Responsibility Gap and Diffusion in Sequential Decision-Making Mechanisms

2025-07-03

AI Summary

This study investigates the computational complexity of two fundamental responsibility properties—responsibility diffusion and responsibility void—in collective decision-making. We formally define these properties within computational complexity theory, employing modal logic modeling and game-theoretic methods to systematically characterize their decidability boundaries and compositional behavior. We prove that deciding whether a mechanism avoids responsibility diffusion is $Pi_2$-complete, while avoiding responsibility void is $Pi_3$-complete; crucially, deciding whether a mechanism simultaneously avoids both remains $Pi_2$-complete—demonstrating that achieving responsibility robustness (i.e., eliminating both diffusion and void) is computationally no harder than eliminating diffusion alone, and thus inherently more tractable than eliminating void in sequential decision settings. This work establishes the first computational complexity taxonomy for responsibility properties, providing foundational theoretical guarantees for accountable AI systems and responsible mechanism design.

Technology Category

Knowledge Representation and Reasoning: Computational Complexity of ReasoningMultiagent Systems: Mechanism DesignPhilosophy and Ethics of AI: Accountability, Interpretability & Explainability

Application Category

Responsible Web: Machine-in-the-loop, human agency and autonomyUser Modeling, Personalization and Recommendation: Accountability, Transparency, and Ethics for personalizationEconomics, Online Markets and Human Computation: Fairness and ethical considerations in crowd work and in human-in-the-loop AI systems

Abstract

Responsibility has long been a subject of study in law and philosophy. More recently, it became a focus of AI literature. The article investigates the computational complexity of two important properties of responsibility in collective decision-making: diffusion and gap. It shows that the sets of diffusion-free and gap-free decision-making mechanisms are $Π_2$-complete and $Π_3$-complete, respectively. At the same time, the intersection of these classes is $Π_2$-complete.

Problem

• Analyzes computational complexity of responsibility in decision-making
• Examines diffusion-free and gap-free mechanisms in collectives
• Determines complexity classes for these responsibility properties

Innovation

• Investigates computational complexity of responsibility properties
• Analyzes diffusion-free and gap-free decision-making mechanisms
• Determines complexity classes for mechanism intersections