Empower the WWE universe
The above two mentioned ways of selection have nothing to do with the WWE universe. They should accept whatever may be the outcome of above two ideas. With Shane boasting about the new era and giving the best to the WWE universe, why not go ahead and empower the WWE universe?
This could be done in two ways. First, name all the N contestants taking part in the leadership race and schedule a poll on the WWE Network or on the WWE App. Let the universe decide who is best for them and vote for him. In the meanwhile, the company could make a few videos and post them on the network about the accomplishments and shortfalls of each of the contestants in the race. A great way to get some business on something that is pre-decided!
The other approach to do this would be to have a test of leadership. Now that we have this entire struggle to filter out the best leader among the lot, why not test that trait itself directly?
Let all 4 of them schedule matches for the upcoming PPV or say an episode of RAW and based on the reviews from the web about the quality of matches, the one that receives the best review would win the match of the race award and the leader who scheduled it would be the GM of SmackDown.