Responsibility Gap and Diffusion in Sequential Decision-Making Mechanisms

TL;DR

This paper analyzes the computational complexity of responsibility diffusion and gaps in collective decision-making mechanisms, revealing their high complexity classes and intersections.

Contribution

It provides a formal complexity classification of responsibility diffusion and gap properties in decision mechanisms, a novel theoretical insight.

Findings

Diffusion-free mechanisms are $ ext{Pi}_2$-complete.

Gap-free mechanisms are $ ext{Pi}_3$-complete.

The intersection of diffusion-free and gap-free mechanisms is $ ext{Pi}_2$-complete.

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 $\Pi_2$-complete and $\Pi_3$-complete, respectively. At the same time, the intersection of these classes is $\Pi_2$-complete.