This paper introduces the Compression-Prediction-Resource Intelligence Efficiency (CPR-IE) metric for comparing intelligent systems under deployment constraints. The metric combines representational economy, predictive quality and resource burden, denoted as $I(C,P,T)$. The analysis separates the representation of raw resource consumption from the aggregation of resulting attributes. Proportional‑increment composition yields logarithmic cumulative burden, while context‑independent ratio response gives power‑law responses to compression, prediction and burden. Reference normalization provides a unified representation. We prove Pareto consistency, unit invariance, boundary behavior, trade‑off identities, ranking‑stability regions and cross‑task aggregation. A translog parent model makes interaction restrictions explicit; further results give cardinal and ordinal identification, sub‑Gaussian finite‑sample ranking guarantees, robust selection under exponent uncertainty and deterministic regret bounds. Minimum description length, algorithmic complexity, proper scoring rules, variational inference and Landauer’s principle motivate measurement choices but do not dictate the formula. CPR‑IE is a constructed efficiency representation, not a universal law or definition of intelligence.
Review: CPR‑IE offers a coherent framework for evaluating systems under multi‑dimensional resource constraints, with solid theoretical foundations and applicability to cross‑task assessment.