For backpackers with heavy packs, I was taught that the person going downhill should step aside and let the uphill-climbing person pass. I believe the theory is that it takes more energy for the person going uphill to stop, wait, and then get going again, than it does for the downhill person. Sometimes the uphill person will stop, smile at the downhill person and say "thanks for offering to let me pass but I can use a rest stop".
For dayhikers with a lightweight pack, this is a nice courtesy but not often known.
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