I think the reasoning behind this is worth making explicit. even if the expected value of the Atkins diet is negative to a randomly selected member of the population, it may still be reliably positive for some very specific small subset. if you have a strong reason to believe that you're a member of that subset, then information about the average is less relevant to you than it might otherwise be. for example, a reduction in calorie intake, while beneficial for the average member of the population, is not beneficial to people who are severely underweight.
Right, thank you for making it explicit.
This seems like an authoritative 25-year research project that the Atkins diet is pretty bad:
http://www.nutritionj.com/content/11/1/40/abstract
Right now my belief is that the Atkins diet is good. It's backed by anecdotal evidence of trying a low-carb diet for 18 months following a 12-month low-fat diet and seemingly getting better results with the low-carb diet.
I'm counting on LWers to tell me how to update my belief in light of this study. Thanks.