The strategy is elegant. Rather than deriving authority from God, tradition, or superior force, contract theory derives it from the people subject to it: a state is legitimate because those it governs could rationally agree to be governed by it. Notice that the argument's real content lies in the premises about what people are like and what they would face without a state — the contract is the conclusion, not the engine.
Hobbes wrote during the English Civil War, and it shows. Without a common power, he argued, people in conditions of rough equality and scarcity would fall into a war of all against all, in which industry, culture and security are impossible. Life in that state he described with a famous string of adjectives ending in "nasty, brutish, and short." Given that, subjects would rationally transfer their rights to a sovereign whose authority is near-absolute — because the alternative is not a better government but no government. His conclusion is severe: there is almost no right of rebellion, since rebellion risks returning to the very condition the contract escaped.
Locke starts elsewhere and arrives elsewhere. His state of nature is inconvenient rather than catastrophic: people already have natural rights to life, liberty and property, and mostly respect them, but disputes lack an impartial judge. Government is therefore a limited trust established for a specific purpose, and one that exceeds it — taking property without consent, ruling arbitrarily — forfeits its authority. This is the argument that shaped the American founding documents, and the difference from Hobbes is instructive: the same method yields nearly opposite politics depending on how dangerous you think we are.
Rousseau reframed the problem. Contracts that merely protect existing holdings, he argued, entrench inequality — the rich have most to gain from securing property. Legitimate authority instead expresses the general will, what citizens will as a collective body aiming at the common good, which is not the sum of private preferences. Under it we obey only ourselves. Critics have long noted the danger in the idea that one can be forced to be free.
The standard objection to all versions is simple: no one signed anything. Consent is supposed to bind, yet nobody consented to the state they were born into, and staying is not obviously agreement when leaving is costly or impossible. Hume pressed this directly, comparing the situation to a sailor carried aboard a ship while asleep who is then said to consent by not leaping into the sea. The modern reply, developed by Rawls, abandons actual consent for hypothetical rational agreement — asking what principles people would choose behind a veil of ignorance about their own position. That preserves the method's justificatory force while conceding the historical point, and it is why the tradition remains central despite an objection that has stood for two and a half centuries.