A learning question !
Here is what I think.
If I write the sentence like:
We live in a world
with rampant crime, recalcitrant children , constant change , and prevailing uncertainty.
Now do we need to repeat WITH again and again ?
No , because all the elements here are phrases.
We live in a world NP, NP, NP and NP.
The above construction is fine. Then why should we need "in which" to be repeated.
Lets look into the sentence again,
We live in a world
in which crime is rampant,
children are recalcitrant,
change is the only constant, and
uncertainty is prevalent.
The above construction is trying to build a ||sm with Independent Clauses.
Like; IC in which IC,IC,IC and IC.
The above construction is not a well appreciated. There are always rules to combine ICs.
So the construction has to use "Dependent Maker".... "in which" in our case.
IC in which IC,in which IC,in which IC and in which IC.
I found a lot of help from another thread and googling on ||sm.