Until about 10 years ago, when I heard Pete Dye mention this at an ASGCA meeting, I hadn't considered left or right in cart path placement, but it makes sense, and I do it now, all things being equal. Generally, if the next hole was on the left side of the hole, I had put the path there, figuring golfers would gravitate to that side, at least at the green area, and take the shortest route to the next tee.
Graves wrote that paths always ought to be on the inside of the dogleg, since golfers want to take the short cut, sort of a "line of charm" thing, but I have always put them on the outside of doglegs, since they become so visible on the inside.
So, there are different thoughts on the subject, including, leaving them out altogether to putting them on BOTH sides of the fw, as well as down the middle, as suggested earlier.