I disagree with this. I think you are 100% right when you say:
>Since neither has any explanatory power that is not already contained in the phenomena they are offered to explain,
That is what these different explanations have in common, for sure. However, you seem to be defining that as parsimony. But there may be a lot of different explanations that are equally wrong, that differ in how complex they are, and those differences are differences in parsimony.
> However, you seem to be defining that as parsimony.
No, it's just, essentially, the numerator of parsimony; the denominator is the complexity added to the model; but a zero numerator makes consideration of the denominator irrelevant. (Normally, you compare parsimony of explanations with non-zero explanatory power, so the denominator matters a lot.)
I see what you are saying, but I guess I just don't accept that definition of parsimony because it includes explanatory power as an input into the value of parsimony. In just about every context I've encountered the concept, it has been used as a means of distinguishing between theories of equal explanatory power.
>Since neither has any explanatory power that is not already contained in the phenomena they are offered to explain,
That is what these different explanations have in common, for sure. However, you seem to be defining that as parsimony. But there may be a lot of different explanations that are equally wrong, that differ in how complex they are, and those differences are differences in parsimony.