What I have in mind is something like these two examples below:
Also, if it is not possible to create a 3D choropleth map in ArcGIS, is there some other GIS software package that can draw 3D choropleth maps other than Maptitude?
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ArcScene is the ESRI approach to doing this. It is likely installed with ArcGIS so you should find it in the start menu.
This is a typical ArcScene map. Basically your attribute value can become the extrusion, you often need to normalize data.