Relative Probability on Finite Outcome Spaces: A Systematic Examination of its Axiomatization, Properties, and Applications
This work addresses foundational issues in probability theory for researchers in mathematics and AI, but it appears incremental as it builds on existing axiomatic frameworks.
The paper tackles the problem of viewing probability as a relative measure rather than an absolute one, focusing on finite outcome spaces by developing three axioms for relative probability functions, providing examples and composition systems, and proving topological closure to preserve information under limits.
This work proposes a view of probability as a relative measure rather than an absolute one. To demonstrate this concept, we focus on finite outcome spaces and develop three fundamental axioms that establish requirements for relative probability functions. We then provide a library of examples of these functions and a system for composing them. Additionally, we discuss a relative version of Bayesian inference and its digital implementation. Finally, we prove the topological closure of the relative probability space, highlighting its ability to preserve information under limits.