As clarified already, this question implies a binary between government and social media, one that is not necessary appropriate or clear-cut. Equally, this question requires us to define how we understand power. Is it power over others? Is it coercive power? Or, is power something more positive and collective, for example, in the sense of Hannah Arendt, in which power exists in the collective capacity of people to realise new beginnings in a public world by speaking and acting with others. In this final sense, government and social media, while quite different and not clearly opposed, are factors that both constrain and enable power through public discussion.
To explain: Government is part of the structures that enable and create space for public discussion to unfold, for people to meet, discuss and engage freely and openly with others. It also limits it, by defining and regulating legitimate activity, and where and how this can take place.
Social media is a means through which communication takes place. It also enables and shapes the possibility and activity of public discussion. They are means through which people can interact with others, with particular forms of openness but also constraints, shaped by the corporate and technological structures through which communication is possible.
So then, what is happening to the importance of ‘government’ as something that constrains and enables public discussion when public discussion moves to take place on social media?
This points our attention to the ways that communication through social media. For example: the use of social media alters how and where government manifests in our everyday experiences, and how it affects our participation in public discussion. It alters how government matters to the nature and power of public discussion, for example, becoming relevant in how it regulates the internet, its use and its supporting infrastructure, or relevant in how government materialises in the use of social media to gather, process and communicate information in different forms.
Social media also introduces new forms of control, apart from those tied to government, such as those tied to Facebook as a corporate entity. Further, we might identify new opportunities for openness in our discussions through social media, as people can shape who they are in ways that are detached from place, physical co-presence and physical appearance.
Therefore, if we take power as something productive, something tied to our shared freedom to publicly and collectively define the world we live in, then maybe we need to be asking a different question. We perhaps need to ask how the combination of the institutions, structures and media through which we meet one another are limiting and enabling the freedom and openness of our discussions.
This question makes no sense because it assumes that the two are separate. In studying media as social phenomena we generally look at three interrelated domains: context of the institutionalization and proliferation of media, media as text, and how media is lived and made sense of. The "government" is complicit in all three of these domains, just as all three of these domains occasion the state.