A popular residential hall on campus, Ersula Hall ("You've tried the rest, now stay at the best."), is inundated with requests for accommodation but can only accommodate 400 students. The ANU decides that the only fair way to distribute the limited number of accommodations is to administer a lottery where every applicant has an equal chance of "winning" one of the 400 spots.
Given the lottery allocation of spots, could trade among students lead to a "Pareto improvement" reallocation where someone is better off and no one is worse off? Explain.