You are categorically opposed to some policy. She on the other hand is utilitarian and while she believes the policy is effective based on her current information she could be persuaded otherwise. You would like to persuade her if you could and in fact you have some information that might but it’s not guaranteed.
She opens the debate about the policy, states her arguments in favor and invites you to give any arguments against. But you are not interested in her information. You are categorically opposed to the policy and nothing would persuade you otherwise.
Moreover you are not even going to engage in the debate by trying to persuade her with your information. Because to do so would be to implicitly acknowledge that this is a debate that could be won by the side with the stronger argument. That entails the risk that she and any observer might judge her arguments to be stronger and take an even firmer position in favor.
You are better off shutting down that front of the debate and insisting that it must be decided as a matter of principle, not utilitarianism.
Cheap Talk 
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April 11, 2012 at 12:34 am
Lones Smith
If each round of conversation is costly, then it becomes a “conversational war of attrition” among two individuals with ex post common interests. Moritz Meyer-ter-Vehn (www.econ.ucla.edu/mtv) is writing on this with me and Kata Bognar. Here, dialogue may in equilibrium end at any stage with certainty in such an “insistent outcome”. What you describe above, if we toss aside the concluding philosophy angle, is the simplest such insistent equilibrium. It turns out that in equilibrium longer conversations are more efficient, and yet paradoxically, are increasingly pointless: the law of diminishing *total* returns to arguing, as it were. Sounds familiar?