Thank you but that did not work. It helped put me on the right track though.
The closest I've gotten is:
The problem is that the sums per Region are still overestimated. I need each Place_ID to be counted only once when adding Amount per Region. Any additional thoughts?
the correct syntax is close to what Eduardo suggested:
sum(aggr(avg([Amount]),[Place_ID], + any other chart dimensions))
I'm additing "any other chart dimensions" to ensure that AGGR is going to serve you correctly...
The core issue, however, is still hidden somewhere in your data model. In a properly designed data model, there shouldn't be any duplication of amounts. I suggest that you revisit your data model and try to eliminate the duplication in the first place.
Learn about AGGR, Set Analysis, and many other advanced techniques in my book QlikView Your Business.