Lately I've been handing projects off to the kids to be in charge of. For science we are building a large scale periodic table. I put Calvin in charge of making sure the element cards get done by everyone. We have over a hundred to do, after all. So he hands out a sheet of cards that need illustrating, then follows up with each sibling to make sure they are making progress. He's encouraging them and helping them come up with ideas. He's polishing up his teaching skills.
I caught Joshua doing an element sheet that Calvin handed to him. No complaining or arguing; just doing and with a good attitude.
Some days I put someone else in charge of math for the day. I have them check each others answers, (catching another person's errors helps reinforce their own knowledge). So the math leader's job is to assign grading and make sure everyone completed their work. I found that it works great when I have a student that needs more help on a concept. This way everyone else can move on with their respective lessons, and I can focus.
For the most part, they work peacefully together. Though it's not a perfect system. When a fight breaks out I back up whoever the leader is by reminding whoever is arguing that "______ is in charge of this project, defer to him/her. You will want the same respect when it's your turn to lead." If the leader is yelling or using bad judgment, I will pull them aside and privately affirm good leadership skills or (if necessary) correct bad behavior.
Consciously teaching my children to be good leaders is one of the many reasons I homeschool.