"To adjudicate the dispute" means to settle or resolve a disagreement or conflict through a formal process, usually with the help of a judge or an impartial third party. Full definition
The Financial Services Commission of Ontario, the government agency who adjudicates disputes between the public and their auto insurers, has become overwhelmed with applications for mediation. (oatleyvigmond.com)
One is the use of U.S. courts for adjudicating disputes that occurred outside of the country. (instituteforlegalreform.com)
In labour relations, access to expedited processes are available if both parties agree (usually as part of a collective agreement) or if at least one party is not fussy about who adjudicates their dispute (through expedited processes mandated by statute). (mackenziedrs.com)