  Recent advancements in machine learning and deep learning have brought
algorithmic fairness into sharp focus, illuminating concerns over
discriminatory decision making that negatively impacts certain individuals or
groups. These concerns have manifested in legal, ethical, and societal
challenges, including the erosion of trust in intelligent systems. In response,
this survey delves into the existing literature on algorithmic fairness,
specifically highlighting its multifaceted social consequences. We introduce a
novel taxonomy based on 'tolerance', a term we define as the degree to which
variations in fairness outcomes are acceptable, providing a structured approach
to understanding the subtleties of fairness within algorithmic decisions. Our
systematic review covers diverse industries, revealing critical insights into
the balance between algorithmic decision making and social equity. By
synthesizing these insights, we outline a series of emerging challenges and
propose strategic directions for future research and policy making, with the
goal of advancing the field towards more equitable algorithmic systems.
