Order-of-Magnitude Influence Diagrams

In this paper, we develop a qualitative theory of influence diagrams that can be used to model and solve sequential decision making tasks when only qualitative (or imprecise) information is available. Our approach is based on an order-of-magnitude approximation of both probabilities and utilities and allows for specifying partially ordered preferences via sets of utility values. We also propose a dedicated variable elimination algorithm that can be applied for solving order-of-magnitude influence diagrams.

💡 Research Summary

The paper introduces Order‑of‑Magnitude Influence Diagrams (O‑MID), a qualitative extension of traditional influence diagrams designed for sequential decision‑making when only imprecise or qualitative information is available. The authors’ central idea is to approximate both probabilities and utilities using an order‑of‑magnitude (OOM) representation. A probability is expressed as ε^k, where ε is an infinitesimally small positive number and k is an integer that captures the relative magnitude (e.g., ε^−2 denotes a “large” probability, ε^3 a “negligible” one). Utilities are similarly written as ε^l·u, where l encodes the utility’s scale and u∈