Pretty simple for a straight utilitarian—option 2 forces 2 to get their second choice rather than first, and option 1 forces 10 to accept their second choice.
Complexities come when you add motives other than “best for the most”. If you’re not trying to optimize preference-satisfaction, but rather to discover value, you can treat the list as instant-run-off voting, and only offer the winners, forcing everyone to take these.
Pretty simple for a straight utilitarian—option 2 forces 2 to get their second choice rather than first, and option 1 forces 10 to accept their second choice.
Complexities come when you add motives other than “best for the most”. If you’re not trying to optimize preference-satisfaction, but rather to discover value, you can treat the list as instant-run-off voting, and only offer the winners, forcing everyone to take these.