Bobby was chosen to be allowed to come on the boat because it would save conflict. He is the son of Dr. Dane, who is a vital member for survival, along with his mother, Mrs. Dane. Although Bobby needs around the clock care, it is worth it to bring him in the long run because both of his parents will be more willing to contribute to the survival of the group if they are with their child. Without Bobby being on the island with his parents, the family would be spilt up. Both of the parents would go insane without their child.
They would not be able to function properly knowing that they abandoned their son, and left him to die. Overall, without Bobby on the island then the entire family would not be able to function properly, and his parents are the people that know how to take care of his specific needs the best out of anyone. All in all, the family comes in a package, and must stick together.