On construction of equitable social welfare orders on infinite utility streams

• Every social welfare order (SWO) satisfying Hammond Equity and Strong Pareto is non-constructive.
• For domain set Y=[0,1]Y=[0,1], every SWO satisfying Pigou–Dalton transfer principle is non-constructive.
• Provides an example of a SWO which can be represented, but which cannot be constructed.

This paper studies the nature of social welfare orders on infinite utility streams, satisfying the consequentialist equity principles known as Hammond Equity and the Pigou–Dalton transfer principle. The first result shows that every social welfare order satisfying Hammond Equity and the Strong Pareto axioms is non-constructive in nature for all non-trivial domains, YY. The second result shows that, when the domain set is Y=[0,1]Y=[0,1], every social welfare order satisfying the Pigou–Dalton transfer principle is non-constructive in nature. Specifically, in both results, we show that the existence of the appropriate social welfare order entails the existence of a non-Ramsey set, a non-constructive object. The second result also provides an example of a social welfare order which can be represented, but which cannot be constructed.