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The first page is pretty much all you need for the context of the conversation. Basically, according to the paper, Black people in the US are significantly more likely to be exonerated of any crime, but especially murder. This inversely means they're significantly more likely to be found guilty of a crime they did not commit.
The reasoning, I assume, for the person to link you that article is because of your statement about crime rates. I believe the other commenter is trying to say that crime rates are not actually equal once you normalize for poverty because of the high rate of false convictions.
Tbh, I'm not really sure what else to say about that. I just wanted to comment my thoughts on your question since I saw how rude the person you commented to was.
It's an interesting concept, and it could certainly due with some studying. My main thought is that if a cohort (poor people) are more likely to commit crimes, it stands to reason they are more likely to be incorrectly convicted of crimes as well. If there are 7x as many crimes in a population, 7x as many incorrect convictions would be a reasonable baseline.
So, my followup question then, if when normalized for poverty or crime rate, is there still a difference in the data? I unfortunately didn't see any discussion of such in the paper, which left me wanting.