> If you do something that causes air in one place to get 1 ppm dirtier and air in another place to get 1 ppm cleaner, and the populations are the same, the net impact on health cancels out.

The average ppm cancel out but the outcomes don't, because you have more sick people: Let's say 12 ppm is the maximum safe ratio for some pollution [edit: assuming it is a pollutant that has local impact, not like CO2 which has global impact]:

1) If place A has 10 ppm and place B has 10 ppm, then nobody is sick

2) If place A has 15 ppm and place B has 5 ppm, then people in place A are sick

Public policy generally doesn't work well with averages and similar analyses, because outcomes are usually discrete for each individual; it's not a stew where you can mix outcomes together and get something good.

As another example, if the economy results in one person making $1 billion and 999,999 making nothing, the average is $1 million per person - but what does that mean? 999,999 people are still in dire poverty. (It does have some significance, for things society does collectively - fund police and fire, and even help for poor people.)