Their behavior can be wise and rational or unwise and rational. To be wise is to take a long term view of your own future when deciding on a behavior. If you take a short term view, similar as with investments, you're pretty much gambling. When you gamble you might gamble based on some rational theory but you typically lose long term and this is what happens a lot of the time with psychopaths who as I said have great difficulty taking a long term view.
A martingale is any of a class of betting strategies that originated from and were popular in 18th century France. The simplest of these strategies was designed for a game in which the gambler wins his stake if a coin comes up heads and loses it if the coin comes up tails. The strategy had the gambler double his bet after every loss, so that the first win would recover all previous losses plus win a profit equal to the original stake. The martingale strategy has been applied to roulette as well, as the probability of hitting either red or black is close to 50%.
Since a gambler with infinite wealth will, almost surely, eventually flip heads, the martingale betting strategy was seen as a sure thing by those who advocated it. Of course, none of the gamblers in fact possessed infinite wealth, and the exponential growth of the bets would eventually bankrupt "unlucky" gamblers who chose to use the martingale.
A narcissist who follows a wise strategy can be perceived at one of the most moral people in society whilst also being completely rational and selfish. Narcissists can manage this because narcissists care a lot about how other people perceive them and this is a key difference which in my opinion is the real thinking behind moral behavior. The moral behavior is something an individual adopts in order to be perceived a certain way by others in society whom they respect or seek the respect of. So it's actually rational behavior to adopt moral behavior but only if you take a long term view and think long term.
Unless you can to prove that being egoistic in this case is irrational. Good luck with that! It's morally bad but not irrational.
I don't have to do that. I can show you that you can be rational but have a short time horizon or you can be rational and have a long time horizon. If you don't believe you are going to live more than 5-10 more years you might not have any reason to care about social conventions of society or adopt the moral norms of your community. But if you do intend to live beyond 10 more years and you intend to stay in that community, then it becomes rational to adopt the moral norms of that community. There is no reason other than rationality to adopt moral behavior in my opinion and if it is irrational to be moral then I would think a lot of people wouldn't be. Going against the moral norms is essentially taking a bet, and there is risk and reward with any bet.
References
- https://en.wikipedia.org/wiki/Martingale_(betting_system)