The essay suggestion would work maybe for the 10-12 year olds, but the 6-10 year olds would not be able to write that well. Also, would they not just pick their 'clique'?
- students only pick one other person, so picking their entire clique wouldn't fit as an answer. further, as good students tend to find one another, it's a good filter for finding people that should be recommended by the teacher but aren't (or vice-versa).
- if a full essay is too much, just ask them to write what they'd do with their scholarship in a few sentences (prose, poem, any form will do). since you're only looking for 2 kids, you only need a question that will highlight the top candidates. no need to properly rank the entire class.