I think entropy is a key to understanding this more deeply. I believe you could consider the unaggregated distribution as the “microstates” and the aggregated one as the “macrostates”. The entropy would then tell you how much information you lose by aggregating in this way.
Minor quibble: The likelihood part of probability is also subjective in the sense that it depends on the evidence the agent is aware of.
I think entropy is a key to understanding this more deeply. I believe you could consider the unaggregated distribution as the “microstates” and the aggregated one as the “macrostates”. The entropy would then tell you how much information you lose by aggregating in this way.
Minor quibble: The likelihood part of probability is also subjective in the sense that it depends on the evidence the agent is aware of.