Nozick's strategy against philosophical anarchism is to show that the minimal state could emerge from a Lockean state of nature through a process that violates no one's rights. Independent individuals form mutual protection associations for self-defence; a dominant protection agency gradually emerges in each geographical area through competition; this dominant agency extends protection to all residents, compensating independents for the restriction of their right to self-help. The result — a minimal state — has arisen by an "invisible hand" process without any social contract or collective decision, and without any rights-violation.
Nozick distinguishes between the minimal state and the ultraminimal state. The ultraminimal state protects only those who purchase its protection. The minimal state protects everyone in its territory and finances this by prohibiting independent enforcement. This prohibition on independents is the crucial step: it makes the minimal state more than a mere private protection agency. But Nozick argues this is legitimate because the state compensates independents for the restriction — and this compensation is not redistributive in the objectionable sense, because it is payment for the right restricted, not a transfer to meet welfare goals.
The book's surprising conclusion is that the minimal state is actually the best possible framework for human flourishing — not by imposing any particular vision of the good life, but by providing a framework within which any individual or group can pursue any vision of the good, provided membership in the community is voluntary. The minimal state is a "meta-utopia": a framework for utopias, allowing Marxist communes, traditional religious communities, experimental cooperatives, and capitalist enterprises to coexist, each governed by its own principles, as long as no one is coerced into participation.
The derivation of the minimal state from the state of nature occupies Part I of Anarchy, State, and Utopia. Nozick's engagement with Locke is throughout; his response to anarchism draws on and critiques John Rawls, Murray Rothbard, and Michael Walzer.