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 for 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 taken 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 Experiment. According to the results, there is a different contribution of each attribute to the improvement of the Society level of utility. The main finding of this study is the identification of a social demand for public goods and services provided by the mountains olive groves. This support for agricultural multifunctionality is heterogeneous in its perception by the citizens and the valuation of the various attributes that the concept involves. Taking into account the impact of an overall improvement in the attribute levels and the socioeconomic characteristics of the respondents, the results suggest that women, people with higher education levels, urban citizens and families with more than three members are those who benefit most from the provision of public goods by agriculture. There is a different contribution of each attribute to the improvement of the Society level of utility. Thus, and taking into account its WTP for each attribute, keeping rural population in their villages and fighting soil erosion (with ~22.61 and ~21.55/individual/year, respectively) seem to be the most valued functions of the mountain olive groves by Andalusian citizens. It follows the improvement of the visual quality of the rural landscapes (~12.20/individual/year) and the reduction of food residuals (~7.14/individual/year). Finally, the results of this study support the new orientation of the CAP which makes decoupled payments on compliance with a range of environmental, food safety, animal and plant health and animal welfare standards, as a result of which, the cross-compliance requirement of the EU agricultural support will, presumably, promote a net increase in social welfare. Yet, according to the results of this research, some efforts should be done to allow cross-compliance to reinforce the objectives of keeping rural population in rural areas and the improvement of the landscape.