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HHI is a super useful metric -- glad you like it!

The squared sum of normalized shares proves to be very useful in a lot of contexts -- not just market share. Voting is one great example.

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Sounds depressing (i.e. ~5000 in a typical US election)

It gets really interesting when you look at the precinct and county level in the US, and similar types of views in European countries where they do real representative government.

It's ironic that national level politics mirrors the kind that the founding fathers did not ever want happening, while local politics has the kind of representation that they actually had in mind (in most places).

I'm not sure that is ironic.

No it's definitely ironic, in the rain on your wedding day kind of way.

Which is to say, the ultimate irony of Ms. Morisette's song is that there is no irony named.

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