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A society of psychopaths could do quite well.
Take for example, ants, bees, and termites.
Perhaps they could do better with sympathy for each other, but I doubt it.

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Since individual ants, bees, and termites all are willing to sacrifice themselves for the good of their colony I think it goes without saying that they are not psychopaths even if they don't feel sympathy for each other. Of course the reason they're not psychopaths despite their lack of sympathy is the fact that they have no emotional capacity whatsoever (i.e. they can't be selfish either).

I don't think it's our "unique familial and tribal organization" that is key, it's the presence of higher brain funtion. If we're going to be social creatures and have higher brain function, we can't be psychopaths.