35 years of Multilateral Environmental Agreements ratifications: a network analysis


With the ratification of Multilateral Environmental Agreements (MEAs) the countries of the international community or of intentional communities—be they political, economic, financial, securitarian or strategic—endow these instruments of international cooperation with significant autonomy. From the 3550 dates of ratification of these MEAs recorded from 1979 to mid-September 2014, we produce a graph whose vertices are the 48 MEAs (ratified at least once) and whose links are induced by the succession of ratifications in time. On this basis we propose a diagnosis on the international acceptance of this type of legal instruments and their vulnerability in a global context that builds on the change in the balance of powers as a result of globalization, the break of the bipolar and then unipolar system, and the rise of new powers. Thus, it appears that a global environmental order has been promoted and implemented with some success in the 90s mainly by liberal Western countries who were then able to lead other countries less likely to bind to the fulfillment of environmental obligations. However, the expansion of this global environmental order now seems frozen, due to the current crisis of multilateralism. The rise of many countries, particularly in the South, whose environmental, political and economic weight grew, confronted with the “stable community” formed in the past 35 years suggests that there is a real power shift in the international arena and consequently, multilateralism needs to reflect this new reality. In other terms, the global environmental order is being slowly reformed. As a consequence, the treaties formed clusters in the past but they did not follow the same pattern since the twenty-first century began.

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  1. 1.

    Boulet R, Barros-Platiau AF, Mazzega P: Country communities underlying the ratification of international environmental treaties, submitted.

  2. 2.


  3. 3.

    Websites describing these institutions and their State members can be easily found on the worldwide web. Like the EU, the MERCOSUR and ASEAN are adopting negotiating agendas that are more political. Although the BASIC Group (Brazil, South Africa, India and China) could be an interesting counter-example, it was not considered because of it is still just a group under disputable institutionalization in the near future.

  4. 4.

    Here the word “partition” is used in a set-theoretic sense: a partition of a set S is a set P of subsets p of S such that the p are pairwise disjoint, the union of all p forms the whole set S, and none of the elements of P is empty.

  5. 5.

    Boulet R, Barros-Platiau AF, Mazzega P: Country communities underlying the ratification of international environmental treaties, submitted.

  6. 6.

    A directed edge in a graph is a link (an arrow) from a source vertex to a target vertex.

  7. 7.

    Here the term “community” is used in the context of graph theory. We shall use the term of “cluster” to name a group (“community”) of MEAs.

  8. 8.

    The density of a graph is the ratio between the number of edges of the graph and the total number of possible edges (if vertices were all linked pairwise).

  9. 9.

    A hierarchical clustering consists, from an initial partition where each single vertex is a community, in gathering gradually two groups. This process of merging can be represented by a dendrogram.

  10. 10.

    The Dice dissimilarity measure how close two vertices are (dis)similar following the idea that the more they have common neighbors, the more they are similar.

  11. 11.

    A spectral clustering is a method to detect community based on first embedding the vertices on an Euclidean space Rk (thanks to eigenvectors of a matrix) and then applying classical statistical methods (like k-means) to make groups.

  12. 12.

    The eigenvector centrality is computed, for a connected graph, by the leading eigenvector of the adjacency matrix. This centrality measure is such that the centrality of a node is proportional to the centrality of its adjacent nodes.

  13. 13.

    This method is based on the Dice dissimilarity computed on the bipartite graph with two sets of vertices, the countries and the treaties, with an edge linking a country with a treaty if this country ratified this treaty.

  14. 14.

    More precisely ratified or approved.


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This study was partly founded by the University of Lyon III, under the project “Multi-scale Complexity of Environmental Law”. We would like to thank Radboud Winkels and Nicola Lettieri for giving us the opportunity to discuss about this work during the workshop Network Analysis in Law which was held in Krakow (Poland) on December 2014.

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Correspondence to Romain Boulet.

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Boulet, R., Barros-Platiau, A.F. & Mazzega, P. 35 years of Multilateral Environmental Agreements ratifications: a network analysis. Artif Intell Law 24, 133–148 (2016). https://doi.org/10.1007/s10506-016-9180-7

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  • Multilateral Environmental Agreements
  • Graph theory
  • Emerging countries
  • Country intentional community
  • Ratification dynamics
  • Global environmental order