Scaling Qualitative Probability

TL;DR

This paper introduces a new relational system-based framework for qualitative probability, demonstrating its coherence and ability to encompass classical and inflated probabilities, thus advancing the theoretical understanding of probabilistic modeling.

Contribution

It develops a novel relational approach to qualitative probability, proving key theorems that connect comparative, classical, and inflated probabilities within a unified structure.

Findings

Any comparative probability can be represented by some probability structure.

Classical probability is a special case of the proposed probability structures.

Inflated probabilities greater than 1 can also be modeled within this framework.

Abstract

There are different approaches to qualitative probability, which includes subjective probability. We developed a representation of qualitative probability based on relational systems, which allows modeling uncertainty by probability structures and is more coherent than existing approaches. This setting makes it possible proving that any comparative probability is induced by some probability structure (Theorem 2.1), that classical probability is a probability structure (Theorem 2.2) and that inflated, i.e., larger than 1, probability is also a probability structure (Theorem 2.3). In addition, we study representation of probability structures by classical probability.