Order-based formulations of conditionality and sufficiency

Develop order-based versions of the conditionality principle and sufficiency principle within the procedure-level framework for statistical inference.

Background

The paper formulates Birnbaum’s conditionality and sufficiency principles as equality-preservation requirements for statistical procedures on finite inference bases. This equivalence-based formulation forces identical inferential outputs across related inference bases and, through closure, across likelihood-related bases.

The authors identify order-based formulations as an unresolved direction because some frequentist interpretations treat conditioning as refining evidential content rather than preserving it exactly. Such formulations would replace equality of outputs with an appropriate order or refinement relation and would extend the procedure-level framework developed in the paper.