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Algorithmic fairness research has traditionally been linked to the disciplines of philosophy, ethics, and economics, where notions of fairness are prescriptive and seek objectivity. Increasingly, however, scholars are turning to the study of what different people perceive to be fair, and how these perceptions can or should help to shape the design of machine learning, particularly in the policy realm. The present work experimentally explores five novel research questions at the intersection of the "Who," "What," and "How" of fairness perceptions. Specifically, we present the results of a multi-factor conjoint analysis study that quantifies the effects of the specific context in which a question is asked, the framing of the given question, and who is answering it. Our results broadly suggest that the "Who" and "What," at least, matter in ways that are 1) not easily explained by any one theoretical perspective, 2) have critical implications for how perceptions of fairness should be measured and/or integrated into algorithmic decision-making systems.