http://www.leg.state.fl.us/statutes/index.cfm?App_mode=Display_Statute&URL=0600-0699/0682/0682.html

This statute lays out Florida's arbitration code. Section 682.04 address court appointment of arbitrators. When parties agree to arbitrate they may make a motion to the court to appoint an arbitrator if the parties have not agreed on a method, the agreed method fails, one or more of the parties failed to respond to the demand for arbitration, or an arbitrator fails to act and a successor has not been appointed.  Additionally Section 682.051 outlines arbitrator immunity and identifies that arbitrators are immune from civil liability.