There are a lot of variables that go into an answer to your question. The chalk mark answer probably comes nearest to getting you the answer.
Look at a couple of things. If the tire tread from side to side is distributing equal weight all the way across, then it will have the best traction and most even wear, but there are different things that come into play besides just air pressure. Rim width. If the rim is wide compared to the tire width, the tread itself tends to exert less pressure in the center of the tread width, just as it does when tire pressure is too low, so it might be necessary to raise the air pressure. If the rim is narrow compared to the tire (12.5" on an 8" rim for example), pulling the bead on each side closer together causes the tread to bulge outward in the center of the tread width. So, in this case, to get a flat footprint, the air pressure may need to be lowered.
What if you don't want a flat footprint? What if you have a tire with a good highway tread pattern in the middle third of the tire and good heavy lugs or paddles on each side of that center tread. You might not want the lugs to hit the concrete. Put the tire on a narrow rim with more air pressure. Make the center stick out and keep the lugs off the road. Is this a good idea? I have no idea. Just thought it up on the spur of the moment to further emphasize the changes you can make.
Bias ply and radial ply behave differently too, but there again, the chalk mark will give you some insight.
The above applies to street running. When you get off road, the rules change.
Doug '97 TJ
Creator of the CBrack