And why scientific principles should be superior to non-scientific ones within the public sphere.
(does the subtitle make me a modernist? well, then let it be so..)
I believe scientific principles making an argument convincing - that is, empirical observation, logic, mathematics, statistics and probability are superior to other principles, such as propaganda, subliminal effects, exploiting people's prejudices and so forth.
The superiority of the former can be illustrated by legislation banning lying in commercials, establishing a moratorium before public elections or, more importantly, the rules guiding a trial procedure of a court.
Now, let us consider an example of a validity of an argument.
When a politician on a verbal attack accusing him of theft reacts with a counter attack, calling the opposition MP a thief, there are two possibilities in considering the convincingness of such an argument.
On the one hand, with the counter-attack, the politician may want to consider and treat theft as a social norm. In that case, it is a valid counter-argument saying, in fact, "it is socially acceptable to steal, look, you do it as well, so why are you treating my behavior as morally inferior?."
In most cases, however, this would not be the stance of the defender. The defending politician would mostly feel that he is playing a non-cooperative Prisoner's dilemma game. However, after some reflection, he would acknowlage, I believe, the superiority of the non-stealing arrangement within the game. Then, the point is to find the way out of the suboptimal equilibrium - be it mutual concessions, establishing monitoring and sanctioning institutions and so forth. (For the solutions, please consult for instance the literature on overcoming anarchy in international relations).
On the other hand, when accepting the social norm of non-stealing rather than the opposite, the counter-attack shall be decisively non-convincing to an erudite observer. Therefore, developing such social norms might play a crucial role in the determinants of convincingness of arguments in a public discussion. For this, understanding the game one is playing and the way out is fundamental.
(Intro: Anyone, who endevors to debate, is a priori believing in the existence of intersubjective principles making an argument convincing. Otherwise, he or she would not debate. In other words, anyone willing to discuss is believing in the possibility of discovering the intersubjective truth.)