The correct claim is not that per capita does not matter but that it alone does not provide you with adequate picture. Imagine a street where 100 people live, and there's a shoot-out there every day. Now imagine a mayor made an order, and another 100 people are forced to move and live on the same street now, and there's still a shoot-out there every day. Can you honestly say the quality of life on that street improved 2x, even though you still have the daily shootings as before, but it's now twice as crowded? I think something is missing in this picture if you make such a conclusion. Of course, per capita numbers show some part of the picture, but you need to see the other parts too.
What you could say, assuming the number of shooting victims per day remained constant, was that people on that street were now 50% less-likely to be killed in a shooting. If you moved enough people onto that street, again assuming a no change in the number of victims, the likely-hood of any individual being shot could be forced into a statistically insignificant number.
The reverse of your hypothetical is basically how high-crime areas come into being. If you have an area where 1 person every day is killed, and half the people leave, you would absolutely say the quality of life in that area declined. Everyone is twice as likely to die.
While per capita is an imperfect number, it's a crazy-good proxy for the thing we worry about – "how likely is crime in this area to affect me?"
> was that people on that street were now 50% less-likely to be killed in a shooting.
If shootings were randomly distributed by a mechanical process with uniform distribution among everybody who has the address registered on this street, it would be true. But that's not how shootings work. You confuse a simplifying assumption - that is made for the purposes of modeling, because it's impossible to model the life of every person - with actual reality of what is happening. What is happening is if there's a shootout every day on the street, and you live on that street, and you are a sane person, you would be afraid to go on that street, because the next person shot could be you. And that's the rational behavior, while "I don't care for the shots I hear, these numbers on screen say it's ok" is wildly irrational.
> If you have an area where 1 person every day is killed, and half the people leave, you would absolutely say the quality of life in that area declined. Everyone is twice as likely to die.
Again, no, because shootings aren't a random lottery allocated uniformly by independent metric, like an address. It's connected to your behavior, so if you go to the street where shootings happen, you risk being shot. And how many people are registered on the same street has very little to do with that.
> it's a crazy-good proxy for the thing we worry about – "how likely is crime in this area to affect me?"
And again, it would be, if we were dealing with uniform random distribution. That's not what actually happens - if 100 people live in a safe neighborhood and I have to walk the street where druggies hash out their quarrels - the averages are not going to help me. Remember, Bill Gates walks into a bar... how richer have you just become by sitting in that bar?
