Each concept is read twice: whether the approach carries it over, and whether the approach's own sources claim it. A concept that the approach claims but does not carry over is a shortfall. A concept that it neither claims nor carries over is an omission, which marks a gap in the field rather than a failure of the work.
Contestability
PartialShortfall · partially preservedDefinition (Philip Pettit, On the People's Terms, 2012)
This concept holds that anyone subject to a decision must have a real route to challenge it. They must be able to inspect the grounds for the decision, contest the outcome, and have the challenge answered. Legitimacy is not settled once by an election or an act of consent. It depends on that route remaining available. On this view, a political order is free when the people its decisions affect can contest them, whether or not its rulers are kind.
Analysis
The approach builds working mechanisms for two of Pettit's three requirements. The grounds can be inspected, because the decision is laid out as named arguments and the links between them. A challenge can be acted on, because the gradient method computes which link weight must change, and by how much, for a chosen conclusion to reach a chosen strength. The third requirement is missing entirely. There is no forum. The deciding system assesses the grounds offered against itself, nobody has standing to file anything, and whoever runs the algorithm sets the target strength.
Non-domination
PartialNot claimedDefinition (Philip Pettit, Republicanism, 1997)
This concept holds that freedom is not the absence of interference. A person is unfree if someone holds unchecked power over them, even if that person never misuses it and means well. A benevolent master still dominates, and so does an authority whose workings cannot be seen. Legitimacy requires power to be checked, and good intentions are not enough.
Analysis
Pettit's paradigm case of domination is an authority whose workings you cannot see. An argumentation framework addresses that part of the objection by laying out the grounds in a form a person can examine. However, the check stops at visibility. The operator builds the framework, sets the weights, chooses the target strength, and decides whether the revision is applied. The power that has been made visible is therefore not made answerable to anyone subject to it.
Public decision record
AbsentOmissionDefinition (Common-law practice)
Rulings on challenges are written down, published, and citable. The legal order's interpretation of its own rules therefore accumulates in public, where it can be studied, invoked, and criticized. This record makes the legal order both predictable and legitimate, since nothing is settled in private and every decision leaves its reasoning on record.
Analysis
Nothing is written down, published, or made citable. Worse for the tradition, the mechanism erases its own history as it works. A successful contestation changes the edge weights until the framework yields the desired strength, and nothing preserves what was contested, on what grounds, or what changed. Common law keeps the overruled case on record so that the line of interpretation stays visible. Here, the earlier state of the framework is simply lost.