AI algorithms used in the public sector, e.g., for allocating social benefits or predicting fraud, often involve multiple public and private stakeholders at various phases of the algorithm's life-cycle. Communication issues between these diverse stakeholders can lead to misinterpretation and misuse of algorithms. We investigate the communication processes for AI fairness-related decisions by conducting interviews with practitioners working on algorithmic systems in the public sector. By applying qualitative coding analysis, we identify key elements of communication processes that underlie fairness-related human decisions. We analyze the division of roles, tasks, skills, and challenges perceived by stakeholders. We formalize the underlying communication issues within a conceptual framework that i. represents the communication patterns ii. outlines missing elements, such as actors who miss skills for their tasks. The framework is used for describing and analyzing key organizational issues for fairness-related decisions. Three general patterns emerge from the analysis: 1. Policy-makers, civil servants, and domain experts are less involved compared to developers throughout a system's life-cycle. This leads to developers taking on extra roles such as advisor, while they potentially miss the required skills and guidance from domain experts. 2. End-users and policy-makers often lack the technical skills to interpret a system's limitations, and rely on developer roles for making decisions concerning fairness issues. 3. Citizens are structurally absent throughout a system's life-cycle, which may lead to decisions that do not include relevant considerations from impacted stakeholders.