The communal strand: common ownership to nurture cooperative human nature, through mutualism, anarcho-communism and anarcho-syndicalism. Named thinkers: Proudhon, Bakunin, Kropotkin and Goldman.
Collectivist anarchism strongly holds that human nature is cooperative, altruistic and sociable. Kropotkin's mutual aid is the natural form of human cooperation; Bakunin stressed human sociability and saw the state, not human nature, as the corrupter.
Both strands reject the state, so collectivists strongly hold this. Their ground is that the state defends economic inequality and props up class power (Bakunin, Kropotkin). Goldman called the state a cold monster and argued for revolution, not reform.
Collectivist anarchism strongly holds common ownership. Private property is rejected as exploitative and replaced with mutual aid, mutualism (Proudhon: possession not property), anarcho-syndicalism and anarcho-communism (Kropotkin: distribution by need).
Collectivists strongly hold that order rests on cooperation. Anarchy is order because cooperative human nature self-organises through mutual aid (Kropotkin). Bakunin: my freedom requires the freedom of others, so solidarity, not self-interest, is the basis.
Collectivist anarchism is internally split on method. Bakunin's propaganda by the deed, Kropotkin's revolution and Goldman's revolution-not-reform all point to collective overthrow, but Proudhon argued the state should be ended by peaceful means, so the strand is mixed.
Collectivists reject the sovereign-individual ideal. Liberty is positive and social: it is realised through cooperative community and mutual aid (Kropotkin), not in the isolated self-sovereign ego. Freedom and equality are treated as inseparable.
The egoist strand: freedom for rational, autonomous, self-interested individuals, through egoism and anarcho-capitalism. Named thinker: Max Stirner; anarcho-capitalism has no named 9PL0 spec thinker.
Individualist anarchism rejects the cooperative reading of human nature. Stirner holds that each person is a sovereign ego, rational and self-interested, with no obligations beyond self-interest. Cooperation happens only when it suits the individual, not from natural altruism.
Both strands reject the state, so individualists strongly hold this too. Their ground is different: the state crushes self-sovereign individual liberty and has no authority over the ego (Stirner). Anarcho-capitalism adds that the market can supply order without a state.
Individualist anarchism rejects common ownership. It wants a free market without state regulation and private property protected as an expression of self-sovereignty (Stirner). Anarcho-capitalism builds everything on an unfettered market, the opposite of collectivist economics.
Individualists reject cooperation as the basis of order. Order comes through rational self-interested agreement: the Union of Egoists cooperates only when it suits each member (Stirner), and anarcho-capitalism reaches order through market exchange rather than mutual aid.
Individualist anarchism rejects collective revolution. Stirner reaches anarchy through insurrection and the assertion of the self-sovereign ego, not mass overthrow of the state. Anarcho-capitalism imagines the state simply withering as private institutions take over its jobs.
Individualist anarchism strongly holds the sovereign-individual ideal. The rational, self-interested ego is the centre of the moral universe (Stirner); no authority, whether state, collective or moral, has any claim over it. Liberty is negative: freedom from all authority.