An Information Principle Based on Partitions

The paper proposes an information principle based on partitions for possible applications to cognition-based judgments and applications in natural phenomena. Looking at information through the lens of variety, which is the set of distinguishable elements of the set, we propose that partitions with only one type of object are counted once, and partitions with k types of objects are counted k times. Put differently, multiple occurrences of an object are considered not to have significance for the observer, or we can say that the objects are indistinguishable unless they are distinct. We explore the implications of this logic that has possible applications to cognition centered systems and present a result related to the frequencies of the objects and contrast them with the first digit frequencies.