Random allocation, preferences, and welfare: a fish story

Flying from Madrid to Boston on an Airbus with two aisles not long ago, two stewardesses proceeded in parallel down the aisles offering food. I asked for the fish, but the stewardess in my aisle was already out of fish. Speaking to her colleague in the other aisle, she ascertained that her colleague still had some fish. Rather than pass the fish across the (empty) seat between them, “my” stewardess told me that, if her colleague still had fish when she completed her aisle, then I could have it. (I chose the vegetable dish…)

We see similar issues when changes are discussed in how to allocate deceased-donor organs for transplants, or some other policy where there has been a previous decision on an order of allocation to randomly arriving agents. To have passed the fish across to me would have disadvantaged some passenger who, but for the demand for fish on my side of the plane, would have been able to eat fish…

Of course, assuming that on which side of the plane passengers are seated is random, the policy of allowing fish to be passed from side to side and not just from front to back would have the same ex-ante welfare properties. But, once the passengers are seated, any change in policy would likely help some passenger only by hurting another.

This kind of discussion comes up from time to time in the allocation of school places, as well as transplant organs.