Information-Weight Interpretation of Probability: A Novel Information-Theoretic Perspective

This paper proposes a novel information-theoretic perspective, where probability is interpreted as information weight and probability density is interpreted as information density. We define “information” as the state of a discrete system or the value of a continuous system. We model discrete systems using multisets. From this, we define information weight as the relative multiplicity of each state with respect to the size of the multiset. By relating a discrete system (multiset) to a discrete random variable, we establish a one‑to‑one correspondence between information weight and conventional probability. We then extend this framework to continuous systems. This information-theoretic perspective, distinct from personal belief, propensity, or frequency-based interpretations, emphasizes the contribution of probability to the informational structure of a system.