It’s a useless and misleading modeling choice to condition on irrelevant data
Strictly speaking, you should always condition on all data you have available. Calling some data D irrelevant is just a shorthand for saying that conditioning on it changes nothing, i.e., Pr(A∣D,X)=Pr(A∣X) . If you can show that conditioning on Ddoes change the probability of interest—as my calculation did in fact show—then this means that D is in fact relevant information, regardless of what your intuition suggests.
even worse to condition on the assumption the unstated irrelevant data is actually relevant enough to change the outcome.
There was no such assumption. I simply did the calculation, and thereby demonstrated that certain data believed to be irrelevant was actually relevant.
Strictly speaking, you should always condition on all data you have available. Calling some data D irrelevant is just a shorthand for saying that conditioning on it changes nothing, i.e., Pr(A∣D,X)=Pr(A∣X) . If you can show that conditioning on D does change the probability of interest—as my calculation did in fact show—then this means that D is in fact relevant information, regardless of what your intuition suggests.
There was no such assumption. I simply did the calculation, and thereby demonstrated that certain data believed to be irrelevant was actually relevant.