If your child is 14 or older, he has a statutory right to make his feelings known to the judge. The state calls this his election, but the judge is not obligated to ultimately rule according to your teenager's wishes. Your child's selection must be in his best interests, and his best interests are determined by the judge, not by the child. The court does not have to abide by his election if the judge decides that it wouldn't be good for him to live with the parent he's chosen.
Evolution of the Law
If you've heard that 14-year-olds can always decide which parent they want to live with in Georgia, this would have been pretty accurate up until 2008. The legislature modified the law at that time. The change is a legal fine point, but it nonetheless affects the rule to a significant extent. Before 2008, a teenager's wishes were controlling unless the parent was unfit. Lack of fitness generally involves egregious circumstances, such as drug addiction or abuse, so the child's election was almost invariably granted. As the law currently reads, the child's election is presumptive – it's assumed that it's good for him unless the court decides otherwise based on the state's best-interests-of-the-child standard. This change gives judges a great deal more latitude and discretion than they had in the past.
Georgia's best-interests standard specifies 17 factors a judge must weigh when determining issues of custody. They include things such as which parent generally met the child's needs when the family was intact, and how willing each parent is to support a relationship between the child and the other parent. They include reference to each parent's physical and mental health, as well as job demands that might curtail the time each parent can devote to the children. A teenager's election acts as something of a tiebreaker. If both you and your spouse are equally good parents according to the standard, then your child's wishes will determine who he lives with. If one parent is the clear choice based on all 17 factors, and if the teenager elects to live with the other parent, it's unlikely that the court will honor his wishes.
Younger children aren't left out of the election process entirely, but they have fewer rights than those who are 14 or older. If your child is between the ages of 11 and 14, the judge can include his preference along with the other 17 best-interests factors. If he's younger than 11, however, the judge will not consider his preference at all.