So what does the arbitrator do here? Roughly, the arbitrator takes a set of reasons for doing or forbearing from some action (in this case playing loud music in the evening). These reasons are already “live” for the two people submitting themselves for arbitration (myself and Paul). The arbitrator then assesses those reasons (and possibly some others we may not have thought of) and issues an authoritative directive. This authoritative directive then replaces the reasons myself and Paul previously had. In other words, it becomes a new preemptive reason for us to act upon.