probatiIts

probatiIts is a term used in theoretical probability to denote a class of probability assignments and estimators designed to preserve defined invariances when the underlying outcome space is transformed. In the probatiIts framework, an assignment P assigns a probability to each event such that certain symmetry operations on the sample space leave the assignment unchanged.

Origin and usage: The term originated in speculative mathematical literature as a shorthand for invariance-based probability reasoning. It is used primarily in discussions of how probabilities should behave under relabeling, coarse-graining, or relabelling of states, and in analyses of robust statistics and algorithmic fairness.

Defining properties: A probatiIts must satisfy non-negativity and normalization; invariance under a specified group G of transformations; and consistency with the probability of unions of disjoint events.

Variants and examples: There are discrete probatiIts and continuous probatiIts; examples include the uniform probatiIts on symmetric spaces, which assign equal probabilities to all states in an orbit under G. In practice, probatiIts provide a theoretical tool for reasoning about probability assignments that do not depend on particular labeling of outcomes.

Applications: used in fairness audits, model evaluation, and philosophical debates about rational belief.