No living citizen of any modern state actually signed a document agreeing to be governed. Social contract theory argues that political authority can still be legitimate — that a government can rightfully hold power over people who never explicitly consented — because rational people, reasoning about their own interests, either would agree to such an arrangement, or have implicitly agreed to it simply by continuing to live within a society and accept its benefits.
Three thinkers, three very different starting points
Thomas Hobbes, writing amid the chaos of the English Civil War, imagined a "state of nature" without government as a condition of constant insecurity — a war of all against all, where life was, in his famous phrase, "solitary, poor, nasty, brutish, and short." For Hobbes, the social contract was people trading away their natural freedom almost entirely for the safety a powerful, near-absolute sovereign could provide. John Locke painted a considerably less grim state of nature, one where people already possessed natural rights to life, liberty, and property, and where government's legitimate purpose was narrower: protecting those pre-existing rights, with people retaining a right to resist or replace a government that failed to do so. Jean-Jacques Rousseau reframed the contract again, arguing legitimate political authority comes from a collective "general will" the people themselves author together, rather than power simply being handed over to a separate ruler.
Consent that was never actually given — but is treated as if it were
The obvious objection is that essentially nobody has ever literally, explicitly consented to their government this way. Locke's own answer to this was the idea of tacit consent — that by voluntarily remaining within a state's territory, using its roads, and accepting the protections of its laws, a person implicitly agrees to be bound by them, in a way roughly analogous to how using a service can imply accepting its terms, even without a formal signature. Critics have pushed back hard on this move, since for most people leaving one's country of birth is enormously costly or simply impractical, which makes "tacit consent" through mere continued residence look less like a genuine choice and more like an assumption doing a great deal of theoretical work.
What we're still unsure about
Social contract theory remains hugely influential in political philosophy — John Rawls's 20th-century "veil of ignorance" is itself a direct descendant of the same basic contractarian move, reasoning about what people would agree to under fair conditions. But the theory's core weak point, the gap between hypothetical or tacit consent and the kind of explicit agreement that grounds obligation in ordinary contract law, has never been fully closed to universal satisfaction. Whether a government's legitimacy really can rest on what people would hypothetically agree to, rather than what any specific person actually did agree to, remains a live and unresolved question dividing political philosophers today.
This sits inside Social Contract Theory, one of seven topics in Ethics, one of five domains in Philosophy, one of seventeen subjects the app can quiz you on.