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When a discussion is unproductive, incivility is often blamed, but this puts the cart before the horse: incivility is often a result of unproductive discussion, not its cause. Productive discussion demands going beyond civility: while civility is very important, four other patterns of behavior are just as important to reaching a productive outcome:
Ignoring precedent, intentionally or not, leads to repeating old arguments, which can frustrate everyone. When participating in a discussion, you should try to understand how similar situations have been handled in the past, and to act in light of that understanding. If there is a precedent for the present situation, but you think an exception should be made, acknowledge the consensus and explain why it shouldn't apply. If you want to challenge the consensus itself, do so at the right venue. ("Precedent" includes – in decreasing order of priority – all the policies, guidelines, and closed discussions that bear on the matter at hand. Global consensus supersedes local consensus.)
Fallacious arguments don't convince, they only frustrate productive discussion. Make sure your conclusions follow logically from the available information, and your argument is objectively and succinctly stated. Justify your assumptions and generalizations. Be precise. Understand where the burden of proof lies, and what the status quo is. When you see logical fallacies being committed, point them out – civilly of course.
Make sure you're talking about the original matter of dispute, and not having a dispute about the dispute, or a dispute about the dispute about the dispute. If you have an issue with how another editor conducts themselves, you may note this, but if discussion continues along that line, it should be taken to another forum (see Wikipedia:Dispute resolution). Once you get more than one level of abstraction away from the original dispute, it is very unlikely that anything you say is going to help resolve that original dispute.
Consensus is determined by the soundness of arguments and the support they receive from different editors, nothow often they are expressed, or whether they have the last word. Closers will review the discussion with this in mind. Repeating yourself to someone who wasn't convinced the first time won't produce your desired outcome – it will only generate aggravation. If you need to clarify a point or address a misunderstanding, go ahead – but make sure you're not just saying the same thing over again.
The point of any discussion is to get to a resolution. If you ignore precedent, employ a logical fallacy, stray into meta-discussion, or argue by exhaustion, you make a productive outcome less likely. If you knowingly do any of these things, you are not acting in good faith, even if you remain civil. So repeat these rules to yourself like a mantra: Acknowledge precedent. Avoid logical fallacies. Don't go meta. Don't repeat yourself.