Supposing any given X has 50% probability of being true of any given m (...)

This isn't a direct claim of fact, but a flat assumption to simplify illustration and calculations. The same argument extends for any arbitrary probability by showing that mathematically, no matter the probability in question (as long as it is a probability, and not a 0 or 1), as the number of possible minds grows towards infinity, the chance of X being true for all minds keeps decreasing in a similar manner.

The hidden assumption behind this, of course, is that I have a high prior that the number of different possible minds is sufficiently high and the probability comparably low enough for this compound probabilistic growth to become critical. Since the number of known different minds already exceeds seven billion and any given random statement of the form "Mind 'm' believes that X is immoral under Y circumstances or context Z" is extremely unlikely to be true for any given mind (and like above, scales to nigh-infinitesimal when conjugating it across all seven billion), I think this hidden assumption is a very reasonable one. An example for clarity:

Mind M ( John B Gato ) believes ( Looking at Jello ) is immoral in context ( Five days and seven minutes after every new moon for a period of three hours, or while scratching one's toe. )

Of course, this is an intuition about moral beliefs, not about being-convinced-by-arguments, but it's an intuition about the diversity of ways human minds process arguments that hints at the possible diversity among non-human mind structures.

"A(m) is true if mind 'm', when presented with the argument A, will change some specific belief / internal state / thought / behavior to state Y"

This is my own model / abstraction of Argument - Mind - Belief/Action. If a UCMA supporter does not believe that arguments lead to any change of belief or behavior in a mind once the argument is made to that mind, then that seems to directly contradict the very idea of a universally compelling argument that persuades any mind.

So the quote above is a model for "If the mind is compelled by the argument, it will have a certain property which allows the argument to compell it" (this property may be a simple emergent property of all possible minds that arises from a combination of the basic necessary properties of all minds, or might be implicit in the structure of logic, which I reckon is a main argument for some of the more sophisticated UCMA supporters).