The objective of this paper was to consider the social value of biological diversity and explore if this value could be expressed in terms of a unidimensional metric in money. Economics distinguishes between use-values and non-use-values, which are critically evaluated for valuing biodiversity. It is shown that these utility-based valuations have severe limitations as they treat species in isolation from their ecological contexts. In contrast, ecosystem ecology regards ecosystems as an integrated non-linear and nonconvex system in which ecosystem functions can be understood as a four-component cycle; exploitation, accumulation of biomass, creative destruction and renewal. Within such a cycle, ecosystems can be seen to have two properties: stability and resilience. A good proxy for resilience is the probability of extinction of species, and social value of biodiversity can be expressed as a partial ordering with this probability as an index. This approach is consistent with decision theory, of which social choice is an important component, pioneered by Arrow.