Halpern et al (2012 An index to assess the health and benefits of the global ocean Nature 488 11397) propose a detailed measure of the state of the human-ocean system against ten societal goals. They devote less attention to the normative foundation of the index, which is crucial for assessing the overall health of the human-ocean system, notably when it comes to aggregation of potentially conflicting goals. Social choice theory provides several possible functional forms for assessing the compound change in various goals. The one chosen by Halpern et al, the arithmetical mean, is not only a specific but also an extreme case. It implicitly allows for unlimited substitution. A one-unit reduction in one goal can be fully offset by a one-unit increase in another with the same weighting factor. For that reason, the current index satisfies an extremely weak sustainability concept. We show that the results in Halpern et al are not robust when one adopts a strong sustainability concept. The overall health score of the ocean decreases, the ranking of the various coastal states changes substantially, and the assessment of sustainable development needs to be partially reversed.