Parties who agree to resolve their differences by arbitration do so by contract. But, because a contract binds only those who agree to it, a dispute among several parties -- some of whom have agreed to arbitration, others who have not -- can create problems. For example, most disputes related to building construction are more complicated than the two-party disputes that arbitration statutes are usually designed to resolve. Because of the broad policy favoring arbitration, most courts are not authorized by modern arbitration statutes to refuse enforcement of an arbitration clause and to go forward with litigation when the dispute involves third-party claims or pending multi-party litigation. Even though many individual judges support the principle that courts should have the discretion to order and expedite arbitration of multiparty disputes by consolidation and other means, a number of State and Federal court decisions reject this notion. 1 appendix and 300 footnotes.