Open data initiatives are characterized, in several countries, by a great extension of the number of data sets made available for access by public administrations, constituencies, businesses and other actors, such as journalists, international institutions and academics, to mention a few. However, most of the open data sets rely on selection criteria, based on a technology-driven perspective, rather than a focus on the potential public and social value of data to be published. Several experiences and reports confirm this issue, such as those of the Open Data Census. However, there are also relevant best practices. The goal of this paper is to investigate the different dimensions of a framework suitable to support public administrations, as well as constituencies, in assessing and benchmarking the social value of open data initiatives. The framework is tested on three initiatives, referring to three different countries, Italy, the United Kingdom and Tunisia. The countries have been selected to provide a focus on European and Mediterranean countries, considering also the difference in legal frameworks (civic law vs. common law countries).