Ayn Rand says: "The only proper purpose of a government is to protect man's rights, which means: to protect him from physical violence." (Galt's Speech, Atlas Shrugged, 1957)
But maybe Rand is wrong. Maybe government really has two purposes: 1) to protect liberty, via individual rights; and 2) to enhance society, via political privileges.
Without a doubt, government exists in order to establish justice, by safeguarding personal, social, and economic freedom. This clearly is its main and most important purpose.
But perhaps government also exists in order to uplift the culture. It does so thru such methods as: A) determining the mode of political organization, such as erecting a system of authority checks and balances, and creating a republic, rather than a pure democracy; B) controlling citizenship, residency, and visitation standards, such as by discriminating against those who excessively commit crime, go on welfare, vote for tyranny, don't speak the local language, don't like the country, etc.; C) granting suffrage, such as only for long-time, upstanding citizens, but not for the uneducated, retarded, demented, anti-libertarian, criminals, welfare recipients, recent immigrants, temporary residents, etc.
If done well, these two proper functions of government can both radically increase the level of human freedom.