If the county and the authority or municipality are unable to agree on either (1) the need for or cost of road improvements under section 469.175, subdivision 1a, or (2) the amount of county administrative costs under section 469.176, subdivision 4h, and the county or municipality demands arbitration, the matter must be submitted to binding arbitration in accordance with sections 572B.01 to 572B.31 and the rules of the American Arbitration Association. Within 30 days after the demand for arbitration, the parties shall each select an arbitrator or agree upon a single arbitrator. If the parties each select an arbitrator, the two arbitrators shall select a third arbitrator within 45 days after the demand for arbitration. Each party shall pay the fees and expenses of the arbitrator it selected and the parties shall share equally the expenses of the third arbitrator or an arbitrator agreed upon mutually by the parties.