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I find from personal life experience that arguing with someone is hardly a good way to try to convince someone of something. You might end up getting whatever you'd like from the person you are trying to convince, but not because you have convinced him or her; it's more likely he ends up doing what you want because he or she is tired from arguing or fed up with it.

I think this can be seen easily in discussion forums on the internet where there are some things that are repeated over... and over... and over... And very few people seem to be convinced by what the other people say, so it's unlikely to be a good way to try to convince someone.

Is there any study of these problems?

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Plenty. The elaboration likelihood model compares the efficacy of persuasive argument under various conditions – this wouldn't be worthwhile if its efficacy were zero. Attention plays an important role: if an audience is inattentive, the semantic content of an argument may matter less than other factors involved in persuasion.

Reactance is also relevant in that arguing with a particularly resistant audience may result in even less compliance and more opposition. This has been studied empirically. It is also not universal; reactance varies with personality and other developmental factors. Thus both compliance and resistance exhibit variation empirically – enough to make persuasive argumentation viable with some people some of the time. This conclusion is also the corollary of a popular (if unscientific) aphorism:

You can fool all the people some of the time and some of the people all the time, but you cannot fool all the people all the time. — Paraphrased from Jacques Abbadie

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