At base, the most popular among those normative approaches themselves are social, at least starting from the generation after Karl Popper, who may be behind your whole 'lot' of philosophers of science.
The overall approach of the school of Kuhn, and the thread of Feyerabend immediately to its 'left' are both entirely social interpretations, even though one is also entirely normative and the other suggests a normative base exists but is better left implicit. Between them, these three names capture the classical arguments.
Thomas Kuhn proposes that what makes a science is a paradigm, a shared model that has enough traction to allow for 'normal science' to take the form of 'puzzle solving' without too blatantly ignoring obvious 'anomalies'. But all of the terms involved are negotiated social constructs. What is 'enough traction'? What makes something simple enough to be a 'puzzle' and not a genuine philosophical problem? When is ignoring something 'too blatant'? All of those are sociological questions, and the discipline will shift when the community as a whole loses consensus and feels any of those subjective lines have been crossed. But that is another socially negotiated boundary -- who is inside and who is outside that community, so that their opinion even lends weight? Kuhn's model of science is really as a sociological process, though a basically conservative one that tries to freeze each consciously negotiated political consensus in place as long as possible.
Paul Feyerabend denies that a discipline even needs a single paradigm, and proposes that even this kind of consensus management is counterproductive. He encourages an unarticulated sense of what is and what is not productive contribution based on a completely social view of who does and who does not get read.
He motivates this lack of boundaries by elaborating the problems faced by Galileo and bases his overall approach in a theory of the meaning of stories, which he grounds in the evolution of hieroglyphic representation and war stories.
So he does not see science as something arbitrary. The direction Galileo moved was forward in a subjective but easily understood sense, and the ability to incorporate theories and models into stories is a real process that he considers a central part of knowing what is and is not science. He explains himself well enough that it is no longer mysterious how he can reject Lysenkoism and approve of traditional Chinese medicine as a useful scientific process. But it is overall a vague, shared psychological/sociological process.
Feyerabend's primary work is addressed to Imre Lakatos, who tries to negotiate a proper balance between Kuhn and Popper, and who may be seen as a good touchpoint to the whole argument.