent from the development of machine learning that builds on the static perspective of pattern recognition. In machine learning applications, however, performativity often surfaces as distribution shift. A predictive model deployed on a digital platform, for example, influences behavior and thereby changes the data-generating distribution. We discuss the recently founded area of performative prediction that provides a definition and conceptual framework to study performativity in machine learning. A key element of performative prediction is a natural equilibrium notion that gives rise to new optimization challenges. What emerges is a distinction between learning and steering, two mechanisms at play in performative prediction. Steering is in turn intimately related to questions of power in digital markets. The notion of performative power that we review gives an answer to the question how much a platform can steer participants through its predictions. We end on a discussion of future directions, such as the role that performativity plays in contesting algorithmic systems.

Motivation & Objective

• To formalize performativity in machine learning, where predictions alter the data-generating process, challenging the traditional assumption of immutable data.
• To address the fundamental problem of prediction in social systems, where forecasts influence behavior—such as in recommendation systems or traffic routing—leading to self-fulfilling or self-negating outcomes.
• To distinguish between two mechanisms in performative prediction: learning (fitting to current data) and steering (shaping future data distributions through model deployment).
• To define and quantify performative power as a measure of a platform’s influence over outcomes via its predictions, relevant for antitrust and regulatory analysis.
• To explore the role of performativity in collective action and algorithmic governance, extending beyond individual prediction to systemic social dynamics.

Proposed method

• Proposes a performative risk formulation: PR(θ) = Risk(θ, D(θ₀)) + [Risk(θ, D(θ)) − Risk(θ, D(θ₀))], separating current performance from steering effects.
• Introduces a performative equilibrium as a fixed point where prediction θ satisfies θ = R(θ), generalizing the GMS theorem (Grunberg, Modigliani, Simon) to machine learning.
• Distinguishes model-free and model-based optimization approaches for finding performative equilibria, analyzing convergence and stability.
• Defines performative power as the extent to which a model can shift the data distribution through its predictions, formalizing influence in digital markets.
• Applies the framework to algorithmic collective action, showing how performative power enables coordinated behavior among agents influenced by shared predictions.
• Uses tools from optimization, statistics, and control theory to analyze stability, convergence, and strategic behavior under performative feedback.

Experimental results

Research questions

• RQ1 Under what conditions can a prediction be self-fulfilling or self-negating when it influences the outcome it seeks to predict?
• RQ2 How can we define and compute a stable equilibrium in machine learning systems where predictions alter the data-generating process?
• RQ3 What is the difference between learning from data and steering the data distribution through model deployment, and how do they jointly affect predictive performance?
• RQ4 How can performative power be formally measured and used to assess market dominance or regulatory risk in digital platforms?
• RQ5 In what ways does performativity enable or constrain collective action in algorithmic systems, and how can this be modeled mathematically?

Key findings

• The performative risk formulation separates current performance from the potential gain from steering, showing that optimal models may prioritize influence over immediate accuracy.
• A performative equilibrium exists when a prediction θ satisfies θ = R(θ), generalizing the GMS theorem to machine learning and ensuring consistency under feedback.
• The distinction between learning and steering reveals that model deployment can be a strategic intervention, not just a statistical fit.
• Performative power is formally defined as the extent to which a model can shift the data distribution, providing a quantifiable metric for influence in digital markets.
• The framework reveals that performativity enables collective action in algorithmic systems, where agents respond to shared predictions in coordinated ways.
• The paper identifies limitations in the current formalism, such as its inability to fully capture Hacking’s looping effect or the performativity of economic theory, suggesting directions for future work.