Re-ranking a list I have a ranked list say A,B,C,D,E,F,G and a subset of this list ranked with another strategy 
lets say D,B,C,F. And my assumption is that the strategy used for ranking the sublist is better because its a feedback strategy. Now I want to re-rank my initial ranked list according to feedback ranking of sublist and initial ranking available. Please, suggest some good algorithm in this direction
 A: You can treat this as a Reinforcement Learning problem, specifically as multi armed bandit problem where every item in the list represents a one armed bandit.
Basic algorithms to solve this can be found in chapter 2 of Sutton,Barto - Reinforcement Learning: An introduction.
In order to apply these algorithms, one has to attach some sort of quality value to each item / arm, for example its (normalized) position in the list. By using smaller initial quality values (based on the initial ranking) than the quality values gained by feedback, you can model your trust in the feedback strategy.
You have stated:

main issue is that feedback is available for only elements that are expected to be good. So other elements never get feedback.

This is called exploration-exploitation tradeoff: Look for new, may be better arms / items (explore) or stick with those which are considered good right now (exploit).
If for example you never gets feedback for A meanwhile everytime D is submitted for feedback it gets ranked at top position, how long are you willing to keep A at the top position ?  By setting the initial / feedback quality values and the algorithm related parameters one can model the sensitivity in this regard.
