  The growing interest in fair AI development is evident. The ''Leave No One
Behind'' initiative urges us to address multiple and intersecting forms of
inequality in accessing services, resources, and opportunities, emphasising the
significance of fairness in AI. This is particularly relevant as an increasing
number of AI tools are applied to decision-making processes, such as resource
allocation and service scheme development, across various sectors such as
health, energy, and housing. Therefore, exploring joint inequalities in these
sectors is significant and valuable for thoroughly understanding overall
inequality and unfairness. This research introduces an innovative approach to
quantify cross-sectoral intersecting discrepancies among user-defined groups
using latent class analysis. These discrepancies can be used to approximate
inequality and provide valuable insights to fairness issues. We validate our
approach using both proprietary and public datasets, including EVENS and Census
2021 (England & Wales) datasets, to examine cross-sectoral intersecting
discrepancies among different ethnic groups. We also verify the reliability of
the quantified discrepancy by conducting a correlation analysis with a
government public metric. Our findings reveal significant discrepancies between
minority ethnic groups, highlighting the need for targeted interventions in
real-world AI applications. Additionally, we demonstrate how the proposed
approach can be used to provide insights into the fairness of machine learning.
