HV - 
I don't know what the lighting spec is.  I don't know if the lights are carbon arc, cfi, LED, arc-powered chemical luminesance, laser excited flux capacitors - heck, they could even be incandescant.  I don't know the layout - distance from the panel to first light, distance between posts.  Neither do the rest of us.  
And that's 24 volts drop on 120V nominal - which would give 94V.  If they are incandescents, that's pretty dim - but they would never burn out.  
As noted by others, one might wish to check the specs on the fixtures for the voltage - could be lower voltage is okay.
However, you have already given the answer:
Why guess?  Check the fixture voltage spec, pick a wire size, calculate the drop at each fixture.  If it is in spec for the fixture, great.  If not bump up the wire.  
And yes, a 3-wire ckt could easily take less copper.  1500W on 240V is only 6.3A.  For #10, 1600', that, only 12V or 6V per side - not bad.  Of course if lights on one phase burnout, the voltage will go down on the side with none burned out (minorly trickey, but true)
I think like the "laser excited flux capacitors" the best. :roll:  
All I've said is true (As long as I didn't write something different than I'm thinking).  And yes, I'm having fun with this one.
ice