Because if you're in the area that a crime is going to occur, but it's only going to happen to k of n people in the area (with k usually equal to 1), you have a lower than certain chance of being involved?
For an example, if you're on a block there's 100% going to be a robbery in the next 5 minutes, if there are also 200 other people on that block, then you still only have a 0.5% chance of being robbed.
Essentially, because so many crimes only involve a single (or relatively few) victim(s), your odds of being involved need to account for how many other people are around you, and not just the odds that it will happen in the same area as you.
Your measure of "per unit area" doesn't account for the fact most people aren't going to be involved with the crime (eg, robbed), but will all be in the same impacted area.
So, essentially, it over-calculates how likely you actually are to be the victim of a crime. Per unit area is only useful if you want to know how close you're likely to be to a crime being committed, and not how likely you are to be the victim.
>Because if you're in the area that a crime is going to occur, but it's only going to happen to k of n people in the area ...
>...Your measure of "per unit area" doesn't account for the fact most people aren't going to be involved with the crime (eg, robbed), but will all be in the same impacted area.
I think those assumptions are where I disagree. a) I care about (not) being near crime, and b) crime doesn't randomly sample across the set of all people, but makes me have to avoid certain times, places, and activities.
I would rather be around more crime, but victim to less of it. Your analysis trades the potential for being a victim more often to be around less total crime, which is why I think it's somewhat suspect. Perhaps that really is a trade you're willing to make, but I'm dubious.
> crime doesn't randomly sample across the set of all people, but makes me have to avoid certain times, places, and activities
Again, per capita measure is more important for figuring out if you should avoid an area than the crimes per area metric. (Also left out of this discussion is the distribution of offenses committed, which is paramount I'd argue.)
An example from where I live: there's higher crime per unit area at 9pm (it varies by time) at the mall downtown than the gas station/bowling alley/billiards room complex where the gang members loiter in the south end of town. (I looked up police numbers, because you made me curious.) But I know which one I'd rather be at based on the distribution of types of crimes and the per capita numbers. Hint: it's not the gas station.
This is a good example of higher numbers of people hiding a lower rate of victimization per person: there are literally hundreds of times more people downtown than at the gas station, so a marginally higher crime per area rate means I'm actually less likely to be involved in a crime. (Given how little of the mall you can see at once, I likely wouldn't even know it happened.)
So let me ask you: what is it you think that the crime per area figure gives you that crime per capita doesn't?
For an example, if you're on a block there's 100% going to be a robbery in the next 5 minutes, if there are also 200 other people on that block, then you still only have a 0.5% chance of being robbed.
Essentially, because so many crimes only involve a single (or relatively few) victim(s), your odds of being involved need to account for how many other people are around you, and not just the odds that it will happen in the same area as you.
Your measure of "per unit area" doesn't account for the fact most people aren't going to be involved with the crime (eg, robbed), but will all be in the same impacted area.
So, essentially, it over-calculates how likely you actually are to be the victim of a crime. Per unit area is only useful if you want to know how close you're likely to be to a crime being committed, and not how likely you are to be the victim.