The New York Times, in their Room for Debate section here, has a debate titled “Should Kids Pick Their Own Punishments.” There are authors who argue for and against the issue. Personally, I think it’s the wrong issue.
Having to punish at all means your system has broken down. It’s much better to see what children have done that is praiseworthy, and focus on that.
This doesn’t mean you don’t allow natural consequences to happen. If your children are rude to you—aren’t saying “please” and “thank you,” explain that their rudeness makes you feel bad, and not inclined to give them whatever they are asking for.
And, lest you think I’m just a wide-eyed radical, I taught high school English for 37 years. I think in that entire time I only gave out two detentions, and my classes were well-behaved and hard-working. I never punished my own children, and they are now all stable, loving, hard-working adults.
The students I had who were always getting grounded were the kids with the behavior problems. The kids who were punished for not doing homework were the kids who, in high school, still didn’t do homework.