This thread exemplifies the problem with "on your left". It can confuse people and get the opposite of the intended result. It also may foster an incorrect belief that the rider being passed has some duty to get out of the way of the rider passing.
If you're passing someone, it's your obligation to do it safely. If you're relying on the rider you're passing to "hold their line" because you said "on your left" you're passing them too closely.
Passing slower riders, I typically say hello, or goodmorning, just to avoid startling them. It keeps them from being Po'd, it doesn't imply any required action by them, and I just assume they will make the stupidist move possible, and oass in a manner to avoid them if they do.
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You could fall off a cliff and die.
You could get lost and die.
You could hit a tree and die.
OR YOU COULD STAY HOME AND FALL OFF THE COUCH AND DIE.