I often meet with parents who are under the impression that a child is able to make his or her own decision about who to live with at a certain age. In Arizona, at any age, "the wish of the child" is only one factor a court considers in determining what type of custody and parenting time arrangement is in the best interest of the child. Although judges start giving the wishes of a child more weight the older the child gets, the child's wish alone (at any age) is rarely the only factor the court will consider in deciding with whom that child lives. There are a few reasons for this logic:
Judges recognize that in an effort to "please" his or her parent, a child might tell each parent what s/he thinks that parent wants to hear. As a result, you sometimes hear BOTH parents claiming that the child wants to live with him/her. In situations like that, it might take some court-assisted "investigation" to know what the child's true desires are. These cases have to be handled with care so as not to place the child in a position of feeling pressured or like s/he will "hurt" one parents feelings if s/he says what s/he really feels.
Courts are also aware that in some cases, older children are motivated by different reasons to "play" their parents against one another. As one example, a teenaged child might express that he wants to live with his father, knowing his dad works often and would not be around to "supervise" his time at home and with friends. Although (1) the father might be an amazing parent and (2) the teenager wants to live with him, it might not be in that child's best interest if the father would not be around very much to "keep tabs" on the child.
Finally, in other cases, an older child might want to live with one parent, but that parent may have significant mental health or substance abuse issues. In situations such as those, before a judge would allow the child to "choose", s/he would probably need to take a closer look at the parent's "fitness" to be the primary residential parent of the child.
Keep in mind that each circumstance is unique, and the age of the child and the weight of the child's "wishes" would depend on the facts of the case.
As always, I would encourage you to consult with an attorney in your home state so you can be advised of the specific laws that apply in your case.
In Massachusetts, there is no certain age that a child can definitively and conclusively choose a visitation schedule. Much depends on the maturity level of the particular child. However, generally speakingm, judges begin to place some weight on a child's stated desires at around age 13. But, a judge will likely not trust a parent's representation about the wishes of his or her child, and the judge will likely want a guardian ad litem to interview the child, investigate what us in the child's best interest, and report back to the judge.