There is No Satisfactory Form of Utilitarianism
In 2000, a paper written by Gustaf Arrhenius called An Imposibility Theorem for Welfarist Axiologies showed that all forms of utilitarianism lead to at least one of three highly undesirable implications. The result is extremely dire for those of us who might have hoped that utilitarianism could give good answers to ethical questions about birth, death and human populations.
A “population axiology” is a way of combining the welfare of many people into a single measure of the welfare of everyone. For instance, adding a numerical measure of everyone’s happiness together is one axiology; averaging their wellbeings is another; summing the monetary wealth of the 1,000,000 poorest people is a third.
Note that two things vary about these population axiologies: what kind of welfare is being measured (“happiness”, “wellbeing”, “monetary wealth”), and how these quantities are combined across the population (“total”, “average”, “sum for the 1,000,000 worst-off people”). Utilitarian ethical theories basically require a population axiology, though there are many non-utilitarian axiologies too.
Ahrrenius’ proof shows that any axiology which satisfies three basic sanity conditions1 necessarily leads to at least one of three distressing conclusions. Each of these conclusions is deeply contrary to our ethical intuitions. Let us meet the three prongs of the dilemma:
Option one: The Repugnant Conclusion
For any population of very happy people, there exists a much larger population with lives barely worth living that is better than the group of very happy people (according to the population axiology).
Option two: The Sadistic Conclusion
Suppose we start with a population of very happy people. For any proposed addition of a sufficiently large number of almost-as-happy people, there is a small number of horribly tortured people that is (according the population axiology) a preferable addition.
Option three: The Very Anti-Egalitarian Conclusion
For any population of two or more people which has uniform happiness, there exists another population of the same size which has lower total and average happiness, and is less equal, but is better (according to the population axiology).
Utilitarianism needs to do a great deal of wriggling to escape these implications. For instance, some of the STM authors favour variants of utilitarianism that are limited to pre-defined populations: we can say what is best in a world containing Mary, Fred and Jane, but not whether the world is better if Abigail also lives in it. Such positions are coherent, but they are unable to address important ethical questions: Should we have children? Should we try to prevent overpopulation? When is it wrong to abort a fetus?
Topic for discussion: is Arrhenius’ impossibility theorem more serious for the project of using utilitarianism to answer questions of public policy than Arrow’s theorem is for the project of using voting systems to elect politicians?
[1] The basic sanity conditions are almost immune to reasonable disagreement. They are:
- The “dominance condition”: if population A is the same size as population B, and every person in A is happier than their equivalent in B, then A is better than B;
- The “addition principle”: if it is bad to add a group of people B to population A, where the people in B are worse off than those in A, then it is at least as bad to add a group of people C, where C is larger than B and those in C are worse off than those in B.
- The “minimal non-extreme priority principle”: there exists a number of people n such that adding a n extremely well-off/happy people and a single person of slightly negative welfare to an original population A is better than not adding anyone to A. It is notable that the Difference Principle advocated by John Rawls does not in general satisfy this principle and is therefore not subject to the Arrhenius theorem.