Some people won't respond positively to any warning called out to them. My point is the subconscious response to a command is to follow the command (even if the person resents it a moment later) verses a description of an action which the brain has to take time to decipher. And these warnings need not be "barked", but should probably be called out respectfully as a warning after the passer has slowed to mostly match speed. The passer still has the responsibility to pass safely; I'm just saying that a command called out as a warning is likely more effective than a description called out as way of a warning. Nobody in their right mind in any situation (car, ped, bike) passes a slower person on their right. What's the purpose of saying "on your left" then? Does anyone ever say "on your right"?

The response is to merely hold their line to aid the passer. Same as saying "on your left", except more effective. Myself currently, I usually just say "pardon" before I pass if it's a path. If I'm on the road, I pass in the car lane and I don't say anything until I've pulled ahead of the person. Then I say "hi" or "good morning/afternoon".

People shouldn't take offense... that is unless they resent the fact that someone is passing them. If so, better train and start racing instead of responding to a simple warning in a passive aggressive manner. A bicyclist passing another bicyclist is a cooperative venture. The passee must stay moving in a straight line. The passer must pass cleanly and safely. If I am passing someone and venture a word of warning and that person is somehow offended, this is their problem, not mine.