Joint Scoring Rules: Zero-Sum Competition Avoids Performative Prediction

TL;DR

The paper tackles performative prediction when eliciting conditional predictions from multiple agents and shows that single symmetric scoring rules cannot deterministically realize the principal's top choice. It proposes a joint zero-sum evaluation among predictors combined with optimistic-max decision making, proving a quasi-strictly proper mechanism that yields honest reporting and identification of the principal's preferred action $a^*$; a uniqueness result argues that zero-sum is essential. The authors demonstrate efficient action search using $O(\log|\mathcal{A}|)$ comparisons and extend the framework to stochastic decision rules, including mean-max and random-max variants, while preserving incentives. Empirical results in a toy environment show that zero-sum training increases predictive accuracy and principal utility and can erase learned performativity, supporting the practical viability of the approach for safer AI systems and Oracle AI applications. Overall, the work provides both theoretical foundations and initial empirical validation for using zero-sum joint scoring to safely harness conditional predictions in decision-making under potential performativity.

Abstract

In a decision-making scenario, a principal could use conditional predictions from an expert agent to inform their choice. However, this approach would introduce a fundamental conflict of interest. An agent optimizing for predictive accuracy is incentivized to manipulate their principal towards more predictable actions, which prevents that principal from being able to deterministically select their true preference. We demonstrate that this impossibility result can be overcome through the joint evaluation of multiple agents. When agents are made to engage in zero-sum competition, their incentive to influence the action taken is eliminated, and the principal can identify and take the action they most prefer. We further prove that this zero-sum setup is unique, efficiently implementable, and applicable under stochastic choice. Experiments in a toy environment demonstrate that training on a zero-sum objective significantly enhances both predictive accuracy and principal utility, and can eliminate previously learned manipulative behavior.

Figures (2)

• Figure 1: Figure 1: (Left) In environments that incentivize performative prediction, training with a zero sum objective avoids the model becoming performative, and results increasing accuracy across predictions. Models trained with no intervention are more accurate for whichever action is chosen, as they influence the choice to be easier to predict, but are less accurate overall. (Right) When no intervention prevents a model from becoming performative, user utility plateaus earlier and at a lower level.
• Figure 2: Figure 2: (Left) A zero-sum objective using two different predictions from the same model results in faster and larger decreases in performativity than an exact zero-sum objective or training in a non-performative environment. (Right) The decrease in performativity leads to higher utility for users, with larger gains for larger drops in performativity.

Theorems & Definitions (13)

• Lemma 1
• Theorem 2
• proof
• Theorem 3
• Theorem 4
• Theorem 5
• Theorem 6
• Theorem 7
• Theorem 8
• Lemma 9