Psychopaths are going to volunteer?

The kind that's not clever/manipulative/rich can't hold most jobs or fit into society, loves risks, is violent and impulsive, desperately wants to be cool, and may have a... troubled past. Any organization that doesn't ask too many questions (think French Foreign Legion), gives them a gun and training, tells them they're elites, and sends them off to kill people, is bound to draw a good many of them.

You don't need psychopaths to get that. And of the people actually willing to make taboo tradeoffs, take risks and hurt or manipulate people it isn't the psychopaths who are most likely to do so in a way that benefits 'society' as opposed to themselves at the expense of society.

Just for the sake of argument (see "recombination" above), you might still need psychopaths for there to be a sufficient amount of favorable genes in the pool so that normal people can get nasty in the altruistic way.

Of course you are correct, thanks for pointing out. I responded to the "tradeoff between brain diversity and murders" without thinking myself.

Still, I don't think psychopathic individuals should be prosecuted a priori, considering that they likely make up 1% of the general population.

train everyone to recognize and counter the strategies that psychopaths use

I like this way of thinking. By the way, there is some research about the weaknesses of psychopaths. From this article:

In this task, the participant has to decide whether to play a card. Initially, the participant’s choice to play is always reinforcing; if the participant plays the card he or she will win points or money. However, as the participant progresses through the pack of cards, the probability of reward decreases. Thus, initially ten out of ten cards are rewarded, then nine out of ten, then eight out of ten continuing on until zero out of ten cards are rewarded. The participant should stop playing the cards when playing means that more cards are associated with punishment rather than reward. That is, they should stop playing the cards when only four out of ten cards are associated with reward. Children with psychopathic tendencies and adult individuals with psychopathy have considerable difficulty with this task; they continue to play the cards even when they are being repeatedly punished and may end up losing all the points that they had gained.

Just making these weaknesses widely known, together with some simple strategies for exploiting them (something like "The Game", just about playing your boss), could change the balance on the playing field...

a TDT without empathy will Win against decision theories like the ones human brains use.

'Winning' is not really the right word here - a rational decision procedure should Win by definition. Clearly, psychopaths have different goals compared to the rest of the population: for simplicity, let's suppose that, compared to neurotypicals, they lack a terminal goal of not inflicting direct costs on others. However, punishing people for lacking certain terminal goals is not quite kosher by modern political/ethical standards. We don't lock people up for not donating enough to developing-world charities, because we understand that the vast majority of interactions are positive sum regardless.

Whether a psychopath approximating TDT could cooperate with a neurotypical person following either TDT or some kind of informal morality - and vice versa - is an interesting question and one that probably does not have an easy answer. However, in theory, TDT-approximating psychopaths should readily cooperate with each other.

It may also be the case that psychopaths are less able to enter precommitments and abide by them due to their overall deficits, which would make them more similar to CDT agents. However, this would not make them "winners" either, in any real sense: far from it. They would stop "winning" as soon as their lack of commitment (and thus non-credibility) was perceived by other agents - which would be quite soon, especially in a more rational world with a higher sanity waterline.

There's only an argument for altruism and cooperation if an agent is certain the other agents are running a decision theory that is as good as its own and their utility functions are similar enough to cooperate.

It also works in society, with a government enforcing law and puts forth other fines and incentives. Furthermore, humans are messy. Our immediate desires, on a lower level, can be quite different from our long-term, reflected, higher goals. It's a matter of impulsiveness which of these wins how frequently.

I don't believe psychopaths have any greater-utility terminal values than getting what they want at the expense of others.

Why "at the expense of others"? That's a property of the world, not of them (which does not excuse what they do).

I don't want to punish psychopaths either. I want to make them less psychopathic.

I apopogize for misreading you. "We didn't eradicate malaria or polio with kinder, gentler methods. Don't leave anything for evolution to work with." sounds rather more... straightforward to me than you apparently meant it. I'm glad that we agree that psychopaths should be helped, whereever possible, to become productive parts of society.

Therapy appears to teach psychopaths better skills at manipulating people.

Then the current therapeutic methods are not well-suited for this task. If we want to go down the road of developing more effective means of psychopath crime prevention, therapy etc., I suggest we Hold Off On Proposing Solutions.