Community structure in the United Nations General Assembly

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Abstract

We study the community structure of networks representing voting on resolutions in the United Nations General Assembly. We construct networks from the voting records of the separate annual sessions between 1946 and 2008 in three different ways: (1) by considering voting similarities as weighted unipartite networks; (2) by considering voting similarities as weighted, signed unipartite networks; and (3) by examining signed bipartite networks in which countries are connected to resolutions. For each formulation, we detect communities by optimizing network modularity using an appropriate null model. We compare and contrast the results that we obtain for these three different network representations. We thereby illustrate the need to consider multiple resolution parameters and explore the effectiveness of each network representation for identifying voting groups amidst the large amount of agreement typical in General Assembly votes.

Highlights

► We study the community structure of voting networks in the UN General Assembly. ► We detect communities by optimizing a quality function. ► We compare and contrast different network representations of voting similarities.

Introduction

The study of networks has a long history in both the mathematical and social sciences [1], and recent investigations have underscored their vibrant interdisciplinary applications and development [2], [3], [4], [5], [6], [7]. The large-scale organization of real-world networks typically includes coexisting modular (horizontal) and hierarchical (vertical) organizational structures. Various attempts to interpret such organization have included the computational identification of structural modules called communities [8], [9], [10], which are obtained by finding groups of nodes such that there are more (or a denser collection of) connections between pairs of nodes in the same group than there are between pairs of nodes assigned to different groups. In principle, communities are not merely structural modules but can have functional importance in network processes. For example, communities in social networks (“cohesive groups” [11]) might correspond to circles of friends or business associates, communities in the World Wide Web might encompass pages on closely related topics, and some communities in biological networks have been shown to be related to functional modules [12], [13].

As discussed at length in two recent review articles [8], [9] and in references therein, the classes of techniques available to detect communities are both voluminous and diverse. They include hierarchical clustering methods such as single linkage clustering, centrality-based methods, local methods, optimization of quality functions such as modularity and similar quantities, spectral partitioning, likelihood-based methods, and more. Investigations of network community structure have been remarkably successful on benchmark examples [8], [14], [15] and have led to interesting insights in several applications, including the role of college football conferences [16] in affecting algorithmic rankings [17]; committee assignments [18], [19], [20], legislation cosponsorship [21], and voting blocs [22] in the US Congress; the examination of functional groups in metabolic [12] and protein interaction [13] networks; the study of ethnic preferences in school friendship networks [23]; the organization of online social networks [24], [25], and the study of social structures in mobile-phone conversation networks [26].

With the newfound wealth of longitudinal data sets on various types of human activity patterns, it has become possible to investigate the temporal dynamics of communities, and this issue has started to attract an increasing amount of attention [26], [27], [28], [29], [30]. It is also potentially useful to study community structure in similarity and correlation networks [31], such as those determined by common voting or legislation-cosponsorship patterns [21], [22], alliances and disputes among nations [32], or more general coupled time series [28], [29]. In such cases, one is faced with numerous choices for how to actually construct the network from the original data–an important issue that has received surprisingly little attention. (An old discussion of some of the available methods is presented in Ref. [33].) In the present paper, we focus on this network construction issue by examining the community structure of networks defined in different ways from roll-call voting patterns in the United Nations General Assembly (UNGA).

The primary goal of this paper is to conduct a comparative investigation of different ways to turn voting data (and similar relational data) into network representations in order to use community detection tools. Community detection can then be used to complement existing approaches such as multidimensional scaling and other data clustering techniques [34], [35]. As we discuss in detail below, there are many ways to turn voting data into networks. In this paper, we will compare three ways of doing so using roll-call voting in the UNGA as an illustrative example. For each network representation, we will examine community structure in the UNGA and how it changes over time, and we will compare the results that we obtain using each network representation. Studying community structure entails partitioning a network, and it might be helpful to do so at different network scales [8], [9]. We consider different scales using resolution parameters and identify results that are robust with respect to different choices of such parameters.

