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Why does the `i` after `h_` need a curly but not after `\sum_`?

A pity that HN can't render TeX or MathJax or whatever.

It doesn't. The rule for TeX is that single-character tokens don't need braces. I assume this is just an artefact of their particular muscle memory.

You can test it here, if you like: https://www.mathjax.org/#demo

HHI and Simpsons are neat new finds.

There's also this other variant of the Simpson's Index: https://www.thesimpsonsindex.com/

Payment processor margins are already very high, especially considering they are basically low-tech utilities.

If the US had functioning antitrust laws it would be looking at their margins and be considering whether to break up some of the existing players, not considering when allow even more mergers.

https://en.wikipedia.org/wiki/Diversity_index