A while ago, I hypothesized that other path users, especially members of the non-cycling public, react (seemingly subconsciously) primarily to the direction they hear; e.g. "on your left" elicits a move to the left in response, since they heard "left". That's why I use a noisemaking device (bell, oddly-shaped horn, stentorian voice, etc.) about 100-50 feet back and follow it with "Good (insert time of day here)". This seems to greatly reduce the unwanted actions, and is usually good for gaining a successful passing maneuver.

Unless I'm in a pure bike event on a closed course. Then it's "On your ***" for consistency.