What is it for an argument to be sufficiently dialectical? Here are two rough desiderata. First, an argument must be composed not merely of reasons that support its conclusion, but of reasons that its target audience can recognize as reasons. Accordingly, a flat-footed appeal to the authority of the Pope in a dispute among Catholics and non-Catholics about the permissibility of stem-cell research is a dialectical failure. Second, an argument must address the most pressing concerns and doubts that prevail among the target audience. That is, in order to attempt resolve a disagreement, we must not only assess the reasons for one of the sides, we must assess the reasons for both sides. So a dialectically proper argument presents not merely a case for one’s preferred view; it must also take into account the going criticisms and objections to one’s conclusion. Those arguments that fail to satisfy these desiderata beg the question.
I understand that these are supposed to be rough, but I find this a somewhat peculiar characterization of 'dialectical success', at least for philosophers to make. It's hard to get more brilliantly successful at argument, in dialectical terms, than Plato's Socrates in the best parts of the Platonic dialogues, but Plato regularly shows Socrates failing to meet the first desideratum, and in some dialogues this is clearly done deliberately. This is because there are other kinds of dialectical success than persuading the target audience -- and one could very well argue that this is precisely the point Plato is making: that dialectical success is not resolution of disagreement but actually engaging in the dialogue itself as lovers of truth. It's true that "flat-footed appeal" to things your target audience won't recognize as reasons is dialectical failure, but I find the "flat-footed" interesting, since it's a qualification that directs attention to itself and suggests a contrast, leaving the question, 'What of non-flat-footed appeals?' hanging in the air. Socrates, not flat-footed at all, more than once appeals to reasons that his target audience can't recognize as reasons because his whole point is to get them to recognize them as reasons even though they don't yet. Perhaps we should speak not of arguments composed of reasons that its target audience can recognize as reasons, but of arguments that are themselves recognizable by the target audience as reasons, when taken as a whole? (It's certainly the case that an argument can be recognized as a reason without being composed of reasons recognized as reasons; sometimes people aren't recognizing reasons as reasons merely because they aren't seeing the forest for the trees. I always think of the third part of Bk. 1 of Hume's Treatise, which is very difficult to follow if you just look at it point by point -- it looks repeatedly like he is overlooking things -- but is suddenly massively more impressive if you look at how the whole thing is structured. This might not quite count, but it's still important to keep in mind that recognizing something as a reason is sometimes a form of recognizing its role in a whole structure of thought, not always on a case-by-case basis. Whether simplicity is a reason for accepting a scientific theory, for instance, depends on what kinds of other reasons there are for accepting it.) I'm not sure.
I'm also somewhat skeptical about the second desiderata; there's something to be said for small successes on secondary matters, since these can sometimes bloom into a common foundation for more significant reasoning. Indeed, I think political argument in modern democracies largely tends to succeed by such a mechanism. Resolution of disagreement is like problem-solving, and while sometimes it's a good idea to go directly to the heart of the problem, sometimes you'll be more successful handling the easy things first -- and sometimes doing so will uncover a more fundamental problem.
In practice what count as the most pressing concerns and doubts are not stable, but constantly shifting, and is actually very difficult to figure out. A possible example of this is the fact that one often finds pro-choice advocates who take the pressing concerns of pro-life advocates to include the moral status of the embryo; whereas pro-life advocates almost never talk about moral status at all unless they are responding in some way to pro-choice advocates using the phrase. We are all a bit like housecats, really. Cats don't really meow when they grow up in the wild, except as a random noise they sometimes make. The reason they meow when raised by us is that we listen to them when they do. Pro-life advocates who only deal with pro-life advocates talk about things like respect, sympathy, innocence, the sorts of things people ordinarily talk about when they talk about how to treat children (or animals, for that matter); they talk about moral status when dealing with pro-choice advocates chiefly, it would seem, because they think the pressing concern of pro-choice advocates is moral status. At least in historical terms, the topic spread to pro-life advocates from pro-choice advocates, not the reverse; pro-choice advocates were talking about moral status long before it became common for pro-life advocates to do so. At the same time, given the state of the argument, it's obvious that this could become a pressing concern for pro-life advocates in trying to give their arguments, and, indeed, it seems to be in the process of slowly becoming so.
The fact of the matter seems to be that we have no real way of knowing what the pressing concerns of people are unless we can count on them honestly giving the arguments that they think we should accept -- those are their actual pressing concerns. This seems to be what Aikin and Talisse have in mind with their comment about considering both sides, but this seems to cut against the first desideratum: I have no way of actually knowing what the other side's pressing concerns are unless they are trying to get me to see them regardless of whether I actually accept them as reasons. If someone is actually going through the trouble of trying to get you to see the importance of his flat-footed appeal to the Pope, you at least know that his Catholic conscience in light of Church teaching is one of his pressing concerns; if he avoids such appeals altogether in the attempt only to present reasons that you would recognize as reasons, how would you ever know that this was a thread informing the disagreement? But if the point of the given argument is to resolve a disagreement, you need to be actively talking about all the things that are actually contributing to the disagreement, regardless of whether one side regards them as real reasons (perhaps especially then).
I think this suggests a way in which the rough desiderata are as yet perhaps too rough to be as useful as they might seem: they both assume that everyone on both sides can have access to the arguments of the other side. But this requires that we already have aired our arguments in the attempt to resolve the disagreement, and found that they weren't adequate; then we can sort out which arguments each side could recognize as reasons, and take into account the actual pressing concerns of the other side, rather than just our own image, perhaps fictional, of what their pressing concerns are. But all this requires a state of argument in which people don't fit either desideratum; and it suggests that part of dialectical success, prior to anything to do with resolution of disagreement, is simply discovering that we do disagree in a way worth further argument, and discovering the real reasons why the disagreement is there. And that, of course, brings us back to Plato: our argument still has a form of dialectical success if we all come away with a better understanding of the issues. By the end of the Gorgias, or the Republic, the actual disagreement has not been resolved at all; but Socrates's arguments have been a success in that now everybody knows what the disagreement really is.