Why Is the Consumer Price Index Controversial?

Quite a bit of technical content there, but the key property of CPI is that it uses the geometric mean rather than the arithmetic [1]. The reason why this is done is clear once you know this inequality: [2]

[1] https://touchstoneblog.org.uk/2010/06/the-difference-between...

[2] https://en.wikipedia.org/wiki/Inequality_of_arithmetic_and_g...

there's a recently developed alternative inflation measure here that looks rather good. https://app.truflation.com/