In addition to ordinary conversations among relatively small numbers of individuals, human societies have public conversations. These are diffuse, ongoing discussions about various topics, which are largely sustained by journalistic activities. They are conversations about news – what is happening now – that members of various groups (such as the residents of a certain country, a certain town, or practitioners of a certain profession) need to know about in their capacity as members of those groups, and about how to react to the news. Our topic in this chapter is a type of resistance to evidence that can arise at the level of these public conversations, rather than at the level of individual agents. We call it “relevance-based resistance to evidence”. A public conversation exhibits this kind of evidence resistance when it becomes overly focused on topics that members of the group that the conversation concerns do not in fact need to know about qua members of the group – topics which are, in a word, irrelevant. We argue that the risks of such relevance-based knowledge resistance are significantly amplified by certain structural features of online discourse.