I'm a game programmer, and I have an answer for my preference of Z being up: I want positive values going into the screen (away from the viewer) but I also want

I'm a game programmer, and I have an answer for my preference of Z being up: I want positive values going into the screen (away from the viewer) but I also want a right handed coordinate system (mostly because physics become more intuitive - especially wrt torque). X is almost always to the right, so this gives me Y and Z to work with. To satisfy both the positive values into the screen and right handedness I need either Z forward and Y down or Y forward and Z up. Since most of the time you draw a graph with an axis going up rather than down, that settles it. It's entirely arbitrary in the end, a single matrix will fix any dispute you have amongst peers.