Note: This is an unedited draft section of my inflation primer manuscript. It is is a chapter about misunderstandings/myths about the CPI. This section aims at claims that economists have fooled around with the methodology to lower the reported inflation numbers. I think one subsection was already published as a draft, but I will leave it in there. At present, I only some overview sections to write, as well as the need to take the axe to a couple sections that ended up overlapping.
I know the context here is CPI but I would agree that there is no meaningful way to calculate price indices, just as there is not for GDP. We use CPI and GDP for cross-country (multiple nations) analyses but our construction of each in each nation is different, so we are still not comparing like for like. That said, it is likely the best we can do.