If person A gives an argument to person B in order to convince them about the truth of claim X, how can B determine how compelling A's argument is in a way that is as objective as possible (i.e. in a way that anyone should be able to verify and agree)? The only types of arguments that exemplify by excellence that idea in my opinion are proofs of mathematical theorems or mathematical claims in general, since if everyone agrees upon the initial axioms and follows the deductive argument step by step, everyone should be able to arrive at the same conclusion, and even an automated theorem proving system should be able to do it as well. Although, to be fair, it's still technically possible to question the truth of a mathematical proof by questioning the initial premises (e.g. why should I accept Zermelo-Fraenkel Axioms?, etc.).
But not all arguments are formal, logical and deductive like mathematical proofs. In Physics for example there are "proofs" that make use of approximations, such as the small-angle approximation. Or in domains that lack a formal mathematical syntax, such as philosophy, philosophical "proofs" rely heavily on the use of everyday natural language to express arguments, which unavoidably introduces a greater degree of ambiguity due to the imprecise meaning of certain words, which leaves room for subjective interpretation, questioning the logical implications, etc. (For example, I'm not sure if a "philosophical proof" can ever be restated in a way that can be verified by an automated theorem prover.)
If B wants to verify how compelling the case is that A is attempting to make to convince them that X is true, how can B go about it in a way that is as objective as possible? Should B give more credence to deductive arguments, abductive arguments or inductive arguments? Should B question and inspect every single premise? How can B determine when a premise is worth being accepted instead of questioned? Can B consider A's case more compelling if A presents multiple, independent arguments?
In sum: are there objective ways to determine how compelling an argument (or a case made by multiple arguments) is?