describes that you want someone else to do something.
Comes from Request: that you want them to give you something.
It is the #formal counterpart to 〜て欲しい.
タバコを吸ってもらいたくない
I don't want you to smoke. (lit. I want don't want to receive the favour of smoking)
Target is denoted with に, just like 〜て欲しい.
子供には携帯電話を持ってもらいたい **I want my child to have **a cell phone.