Measuring algorithmic interpretability: A human-learning-based framework and the corresponding cognitive complexity score

Algorithmic interpretability is necessary to build trust, ensure fairness, and track accountability. However, there is no existing formal measurement method for algorithmic interpretability. In this work, we build upon programming language theory and cognitive load theory to develop a framework for measuring algorithmic interpretability. The proposed measurement framework reflects the process of a human learning an algorithm. We show that the measurement framework and the resulting cognitive complexity score have the following desirable properties - universality, computability, uniqueness, and monotonicity. We illustrate the measurement framework through a toy example, describe the framework and its conceptual underpinnings, and demonstrate the benefits of the framework, in particular for managers considering tradeoffs when selecting algorithms.