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How does algorithmic governance in the platform economy maintain its legitimacy despite opaque rules producing unpredictable results? Existing literature has largely explained platform power through coercion—monopolistic market power or digital surveillance—neglecting how it is sustained through legitimacy: providers' belief in the system's rationality, including coherence, efficiency, or fairness. The gap exists as current organizational literature has largely focused on bureaucratic governance, where stable and transparent rules ensure legitimacy, thus failing to explain legitimacy in algorithmic governance absent stability and transparency. Through text analysis of online community data and interviews with 24 YouTube content creators, this paper analyzes mechanisms that attenuate grievances and legitimize algorithmic governance despite opacity and unpredictability. I identify three grievance attenuation mechanisms—individualization, externalization, and structuralization—that deflect moral responsibility away from platforms. I then discuss the theoretical implications of the finding. I identify how each mechanism is underpinned by three different understandings—mechanical, adaptive, and generative—of rule, rationality, and legitimacy. I then demonstrate how these understandings reconstruct Weber's concept of legal-rational legitimacy in the context of post-bureaucratic governance. Finally, I show how these rationalities lead to skepticism about algorithmic transparency. This paper contributes to the literature on platform governance and organizational sociology by demonstrating how algorithmic governance maintains authority through legitimacy. In doing so, it offers a theoretical update to the understanding of rule, rationality, and legitimacy within rapidly changing organizational and technological contexts.