Agricultural multifunctionality is the recognition of the joint exercise of economic, environmental and social functions by this sector. In order to make this concept operative to support the design of public policies, it is necessary to estimate the social demand for such functions. The main objective of this article is to present an empirical application in this line. For this purpose we have adopted the agricultural system of mountain olive groves in Andalusia (Southern Spain) at risk of abandonment after the decoupling of the EU subsidies as a case study. The economic valuation technique used is the Choice Experiments. According to the results, each attribute included in the concept of multifunctionality makes a different contribution to the improvement of the utility at societal level. Thus, and taking into account its willingness to pay (WTP) for each attribute, maintaining rural population levels in villages and fighting soil erosion seem to be the functions most valued by citizens of Andalusia. These functions are followed by improvement in the visual quality of the rural landscapes and the reduction of phytosanitary residues in food. Finally, although the results suggest that there is a significant demand for the various functions, this demand is heterogeneous, and depends on the socio-economic characteristics of the individuals.