Algorithm fairness in the application of artificial intelligence (AI) is essential for a better society. As the foundational axiom of social mechanisms, fairness consists of multiple facets. Although the machine learning (ML) community has focused on intersectionality as a matter of statistical parity, especially in discrimination issues, an emerging body of literature addresses another facet -- monotonicity. Based on domain expertise, monotonicity plays a vital role in numerous fairness-related areas, where violations could misguide human decisions and lead to disastrous consequences. In this paper, we first systematically evaluate the significance of applying monotonic neural additive models (MNAMs), which use a fairness-aware ML algorithm to enforce both individual and pairwise monotonicity principles, for the fairness of AI ethics and society. We have found, through a hybrid method of theoretical reasoning, simulation, and extensive empirical analysis, that considering monotonicity axioms is essential in all areas of fairness, including criminology, education, health care, and finance. Our research contributes to the interdisciplinary research at the interface of AI ethics, explainable AI (XAI), and human-computer interactions (HCIs). By evidencing the catastrophic consequences if monotonicity is not met, we address the significance of monotonicity requirements in AI applications. Furthermore, we demonstrate that MNAMs are an effective fairness-aware ML approach by imposing monotonicity restrictions integrating human intelligence.
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