Thank you, that's a great formalism. Under your terminology, my position is that there is a difference between someone with addiction, vs. someone with consistent first/second-order preferences, and that this difference is so empirically significant as to justify having different terms, and that this difference is experimentally detectable (at least in hypothetical situations).

Of course, your definitions define addiction by that experimental difference, and that's something I'd want to avoid.

Vladimir_M's point, in turn, is that people with consistent first/second order preferences that are not socially acceptable try to persuade others it is actually a case of addiction in order to increase the net benefit of indulging that preference. I agree with him that this is often what's going on, but disagree that it can account for all cases, thereby necessitating the distinction of the separate category of akrasia (and addiction).