One of the criteria of IBE is simplicity.
How to determine which explanation is simpler if there are two types of simplicity: one type counts the number of hearings, and the other type counts the number of explanations.
If one explanation has fewer entities and the other explanation has fewer explanations, which is simpler?
I cannot understand who should decide this.
It's an ad-hoc aesthetic judgment that powers a rule of thumb, not a reliable heuristic. The simplicity rule is a very crude approximation of doing real statistics with real measurements. As you suggest, you can always subdivide contingent entities or extend contingent explanations farther down the causal chain if you start counting like the counted number means something. If we were doing stats, this wouldn't do anything - we'd just be replacing numbers with expressions that come out to the same number.
Kolmogrov complexity is one objective-ish measure of simplicity. The downside is, many hypotheses aren't well formulated enough to even have a vague range of their kolmogrov complexity.
Basically, any theory you can simulate has a kolmogrov complexity, so we can estimate the kolmogrov complexity of Newtonian mechanics, relativity and quantum physics. Relativity has a HIGHER complexity than Newtonian mechanics, but it also explains more things so it has the edge regardless of being more complex.
In comparison, the kolmogrov complexity of your average religion is... harder to estimate, for obvious reasons
You have to take relative probabilities into account. A theory which explains a phenomenon in terms of 50 facts which are known to be true can more plausible than an explanation based on only one assumption which has a probability less than 1.
If you ask me how my car works, I can provide an explanation which involves a large number of entities, such as a crankshaft, pistons, fuel injectors, air filter, etc etc, or I can say a magic fairy makes it go. The second explanation has far fewer entities but is not better.
In my perspective, anchored in a neurobiological understanding of the world, the 'simplest' explanation would be the one that aligns most closely with what we know about how the brain works. Ontological simplicity and explanatory simplicity aren't always at odds. A theory that posits fewer entities, if those entities are consistent with neurobiological data, may provide a more unified explanation for a range of phenomena.
Determining 'simplicity' isn't an arbitrary decision made by a single person. It's a collective process in the scientific and philosophical community, grounded in evidence. The 'simplest' explanation will be the one that best fits the data, explains the most phenomena, and makes the fewest unsupported assumptions.
Remember, Occam's Razor is a heuristic, not an absolute rule. Simplicity is one among many factors in theory choice. Others include empirical accuracy, coherence with other accepted theories, and explanatory breadth and depth. So, simplicity is a guide, but it doesn't always dictate the best theory.
