How do you say "Do you prefer me wearing the hat to me not wearing the hat"?

Question

Answer

"Would you prefer me to wear a hat or not wear a hat?"

Answer

Like others have said, many ways to express it.

Do/would you prefer me wearing the hat ?
Do/would you prefer me wearing the hat, or not ? 
Should I wear a hat ?
Should I wear a hat, or not ?

Answer

I think there are a few different ways to say it. 
1. Do you prefer me to wear the hat or not?
2. Do you prefer that I wear the hat or not?
3. Do your prefer me wearing the hat or not?

We use "to" when talking about a choice between two things ("I prefer coffee to tea"), but your example is more of a either-or question which doesn't need the "prefer one to the other" structure.

Answer

Do you prefer if I wear the hat or not?

Answer

Voce prefere que eu use chapeu ou nao?

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