Normalizing alpha values of lines in display list

I have a display list that draws a bunch of lines, some of them overlap, some of them do not. What I would like to do is blend them together so areas with overlapping lines are more opaque. I can do this using alpha blending without a problem.

The issue is that I would like to normalize the transparency values, for example I would like the minimum alpha to be 0.5 for example and the maximum to be 1.0. So in a case where I have 3 lines drawn and 2 of them fully overlap, the overlapping ones would show with an opacity of 1.0 and the single line with 0.5. Is there a way to do this?