The social contract is simply a more formal explanation and exploration of exactly what you just described. It is sort of the bridge between basic human behavior and a codified set of rules governing society. The golden rule is great and all but it is actually really difficult to codify that in black and white legislation. There's been tons of speculation about it over the centuries. Guys like Hobbes, Rousseau, and Locke for example; and then their work heavily influenced the american founders like Jefferson, Monroe, Madison, and other political titans like them.