Alternatives to cap-based weighting in index funds

There is a simple mathematical parameter describing diversification of a portfolio:

https://investiforum.medium.com/the-herfindahl-hirschman-index-how-diversified-are-your-etfs-f7ab4389d311

You may want to take a look at it.

And I also see that this website even provides calculated HHI for ETFs:

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