I must admit I find the notion from the video that Narveson suggests we all be sociopaths or would not jump into the pond rather perplexing. I guess it is solely because I interpret Narveson’s cost/benefit categories differently than the video; as an elaboration of examples?  Narveson himself deems it a characterization and I don’t really see anything that signifies that these are co-consecutive rules that must all be met, just an explanation that these are some examples of why “time of need” can be a misleadingly simple concept and thus its obligation should be restricted.  Ultimately I admit I think Narveson puts a distasteful spin on what he is saying because of this but this is a mirror image of Singer, who could be charged oppositely in not giving any leads as to deriving his moral weight.  Narveson perhaps could have strengthened his argument by sticking to “time of need”/”cost-benefit” instead of going off on his “characterization”.  But his characterization and our subsequent disagreement with it in some sense simply further proves why we should heed his worries about individual differences. I see in both thinkers’ nuances that I need more information on, particularly the nuance of “obligation vs ought”, to reach a conclusion on where they stand absolutely and in fact whether they are even different at all. But from my understanding of the excerpts both Narveson and Singer clearly ought to go for a swim. 
   From the standpoint that Narveson’s “cost-benefit analysis” is functionally the same as Singer’s moral weight, Narveson and Singer have equivalent ought principles, and when the same premises (moral weight/ cost-benefit says jump in) are plugged in the same output is garnered as far as ought goes.  In this manner both Narveson and Singer can be said to clearly recommend, should, ought, to jump into the pond at the cost of becoming wet, for anyone who recognizes such a cost/weight disparity. Narveson’s view only suggests that a sociopathic person, in following their own cost-benefit analysis, would not derive an ought/should, and would perform sociopathic actions as a sociopath. This is reasonable and I see no reason as to why it wouldn’t be the same conclusion Singer’s principle would reach if a sociopathic person carried out Singer’s moral weight analysis. In this manner, the only difference between Narvesons ought principle and Singer’s ought principle is that Singer stretches the principle beyond ought to obligation after originally only using the word ought in his principle formulation.  From this, it could be said Narveson is in complete agreement with Singer’s principle and all the ought it entails but not the further distinction that it is an obligation or a matter of justice. 
However, Singer does not explain his shift from ought to obligation or what that means while Narveson explicitly does.  This presents a further problem of transliteration across excerpts. Just as I don’t understand what is in the text to suggest that Narveson would not recommend jumping in, in the hypothetical situation of Singer’s, there also isn’t really anything in Singer that strongly points to considering those who do not make the jump to be criminals (he only states they have done wrong and the excerpt cuts off… although it would appear Singer has no moral neutral and thus not-good is automatically doing wrong?).  In contrast, Narveson makes it clear he would recommend to any normal person to jump in and save the child but not say that they should be charged with a crime for not doing so.  Narveson would say “sociopath Jeff” is un-virtuous but not a criminal, on the other hand, Singer suggests sociopath Jeff is someone who “has done wrong”. In contradistinction to Singer, Narveson states only if we are the cause may we be obligated or must we do something.  Narveson appears to find such a leap of Singer’s & his own version to the level of obligation problematic because indication of obligation, must, necessity, or law begins to reach toward justice and enforcement.  Hence his limitation of must to things we directly cause, which we do in fact generally place under the rule of justice and accept resulting punishment through law.
In my opinion, Narveson could be said to fail in scope as he does not do justice to the reality of recognizable shared needs as expressed in the video, and presented above, probably out of fear of grounds for enforcement, or reduction of his “Liberty”. However, Narveson presents an argument that does justice to the multifaceted nature of experience and the potential lack of knowledge we may have as actors.  Singer can be said to fail in his scope, as his hypothetical pond is a strawman that ultimately does not extend to our complex world satisfyingly enough to be able to easily extend this “should” to the level of obligation or perhaps “law”.  However, Singer does justice to the fact that in the modern world, we simply do often know well enough what we ought be doing, or may agree on as good, but fail to act in a way that reflects this and perhaps need a push or should feel more obligated to carry out what we recognize to be good.   In a way, we may say Narveson gets into trouble leaving the pond and Singer gets into trouble staying in it. I am curious as to how expansions of the text would affect my understanding of their terms and conclusions.  I like Narveson’s open-endedness but if Singer explains obligation weaker than Narveson seems to, I see no reason not to agree with Singer over Narveson based on their underlying similarity and Narveson’s somewhat irrational yet simultaneously understandable fears.  Given these issues, Caputo’s non-deducible/pre-rational definition of obligation provides much respite from the frustrations of both Narveson and Singer.  Very interesting, and perhaps one of the most beautifully written bits of philosophy I’ve ever read, with a largely separate worldview to both, that presents solutions to the frustrations above but with frustrations of its own.
What am I missing here?  Is this just all on account of my understanding of Narveson’s characterization?  Is it something to do with the definition of a sociopath? If a sociopath was by the pond and followed Singer’s principle is there something baked in it I am missing that makes the sociopath know what to take as morally good even in their mental condition?  Is it because Narveson’s examples suggest analysis of moral weight is a solitary activity and Singer doesn’t explain how we decide moral weight but perhaps elaborates elsewhere?