This study examines support for regulation of and by platforms and provides insights into public perceptions of platform governance. While much of the public discourse surrounding platforms evolves at a policy level between think tanks, journalists, academics and political actors, little attention is paid to how people think about regulation of and by platforms. Through a representative survey study of US internet users (N = 1,022), we explore antecedents of support for social media content moderation by platforms, as well as for regulation of social media platforms by the government. We connect these findings to presumed effects on self (PME1) and others (PME3), concepts that lie at the core of third-person effect (TPE) and influence of presumed influence (IPI) scholarship. We identify third-person perceptions for social media content: Perceived negative effects are stronger for others than for oneself. A first-person perception operates on the platform level: The beneficial effects of social media platforms are perceived to be stronger for the self than for society. At the behavioral level, we identify age, education, opposition to censorship, and perceived negative effects of social media content on others (PME3) as significant predictors of support for content moderation. Concerning support for regulation of platforms by the government, we find significant effects of opposition to censorship, perceived intentional censorship, frequency of social media use, and trust in platforms. We argue that stakeholders involved in platform governance must take more seriously the attitudes of their constituents.