It would seem to me that a self-interested person would recognize that cooperation among and with many others satisfies that self-interest. 
It would seem to me that a self-interested person would recognize that cooperation among and with many others satisfies that self-interest.
“Altruism” was a term that became popular during the eighteenth century, when religion was in eclipse and it was argued that you could construct a society by persuading people to behave reasonably. The more traditional term was morality, based in turn on religion.
The problem with altruism based on reason is that the motivations are not strong enough. Some people will behave reasonably. They will treat others well so they will be treated well. But plenty of others will act differently, and the system will break down. So, as Hobbes pointed out, in the state of selfish nature you need a strong monarchy and magistrates to keep order. Criminals are hanged or deported, and that encourages the others to stay out of trouble because they fear the consequences of disobedience.
The American system was better: a citizenry who were basically religious and who valued freedom enough to control themselves, rather than have a monarch to control them. As Toqueville noticed, American freedom relies on religion and morality to keep it working. Remove those, and you will descend into a police state.
Because of the inherent orneriness of most people, or original sin as Christians call it, there will always be at least some criminals and troublemakers. The question is, how many? Few enough to control with a reasonable number of police and courts, or enough to upset the politics of the state and make it impossible to have a free people? Experience shows that without religion, the only solution is overwhelming state power—not a satisfactory solution for people who have been bred in freedom.