What are some exercises to reduce the size of a big butt?

There is no way to reduce fat from any one area of the body alone. This type of "Spot Reduction" is a myth. Your body loses fat from all areas of the body equally.

Doing gluteal exercises will firm and tone up the muscle under the fat, but has no direct effect on the fat itself.

General weight loss is the ONLY way to lose weight from any area of the body.