I feel like those links are more useful than the target essay.

Reading through them, I wonder why CPIs aren't based on empirical correlational patterns between prices over time? Sort of like in these articles:

https://iopscience.iop.org/article/10.1088/1742-6596/1796/1/... https://www.ecb.europa.eu/pub/pdf/scpwps/ecbwp1011.pdf

Or maybe they are? I'm not an expert in this and reading through some of the government literature there's no mention of this.

Then at least you would know that a given price marker is a good empirical index of how other prices are changing also, at least for a given dimension/component.