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Those twins studies constitutes a low-power measurement of effects of whatever it is that parents in the broad population happen to be doing during the time period of the study. It should not be confused with a measurement of the effects of best practice. Many professional and parent-mediated interventions have been shown to have significant effects in random controlled trials or by other means that are not confounded by genetics. As a broad estimate, any intervention that health insurance will pay is such an evidence-based intervention and there are more outside of that category, the standard for which evidence-based intervention are cover vary from state to state, nation to nation. Some of these have long-term effects.

You write "barring...trauma". Is the definition of "trauma" broad enough to capture all the evidence-based interventions?

The link on "AI needing a caregiver" links to your profile and I can't find the post about AI needing a caregiver.

Thoughts in relation to AI learning...

Parents tend to be a bit obsessed with setting limits. Setting limits is sometimes necessary, but parents tend rely too much on reacting to limit crossings. If you trained a robot by only reacting to limit crossings then the robot might well spend all it's time bouncing off the limit.

Think of a limit as a border on a region of acceptable behavior. The Kazdin method relies on incrementally (in small behavior shaping steps) drawing the child toward the optimal point in that region of acceptable behavior. If you train a robot this way, then the robot will tend stay sufficiently close to the optimal location, well away from the limits.

I still don't think you are reinforcing separation. You are not giving them a tangible or intangible reward when they separate. Also, I don't see that the mere act of separating them will alienate them from each other.

But I can see that it's plausible that there might be a better strategy than separating them.

You mention inner motivation, competing children, conflict/violent outbreaks. I don't think you yet have a proper analysis of this violent behavior.

I don't think of competition as bad in and of itself. Kids can compete to improve in the direction you want them to improve and you can direct sometimes this process merely by directing your attention toward the preferred behavior.

The violent conflicts are probably not caused by inner motivation. It probably the kids motivating each other's behavior. The problem is that, like inner motivation, it's not your behavior that is reinforcing the conflict, so it can be a bit harder to address. The dynamics might be the Patterson Coercive Cycle, only between two siblings rather than a parent and child:

I think the usual approach is to separate the kids. Why do you say "reinforce separating them"? You probably are not reinforcing the conflict by separating them. It probably puts conflicts on extinction if you put them both in time out.

Otherwise, you'd have to make sure the aggression does not get it's reward. That is possible but seems hard. Or you could come up with alternative behaviors that had the same function as the aggression, but I don't have any good ideas on how to do that, but you could come up with competitions that are less likely to lead to aggression.

Also, this Kindness Chart, or something like it might help:

Inner motivation is a different issue, I think. Typically you change the behavior to a better one that fulfills the same inner motivation.

One thing you did not discuss is fading. Fade tokens to just use praise and positive attention. Fade constant praise to occasional random praise. Random reinforcement makes a habit more robust and less prone to extinction. (I think of fading as moving toward occasionally reminding the kid that the behavior is evidence of his good character, his virtues, but I a not sure that is explicit in Kazdin's book.)

A central idea is catch them being good and reinforce. Then, after a period of constant reinforcement, fade. If the target behavior does not happen then you can't just catch them doing it. So, use methods to get it started: simulation, prompting, token reward charts. (Also, you might shape if starting with some existing behavior.)

Prompting is a technique to get more compliance to commands. Get close to the kid, speak calmly, touch, don't use a question. Avoid prompting more than a few times (3 or 4) without compliance (nagging). Instead, come up with a different strategy.

The term punishment kind of tricky in this context. Kazdin is a behaviorist writing a parenting book. In behaviorism, the term has a different meaning from it's typical use by parents.

In behaviorism, "positive" means adding something, and "negative" means taking something away. A reinforcement increases a behavior, a punishment decreases a behavior. So in behaviorism efficacy is built into the definition, if it does not decrease behavior then it's not a punishment.

In parenting, punishments are typically used incorrectly, overused, have bad side effects. And, most importantly, it's often not the best alternative because research has found better alternatives. Also, parents are reinforced to punish because they tend to be rewarded with short-term reinforcement, so it can be part of a vicious cycle. What parents consider a punishment might actually be reinforcement, for instance (1) yelling at your kid can make you look like a vanquished foe (2) if the kid can divert the parent into a predictable punishment mode, the parent might not follow through on something that the kid wanted to avoid even more.

If I recall correctly, Kazdin's does not tell parents to never use short-term grounding (or withdrawal of privilege), and that's a negative punishment in behaviorism. He says long-term grounding is no more effective and just causes resentment with no extra benefit.

Another issue with punishment is that it amounts to an attempt to replace a behavior with nothing (as was pointed out the the main article). Behaviors exists because they have a function, but mere elimination means the function is not addressed. Tends to be better to replace the behavior with something that has the same function. For instance, replace an unwanted behavior that functions to get attention with a wanted behavior and give that attention, so that the wanted behavior fulfills the existing function.

And as you point out, punishment tends to train avoidance of the parent and sneakiness.

In summary, punishment has bad side effects and it's not a tool for building up a system of wanted behaviors.

Good point, I was trying to briefly summarize Marcuse's view but I did not do a good job.

Marcuse view was that we think of ours as a materialist culture, but we are beyond the need for material goods in the sense that our productive capacity far exceeds our needs (but of course, we distribute unevenly so that there are still some in material need.). Demand is driven by emotional needs rather than material needs. And the stuff we buy often does not satisfy the emotional need, hence demand becomes unbounded.

But a musical instrument is perhaps something that can lead to emotional fulfillment.

(Marcuse was a sort of neo-Marxist and was pushing the idea that the capitalist system exploited this to create unbounded demand. I don't mean to push that view, I just think some of the premises of his argument have merit and is relevant to the topic. After all, some of the pre-capitalist rich seemed have an unbounded desire for riches.)

Trying to channel Marcuse from memory, here goes: We have a finite need for money. We need it for is adequate food and shelter. But unsatisfied emotional needs can be effectively unbounded. It's possible for the culture to convert the things that money can buy into something that we seek because of unsatisfied emotional needs. From hence flows the unbounded need for money.

Marcuse would substitute "capitalist" for "culture". But perhaps it's just something about human nature. Perhaps it's the dopamine system in our brains. Not sure why it works this way (assuming it does indeed work this way).

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