TBH the #1 rule should be: set a limit of time for arguing with individuals or groups of individuals who are dogmatically sure in something for which they don't even provide any argument for that could conceivably been this convincing to them. E.g. "why you are so sure exactly 1 God exist", "well, there's a book, which i agree doesn't make a whole lot of sense, it says it was written by God..." what ever, clearly you aren't updating your beliefs to '50% sure god exists' when presented with comparable quality argument that god doesn't exist, and by induction, no amount of argument can work, therefore there's no use arguing.
Unproductive arguments usually are genuinely result of at least one side being stupid, or insane, or doesn't care. Typically the count is 2, because why the hell is the other person arguing with the stupid, or insane? edit: there can be reason in public arguments though.
edit: also, this is why steel-man ing the other side arguments don't work in practice. Usually, if it could have worked, there wouldn't have been an argument in the first place. In theory, 2 intelligent people come to intelligent disagreement, and one side can steel-man other side's argument and then disprove it, and the other person will be enlightened. In practice, virtually all of the time, at least one side is being stupid, and often that includes you, and nothing good is going to happen out of your motivated re-interpretation of other side's argument. edit: actually, scratch that. If you can steel-man other side's argument that they didn't steel-man already, that would typically be result of other side's lower intelligence or ignorance to begin with. Proving lower and upper bounds in math, that's the steel man that works, but in verbal stuff, not so much.
We've all had arguments that seemed like a complete waste of time in retrospect. But at the same time, arguments (between scientists, policy analysts, and others) play a critical part in moving society forward. You can imagine how lousy things would be if no one ever engaged those who disagreed with them.
This is a list of tips for having "productive" arguments. For the purposes of this list, "productive" means improving the accuracy of at least one person's views on some important topic. By this definition, arguments where no one changes their mind are unproductive. So are arguments about unimportant topics like which Pink Floyd album is the best.
Why do we want productive arguments? Same reason we want Wikipedia: so people are more knowledgeable. And just like the case of Wikipedia, there is a strong selfish imperative here: arguing can make you more knowledgeable, if you're willing to change your mind when another arguer has better points.
Arguments can also be negatively productive if everyone moves further from the truth on net. This could happen if, for example, the truth was somewhere in between two arguers, but they both left the argument even more sure of themselves.
These tips are derived from my personal experience arguing.
Keep it Friendly
Probably the biggest barrier to productive arguments is the desire of arguers to save face and avoid publicly admitting they were wrong. Obviously, it's hard for anyone's views to get more accurate if no one's views ever change.
Inquire about Implausible-Sounding Assertions Before Expressing an Opinion
If someone suggests something you find implausible, start asking friendly questions to get them to clarify and justify their statement. If their reasoning seems genuinely bad, you can refute it then.
As a bonus, doing nothing but ask questions can be a good way to save face if the implausible assertion-maker turns out to be right.
Be careful about rejecting highly implausible ideas out of hand. Ideally, you want your rationality to be a level where even if you started out with a crazy belief like Scientology, you'd still be able to get rid of it. But for a Scientologist to berid themselves of Scientology, they have to consider ideas that initially seen extremely unlikely.
It's been argued that many mainstream skeptics aren't really that good at critically evaluating ideas, just dismissing ones that seem implausible.
Isolate Specific Points of Disagreement
Stick to one topic at a time, until someone changes their mind or the topic is declared not worth pursuing. If your discussion constantly jumps from one point of disagreement to another, reaching consensus on anything will be difficult.
You can use hypothetical-oriented thinking like conditional probabilities and the least convenient possible world to figure out exactly what it is you disagree on with regard to a given topic. Once you've creatively helped yourself or another arguer clarify beliefs, sharing intuitions on specific "irreducible" assertions or anticipated outcomes that aren't easily decomposed can improve both of your probability estimates.
Don't Straw Man Fellow Arguers, Steel Man Them Instead
You might think that a productive argument is one where the smartest person wins, but that's not always the case. Smart people can be wrong too. And a smart person successfully convincing less intelligent folks of their delusion counts as a negatively productive argument (see definition above).
Play for all sides, in case you're the smartest person in the argument.
Rewrite fellow arguers' arguments so they're even stronger, and think of new ones. Arguments for new positions, even—they don't have anyone playing for them. And if you end up convincing yourself of something you didn't previously believe, so much the better.
If You See an Opportunity To Improve the Accuracy of Your Knowledge, Take It!
This is often called losing an argument, but you're actually the winner: you and your arguing partner both invested time to argue, but you were the only one who received significantly improved knowledge.
If you're worried about losing face or seeing your coalition (research group, political party, etc.) diminish in importance from you admitting that you were wrong, here are some ideas:
Some of these techniques may seem dodgy, and honestly I think you'll usually do better by explaining what actually changed your mind. But they're a small price to pay for more accurate knowledge. Better to tell unimportant false statements to others than important false statements to yourself.
Have Low "Belief Inertia"
It's actually pretty rare that the evidence that you're wrong comes suddenly—usually you can see things turning against you. As an advanced move, cultivate the ability to update your degree of certainty in real time to new arguments, and tell fellow arguers if you find an argument of theirs persuasive. This can actually be a good way to make friends. It also encourages other arguers to share additional arguments with you, which could be valuable data.
One psychologist I agree with suggested that people ask
If folks don't have to drag you around like this for you to change your mind, you don't actually lose much face. It's only long-overdue capitulations that result in significant face loss. And the longer you put your capitulation off, the worse things get. Quickly updating in response to new evidence seems to preserve face in my experience.
If your belief inertia is low and you steel-man everything, you'll reach the super chill state of not having a "side" in any given argument. You'll play for all sides and you won't care who wins. You'll have achieved equanimity, content with the world as it actually is, not how you wish it was.