Definition formula for probabilities of independent events as a consequence of the Insufficient Reason Principle

TL;DR

This paper derives the standard probability formula for independent events from the Insufficient Reason Principle, using the Maximum Relative Divergence Principle on order-comonotonic functions, providing a theoretical foundation for independence.

Contribution

It introduces a novel derivation of the probability formula for independent events based on the Insufficient Reason Principle and the Maximum Relative Divergence Principle.

Findings

Standard probability formula derived from the Insufficient Reason Principle

Uses the Maximum Relative Divergence Principle for order-comonotonic functions

Provides a theoretical foundation for independence in probability theory

Abstract

The standard definition formula for probabilities of independent events is derived as a consequence of the Insufficient Reason Principle expressed as the Maximum Relative Divergence Principle for grading (order-comonotonic) functions on a totally ordered set.