I have said this before to no avail, getting no attention from either side. What Percy is basically saying is that any useful definition of information requires you to provide a
metric.
It MUST satisfy those exact properties or else you cannot use that definition to do useful things such as build an algorithm that tells you when one thing has "more" or "less" information than another thing. Or equivalently, to tell if information has "increased" or "decreased".
Without proving that your metric satisfies all 4 strong properties of a metric:
1. non-negativity
2. identity
3. symmetry
4. triangle inequality
You cannot use words such as "more", "less", "increasing", "decreasing".
In particular, byte counts are an invalid metric because they do not satisfy the 2nd property which is pretty significant.
If a nation expects to be ignorant and free, in a state of civilization, it expects what never was and never will be. --Thomas Jefferson