In the following passage, are the words in italics an independent clause, a subordinate clause, or a fragment? each candidate will have exactly the same rights to formulate his or her policy proposals. “but not to compel the media to pay attention.”

In this passage, the words in italics “But not to compel the media to pay attention.,” are a fragment of the whole sentence or clause because, by itself, the fragment does not make much sense when you isolate it from the main clause, as the independent clause does (e.g. "Each candidate will have exactly the same rights to formulate his or her policy proposals.") As you see, this sentence makes perfect sense even without the fragment that starts from "But...," and it cannot either be a subordinate clause since the conjunction 'but' is a coordinating conjunction that gives equal importance to two ideas; it is only used for coordinate clauses (i.e. two main sentences.)