Hobbes and Locke both have a layered notion of society; there is a "natural state" of humanity, flowing from human nature, and society is justified by its improvement over that natural state. For Hobbes, human nature is ugly, for Locke, it is beautiful. This distance leads them to very different conceptions of the appropriate role of the state.
For Hobbes, human nature amounts to what we call power politics; people directly seek their interests through use of force, and those most able to muster force best enact their will. (Relationship to N's 「Will to Power」 is a topic for another essay). Satisfaction of the Id is the primary concern of people in their natural state (note that my addition of Freud into this is an anachronism); the natural state of humanity is brutish. The state is justified in that a sovereign is needed to restrict/monopolise the use of force, and that presumption of a social contract is derived from the observation that self-restraint in use of force, enforced by the state, betters the common lot of humanity. (For more on this, read Leviathan)
For Locke, human nature is harmonious; most people are good-natured, and while some are selfish, the natural state of humanity is tolerable. People have the ability to defend their bodies and their properties, and recognise this right in others. In this model, the social contract derives from a desire to better organise rights to property and improve on the already-good natural state. Locke's notion of civil society is based on making the freedom of already-decent people more regular, not a mechanism to keep brutish people in line. (For more on this, read 「Two Treatises of Government」)
How are we to judge human nature? Is there a state of nature?
I don't think Locke or Hobbes are correct; human nature is not so aptly summarised, and while simplifying it into brutish or decent allows one to make interesting claims about the justification for society, it's too facile. I believe that the nature of man depends on the culture of man; inculturation shapes us, providing us norms for treatment of others. A kind culture produces mostly kind people. However, any kind culture must be defended; either the people broadly retain the willingness to resort to power politics when threatened, or they will be commanded by those who become their leaders (usually by conquest) who retain that ability. The people's hearts must neither be too hard nor too soft, if they wish to be involved in their governance. Like Locke and Hobbes, I don't believe a state of nature is stable; without organisation, the temptation to dominate others by force (or to refuse to contribute appropriately to the community) will be exercised by the less-socialised, preventing any prolonged lawlessness from being complete. The economies of scale of power will eventually bring about tribes (and possibly states), and the initial forms of those social organisations will likely be primarily for the benefit of the person/family organising them.
The job of civilisation is to encourage buy-in to mindsets progressively more distant from the uglier sides of human nature, while cultivating its more social sides. Advancement in forms of government must match this cultivation of virtue; societies that depend on goodwill between people cannot function with either a Hobbesian analysis (which presumes a rotten human nature, tamable only through force) nor a Lockeian analysis (which neglects the nurturing of a culture because it holds that virtue is easy).
So, with this understanding of human nature, we see the state as being one party responsible for the maintenance and growth of values that better its people, but also expressing and organising that virtue towards the betterment of humanity, through its institutions.
This betterment is not served by a permanent definition of the public good so much as a commitment to form one and continue adapting it to the possibilities of the times. The specific form of the state and its institutions is important, but its theory cannot be considered seperately from the character of the people that inhabit that society; a society that can assume goodwill, reasonability, and limits to selfishness can thrive with institutions that would not work for a more selfish people. Likewise, anti-corruption reforms are empty when whatever form of corruption is being fought is accepted by society.
A successful virtuous society prizes empathy, commitment to the well-being of all, and remains willing to do what's necessary to protect itself. As socialists, we insist that privilege and property are always provisional, and that ownership of the means of production is not necessary to get the advantages of competitive markets. We reject pacifism along with any idealism that would make implementation/preservation of our values unrealistic. We require the state to support the good of society, but recognise that empathy must have its roots in culture if society is to thrive.