Disney is a popular vacation destination and crowded most of the time. I don't think there is any magic that lets some 3rd party predict the future and certainly not to the extent of deciding which park to do on a particular day. Even Disney has no idea how many locals with AP's will decide to show up some day when there is good weather. With a group that size, one consideration might be to split up into smaller groups. Some may like 1 park better than the others. Some may want to shop while others prefer to do rides/shows. If one person is deciding what 10 others want to do, I think everyone will be a bit disappointed in having to do whatever the 'lead' person has decided.
No amount of advance planning will make the park any less crowded. I think the adults in your group should get together prior to your trip and discuss how they think this will work to avoid surprises. It would be a huge mistake to not discuss it prior to your vacation and then have 11 people standing around at the entrance to your first park trying to decide where to go and what to do next. Everyone may not have the same budget, so while some may want to purchase those various Genie options, others may not.
You may also have some who want to sleep in, while others may be the go-go-go types up at the crack of dawn and racing off to be one of the first at a particular park. Smaller children often require a nap during the day. Some may want to do the park all day long, while others might prefer to relax by the pool. I doubt everyone has the same idea how to enjoy their vacation. If you split up, you could decide to meet at a certain place/time and have lunch or dinner together.