You knew that inmates have few rights, and I guess if the public had a chance to vote on the issue, inmates would have no rights at all. For the moment, inmates do have limited free speech rights. But they are not allowed to advocate work stoppages in jail.
The case is Pilgrim v. Luther, decided on July 6. Pilgrim was incarcerated at Sing Sing Correctional Facility when a search of his cell revealed three copies of a pamplet entitled, "Wake Up!" The pamphlet encouraged inmates to engage in work stoppages and other disruptive behavior at the prison. Pilgrim was punished for this.
A New York prison regulation (section 104.12, to be exact) prohibits inmates from leading or participating in work stoppages, sit-ins "or other actions which may be detrimental to the the order of the facility." In Daumutef v. O'Keefe, 98 F.3d 22 (2d Cir. 1996), the Court of Appeals held that, consistent with Supreme Court precedent which grants prison officials leeway in regulating expressive inmate behavior, section 104.12 does not violate the First Amendment as applied to inmates who circulated a petition asking for better prison conditions.
The Daumutef precedent applies here: Sing-Sing officials are allowed to punish Pilgrim for advocating work-stoppages. The Court of Appeals (Cabranes, Miner and Stein) notes that "The Supreme Court has held that 'in the prison context, an inmate does not retain those First Amendment rights that are inconsistent with his status as a prisoner or with the legitimate penological objectives of the corrections system.'" As "work stoppages are deliberate disruptions of the regular order of the prison environment and are a species of [the kind of] 'organized union activity' [prohibited under Supreme Court precedent]," Pilgrim had no right under the First Amendment to advocate this, especially where "other less disruptive means of airing grievances are available."