Preference-based argumentation

There are many takes on preference-based argumentation with different ways of representing preferences, for example:
- Assigning values to arguments and allowing audiences to vary in their ranking of the values;
- Allowing attacks on attacks, e.g. "C attacks 'A attacks B'";
- Rule-based, e.g. "B > A if happy" and "A > B if sad".
- Fact-based, e.g. "B > A".

These preference-based frameworks differentiate between attack and defeat. For example, in the value-based approach “… if an argument attacks an argument whose value is preferred it can be accepted, and yet not defeat the argument it attacks… An argument A defeatsa an argument B for audience a iff both attacks(A, b) and not valpref(val(B), val(A)).”

There are other definitions of defeat. For example:
- (A defeats B) if (A attacks B, A is preferred to B and B is not preferred to A).
- (A defeats B) if (A attacks B and B does not have higher value than A).
- (A defeats B) if (A attacks B and there is no attack on A's attack).
Some element of non-determinism still seems to remain. For example, what of those attacks for which the condition of defeat is not met, what can be said of them?

Whether the original problem of a possible non-determinance between two arguments can be completely eradicated is an interesting question.