So I have been on both sides of this paradox in my career. You apply for a job/promotion and you don't get it and then you are given the assignment of training the new person that got it.
Do you:
A) Say "No way! Let him or her struggle on their own."
B) Say "This sucks, but I am going to be the bigger person and do it anyways."
C) Say "This sucks. If they ask me for help I will assist but if they don't ask, I ain't going out of my way to help them"
D) Quit and figure that action will show your boss something.
Having been on both ends of the spectrum I can tell you from a management and resume building perspective option B is the best way to go. One of the things that helped me advance in my career is taking on the jobs that no one wanted to do, even if the ones that "should" have done it were higher paid than me. This allowed me to become the trusted employee of my supervisor. He knew he could count on me if he got into a jam. Even though I was a mid-level employee and not a journeyman, I would tackle any request with the enthusiasm and vigor to get it done and get it done right. I kept applying for promotions and not getting them (it was being decided 2 levels higher than my boss). Eventually I got it and then the supervisor took me under his wing and showed me the ropes of supervision. This allowed me to gain valuable resume building experiences that helped my move into management later.
Now having been the new person I have also been on the receiving end of all 4 options. In the cases where I was helped, I was able to help the non-selected people advance their career. Heck in some of the A and C scenarios I was able to assist the people, even though they had not been nice to me. I understood their frustration, but not their method. What I pointed out to them was that sometimes management did this to see how they handled the situation. If they handled it well, then they were promotion worthy for future promotions. If they handled it poorly, then it confirmed they made the right decision by not selecting that person. I have seen many a co-worker kill their career defending a promotion they didn't win.
My advice to those of you who find yourself in this situation: Help the new person. You do yourself no favors being a donkey. Use the situation to your advantage. I used to put down on my resume that I trained higher level people. When asked about it in interviews, I explained the situation and the interviewers were impressed with my team-first attitude.
