That's an interesting hypothesis, and worth looking into. If the group is a graph connected by people becoming aware of the campaign, participating in it, and forgetting about it, then there's a feedback loop that should taper off in a predictable way. This would gel with what seems to happen.

And as you point out, there's also a moment where the event becomes calcified, earning an entry into some wiki that records the biggest campaigns against individuals. This also seems to have the effect of permanently branding the individual so that if they do anything else perceived as a violation by a member of the group, a significant chunk of the network can reactivate quickly for a second round.

There's also a thin line between observation and participation. Someone might be passively aware of what's going on from reading 4chan or seeing it here, and they might comment, and the comment (maybe a suggestion) could galvanize the network to act in some way (call her employer). Each individual who does this may feel moral responsibility only for a trivial fraction of the damage. "All I did was make one phone call. I'm not responsible for what other people do."

Add that to a good technological mechanism for acting anonymously, and we get what we're seeing: a huge campaign of harassment unencumbered by moral and social concerns. Somewhat different from a family drama but not totally so. I'm sure there are sociological studies on how "shunning" works, but if you could get a hook into the numbers here, maybe there's a pattern that has general properties that subsume cases where people are more accountable and less anonymous.

The other question that interests me is whether there's a point in the "ramping up" side of the distribution where an active intervention of some kind can mute it.

The only criteria for participation in Anonymous, for example, is a commitment to the "lulz" at hand. If you're not in the current campaign, you're not provably in Anonymous. For example, just after the name began to be appropriated by people at the edges who were mostly interested in targeting scientology, and described in the news as a good campaign against a cult, we saw an attack on an epileptic support forum. This had the effect of purging people who claimed to be Anonymous but morally disavowed it. That's synonymous (hmm) with splintering the group, but the criterion of doing it solely for laughs was retained by one group and lost by the other. It'd be reasonable to call the former the "core." So there IS a form of accountability in Anonymous, and it operates strictly in the moral dimension of the action.

That would imply that both the ramping up and ramping down of a campaign is exactly the same as the size of the group (as defined by devotion to "lulz") at any given moment. Perhaps tautological, but different from a family. Apply this generally to all anonymous distributed groups. It also implies that an action that subverts the moral identity of the group can subvert a campaign. If you do something so reprehensible that a large contingent of the individuals in the campaign are compelled to disavow it, then you could effectively kill the distributed campaign. Is that a net win? Probably only if you convince enough people that you did it without actually doing it. Another possibility is to engineer a compelling distraction that draws in members of the campaign. But it seems to me that with enough knowledge, an individual or a smaller group can actively and deliberately affect the tapering off, either through manipulation of attention span or manipulation of moral alignment.