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A lot of indexes and measurements are like this though when there is a potentially infinite range on one side.

Erdős numbers for instance, a higher number indicates less distance to Erdős.

Maybe. I think one thing that contributes to my interpretation is that "peace" is something you can have more or less of, but you can't have more or less Erdős. So seeing "Erdős number" I just think "measuring something about Erdős", but seeing "peace index" I get a slightly more specific feeling of "measuring the amount/quantity/duration of peace".

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