If you cannot directly refute someone's principles, you strike indirectly with an attack on their confidence in those principles. Question their certainty of the principles' validity: "How can you be sure you're right?"
Whose authority? If an argument is to be resolved by such an appeal, the authority must be one recognized by both parties. A justice system which does not recognize the rights of the individual will not provide a satisfactory authority. The only way the appeal to authority can be a viable means of conflict resolution is if both parties can agree on a completely neutral, objective authority to decide the issue. Where does one exist? Only in the facts of reality.
Who decides? In all issues pertaining to objectivity, the ultimate authority is reality-and the mind of every individual who judges the evidence by the objective method of judgment: logic.