Theoretical Analysis of the Impact of Missing Data in Sensitive Attributes on the p%-rule Fairness Metric

• Dimas Cassimiro Nascimento Federal University of Agreste of Pernambuco
• Daliton da Silva Federal University of Agreste of Pernambuco
• Luis Filipe Alves Pereira Federal University of Agreste of Pernambuco

DOI: https://doi.org/10.5753/sbbd.2025.247565

Abstract

Algorithmic fairness assessment has become a central topic in the analysis of automated decision-making systems. In this paper, we investigate how the use of imputation techniques to fill in missing sensitive data can affect the value of the p%-rule metric, depending on the degree of imputation error. We propose a formal mathematical model to quantify this impact, considering symmetric and bidirectional imputation errors. Additionally, we analyze the minimum number of manual corrections required to achieve a desired improvement in the fairness metric. The results provide a quantitative foundation for understanding the trade-offs between the cost of manual intervention and the quality of imputed data in algorithmic fairness analysis.

Keywords: fairness, missing data, sensitive attributes

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