It is unfortunate that Kropotkin's intellectual descendants, the anarcho-communists, rejected the strongest part of Bakunin's analysis, the anti-statism, and emphasized the weakest part, poor economics and self-immolating altruism in the name of "humanity." Kropotkin stressed this altruism, writing extensively about "mutual aid," but interpreted it as a negative-sum game. In other words, he saw mutual aid as non-profit selfless altruism; he seemed to have no clue about the insight of the individual anarchists - that social interaction could be a win-win situation. The modern notion of free markets, and trade being beneficial ex ante to both parties in a transaction, while understood by Warren, Spooner, and Tucker, were apparently beyond the pale of Prince Kropotkin.

Kropotkin was one of the originators of the mistaken notion that anarchism opposes social hierarchies of all types, rather than only imposed, coercive hierarchies. This rejection of voluntary leadership and natural hierarchies have continued to this day, much like the terrorism of "propaganda of the deed," in giving anarchism a bad name.

That is why Anarchy, when it works to destroy authority in all its aspects, when it demands the abrogation of laws and the abolition of the mechanism that serves to impose them, when it refuses all hierarchical organization and preaches free agreement - at the same time strives to maintain and enlarge the precious kernel of social customs without which no human or animal society can exist. - Peter Kropotkin, Anarchism: Its Philosophy and Ideal (1896)