Depends. If I'm confident that I can win the endgame (which normally is the case when up material), I trade down. It simply reduces the chance to make mistakes and lose the material advantage.
When to trade down?
another conflicting principle to consider when you should trade down queens.
if your opponent has an attack against you. you trade down queens.
I was up material in a game and decided to trade down queens and suddenly my attack was gone. this was a mistake.
Q:What if your up material and your opponent is cramped do you trade down?
A: that depends on the position and what material I have. If I have knights it might be best to keep the cramped position. if he has knights and you have bishop a trade might open the position.
Depends on how much material you are up, but up significant material (enough that you are sure you will win the endgame easily), the "trade down up material" rule will almost always outweigh the "don't trade down with a space advantage" rule.
Why even bother wondering? If you're up material AND have an attack the game is basically won.
try playing against a computer a picece up and you will see that it is not that easy.
Try playing against a helloween gambit player and you will see that you lose if you make the wrong plan against the helloween gambit. The gambit sacrifices a knight
I have otb been down a piece and had a attack against me and won or drawn.
I made a blunder but my opponent made an even bigger.
When your up material you should trade down to increase your advantage ratio wise.
When you have your opponent cramped you shouldn't trade down to keep your opponent cramped.
What if your up material and your opponent is cramped do you trade down?