The OECD's Assessment of Higher Education Learning Outcomes (AHELO) project is an important contribution to discussions of how to define and measure the quality of global higher education. There is a genuine need for quality measures that can help to ensure students have equitable access to high-quality higher education wherever they study but do not reinforce existing institutional hierarchies that are simply based on historical reputation. However, I identify three problems with the approach that has been taken to AHELO which mean that even if it succeeded in its own terms, it would not meet this need. I conclude by arguing that rather than pursuing the illusion of a simple and robust measure of the comparative quality of learning outcomes globally, we should focus on the more everyday task of engaging stakeholders internationally in discussions about the development of high-quality undergraduate higher education