The spaceship problem

Suppose you have to plan a very long term mission in space. It will last for many years, and you need to provide a group of people the means to live in a hermetic environment. You do not have access to Star Trek technologies like warp speed, replication and teleportation. Your population can reproduce, but life length and quality of life depends on resources and population density. How many people should be on such a mission? This is known as the spaceship problem. Of course, economists have something to say about this.

Pierre-André Jouvet and Grégory Ponthière are not going to solve the problem, there are too many biological and physical constraints, but they point out that the solution will yield solutions that contradict utilitarianism. They focus on the trade-off between the number of people and their life length. Indeed, longevity impacts population size and thus density. They assume that a social planner uses the sum of residents' utilities as a criterion and, unfortunately, that resources are unlimited, which makes the paper stray away from Economics.

What Jouvet and Ponthière really want to do it is compare different social welfare criteria in this environment. The Classical Utilitarian, for example, sums the utility of all individuals, the Average Utilitarian only the living ones. In a model without reproduction and a finite mission time, Classical Utilitarianism yields a small population living very long, while the second may want to have a large population that lives for a short time. Add reproduction to the mix and anything can happen depending on parameters values and initial population size. Make the mission life infinite, and the authors run into problems and need to define additional social welfare parameters. That is mainly due to the fact that there is no discounting, and infinitively lived economies and ill-defined.

What do I learn from this exercise? It is not very clear, except that social welfare criteria matter, adding utilities gives us a lot of trouble and that discounting is essential. But we knew that already, even when the spaceship is called Earth.

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