Alternative Dispute Resolution Promotion Act of 1986 - Requires that each attorney representing a party in a civil action advise that party of the existence and availability of alternative dispute resolution options. Requires such attorneys to file notice with the court certifying that their clients were so advised and indicating whether the parties will agree to any such option. Allows the court to impose sanctions upon an offeree who unreasonably rejects an offer of alternative dispute resolution. States that neither the acceptance nor rejection by any party of an offer to engage in an alternative dispute resolution proceeding shall be admissible as evidence in any further proceedings.