One way is for an admin who is not party to the conflict to summarize the presented arguments, existing rules and precedents, and write a decision. Serious irr

One way is for an admin who is not party to the conflict to summarize the presented arguments, existing rules and precedents, and write a decision. Serious irresolvable conflicts are decided by the Arbitration Committee for the particular language edition of Wikipedia, and the committee's decisions are binding. Each language editions of Wikipedia has its own slightly different take on how the Arbitration Committee is selected and how it makes decisions, but the general gist is that commissioners are highly active editors (not necessarily administrators) who are elected for a limited term by a vote of active editors.