Melee fighters overcome Rangers because swords can cut through leather armour with ease. Melee armour is also effective at protecting against ranged ammunition, as flying projectiles cannot penetrate melee fighters' thick metal plate armour.
Rangers are able to overcome Magic users because of their long range capabilities, as well as ammunition which is able to penetrate through magic users' robes. Ranged armour is usually crafted from thick animal hides and is highly resistant to magical attacks.
Magic users overcome Melee fighters because Melee armour "conducts" magical energy, making magic attacks very effective against those wearing full Melee armour. Effective mages are also able to use binding or ice spells to hold warriors and prevent them from reaching their targets.