In the Human Path, Jack never gets to wield the Arbitrator, Cairn's sword. An arbitrator is a person officially appointed to settle a dispute, and the route split hinges on the choice of either "following Ridley" or "meeting Larks at the castle"; the first choice can thus be interpreted as Jack choosing Ridley over knighthood, just as Cairn before him chose to slay the Water Dragon. In taking the second choice, Jack lets himself be used as a tool (by both Radiata Castle and Lucian). He frames his vengeance on Lucian as a "mission" (which would've been a callback to the deleted scene of Larks asking Jack to bring back Ridley dead or alive). Besides the implication that Jack sensed the taint of algandars on the sword, it's implied that Jack in the Human Path never sees himself as an arbitrator.
