Physical, subjective and analogical probability

TL;DR

This paper proposes a dual framework for understanding probability by distinguishing between physical probabilities, which are objective and symmetry-based, and analogical probabilities, which are subjective and based on analogy, enhancing real-world probabilistic reasoning.

Contribution

It introduces a novel distinction between physical and analogical probabilities, providing definitions, properties, and applications for better modeling of uncertainty in various contexts.

Findings

Physical probabilities are objective and symmetry-based.

Analogical probabilities are subjective and based on analogy.

Analogical probabilities facilitate reasoning about hypotheses with observed data.

Abstract

The aim of this paper is to show that the concept of probability is best understood by dividing this concept into two different types of probability, namely physical probability and analogical probability. Loosely speaking, a physical probability is a probability that applies to the outcomes of an experiment that have been judged as being equally likely on the basis of physical symmetry. Physical probabilities are arguably in some sense 'objective' and possess all the standard properties of the concept of probability. On the other hand, an analogical probability is defined by making an analogy between the uncertainty surrounding an event of interest and the uncertainty surrounding an event that has a physical probability. Analogical probabilities are undeniably subjective probabilities and are not obliged to have all the standard mathematical properties possessed by physical probabilities, e.g. they may not have the property of additivity or obey the standard definition of conditional probability. Nevertheless, analogical probabilities have extra properties, which are not possessed by physical probabilities, that assist in their direct elicitation, general derivation, comparison and justification. More specifically, these properties facilitate the application of analogical probability to real-world problems that can not be adequately resolved by using only physical probability, e.g. probabilistic inference about hypotheses on the basis of observed data. Careful definitions are given of the concepts that are introduced and, where appropriate, examples of the application of these concepts are presented for additional clarity.