When I use graduated symbols for a polygon layer to display population density, the layer is always displayed on top of all the other layers even if I dragged it to the bottom of the Table of Contents.
Any idea how to solve this?
The short answer is you can't. The graduated symbols are treated more like labels (which essentially they are - special labels at the centroid of the polygon), which draw on top of all actual features. Layer order will control the draw order of various graduated symbol layers. It also controls the draw order of the background of a graduated symbol layer; just not the symbols themselves.
There is an Esri discussion thread on this at https://geonet.esri.com/thread/52106