1.    Right-privilege/Justice Holmes approach:  The government and
the individual are treated equally as free agents, mutually competent
to determine their own best interests and we measure the terms of
their arrangement according to general principles of the common law
of contracts.  For example, in McAuliffe, Holmes wrote an opinion
concerning a cop who had been fired following some public remarks
critical of how the police dept. was run.  “The petitioner may have a
constitutional right to talk politics, but he has no constitutional
right to be a policeman.  There are few jobs for hire in which the
servant does not agree to suspect his constitutional right of free
speech, as well as of idleness, by implied terms of the contract.
The servant cannot complain, as he takes the employment on the terms
which are offered to him.”  This is yet another example of Holmes’
conservatism when it comes to the First Am.  The “right-privilege”
approach was abandoned for the next approach.
2.    Frost & Frost/Justice Sutherland approach:  This approach
superseded the “right-privilege” approach.  Under the Frost & Frost
approach—contrary of the right-privilege approach—the common law of
contracts is essentially irrelevant and cannot be invoked.  Rather,
the First Am. disallows government from imposing restrictions on free
speech, as much so by contract as by any other advice.  The government can place no restrictions on an employee’s speech.  The rationale here is what government cannot do to anyone directly (because barred by the First Am.), neither can it do directly by offering a “trade” (restrictions on employee’s First Am. rights in exchange for his employment with the government).
3.    Pickering approach:  This approach is somewhere in between
the two above approaches.  The First Am. prevents certain government
restrictions, while it allows others.  “The problem in any case is to
arrive at a balance between the interests of the [government employee], as a citizen, in commenting upon matters of public concern and the interest of the State, as an employer, in promoting the efficiency of the public services it performs through its employees.”
This is the famous Pickering balancing test.