Displaying transparent overlapping polygons in ArcGIS for Desktop?

I'm trying to draw home range maps in ArcGIS 10.1 and am having difficulty displaying them as I would like.

The home ranges are in the form of polygons and many of them overlap. I'm trying to get a display setting that allows all polygons to be displayed at once, particularly where they overlap.

Essentially what I'm trying to do is display the polygons in the same way that the standard primary colour illustration appears, with three overlapping circles of different colours. The important part here is that where the polygons overlap they will combine to make a new colour, thus clearly demonstrating the overlapping area. Another way this is often done is to display each polygon with a unique crosshatching. For instance polygon 1 could have a left-facing diagonal hash, while polygon 2 could have a right-facing diagonal hash. Where they overlap, a cross-hatch pattern would be observed.

Transparency works in relation to other layers in the map, but unfortunately it doesn't seem to work in terms of each polygon within the layer. Same goes for defining the symbology level (essentially they all need to be on the same level).

I've seen this done with many other maps of animal home ranges or other overlapping zones, so I'm assuming there's got to be a way of doing this.