As discussed in a recent review [36], network analysis has led to interesting insights in the field of international relations–just as it has in numerous other fields in the social, physical, biological, and information sciences [1], [3], [4], [7]. For example, a networks perspective has proven to be important for political studies of social balance [37], [38], [39]. Additionally, elements of the Correlates of War (CoW) data [40], [41] have been studied using network methods [32], [42], and we expect that other available data can also be studied insightfully. Previous studies of UNGA roll-call data have been successful at grouping countries using NOMINATE scores, which assign ideological coordinates to voting members and can be used to introduce partitions in policy space [34], [43]. Empirical investigation of UNGA voting behavior has become readily accessible due to Voeten’s organization of the UNGA voting data [44]. Voeten analyzed this data using NOMINATE scores to study Cold War and Post-Cold-War voting behavior [43]. Lloyd applied network analysis and correspondence analysis to similar data to show that the so-called “Clash of Civilizations” does not occur along civilizational lines (as one might have expected from its name) but rather via a North–South division that arises from economic differences; Lloyd concluded that this division has resulted in varying levels of support for human-rights treaties [45]. Motivated by the previously demonstrated utility of studying community structure in network representations of voting data [22] and legislation cosponsorship data [21] for the United States Congress, we investigate in this paper the community structure of network representations of the UNGA (based on the patterns of roll-call voting on resolutions) to see if such methodologies can help to identify and understand international voting blocs.

The rest of this paper is organized as follows. In Section 2, we give a brief introduction to the United Nations General Assembly voting data and discuss the different ways that we will represent this data in the form of networks. In particular, we construct (1) weighted networks defined by the numbers of voting agreements between pairs of countries; (2) weighted, signed networks in which we separately consider voting agreements and disagreements between countries; and (3) signed bipartite networks between countries and resolutions that directly indicate yes (+1) and no (−1) votes. In Section 3, we briefly review community detection via optimization of modularity and its generalizations, and we emphasize the use of appropriate null models with resolution parameters for each of the three network representations that we consider. We then investigate community structure in the UNGA using each of these three formulations and compare our three sets of results. In Section 4, we study the set of resolutions in each session using voting agreements and use our computations to identify historical trends and changes in the UNGA’s community structure. We then discuss case studies by going into further detail in one session from each of three different periods in the UNGA’s history. We investigate these three sessions (the 11th, 36th, and 58th Sessions) in terms of voting agreements and disagreements in Section 5 and as bipartite networks with positive and negative edges in Section 6. We close with concluding observations in Section 7.

Section snippets

Network representations of UNGA voting data

Unlike the other component bodies of the United Nations (UN), the United Nations General Assembly (UNGA) provides equal representation to all member nations [46]. Each nation gets one vote, and UNGA representatives can debate international issues and non-binding resolutions. In recent years, this setting has motivated collaboration among developing countries to create a “North–South” division. However, it is unclear how applicable this grouping is in other settings or how cohesive it is on

Community detection by optimization of generalized modularity

We detect communities by optimizing the quality function known as modularity [55], [56], [57], and we also consider some of its generalizations. (Numerous other graph partitioning methods can of course be employed [8], [9].) We take the partition with the highest quality value that we can obtain from among three computational heuristics–spectral bipartitioning [57], [58], spectral tripartitioning [59], and the locally greedy “Louvain” method [60]–which we subsequently follow in each case by

Networks of voting agreements

We first consider the weighted, unipartite UNGA networks that we constructed by considering the level of agreement between countries. We maximize Newman–Girvan modularity, which is given by Eq. (3) with the default resolution parameter value γ=1, for each of the UNGA sessions. To provide additional context for our discussion, we remark that modularity can be used as a measure of polarization among voting parties [21], [22].

In Fig. 2, we show that beginning near the 1964 declaration of the Group

Networks of voting agreements and disagreements

In this section, we study the signed unipartite networks that we obtain by treating the positive and negative edges separately. As indicated in Section 3, this yields a null model with two terms and a resolution parameter (γ and λ) for each of them. Using the network of agreements and disagreements described in Section 2, we sweep over different values of the two resolution parameters and plot surfaces for the numbers of communities in Fig. 8. In these plots, we have color-coded each surface by

Bipartite voting networks with positive and negative edges

In this section, we use the signed bipartite modularity from Section 3 to study networks of yes and no votes, which we represent using positive and negative edges between UNGA countries and the resolutions on which they voted. (We do not include abstentions in this representation.) As before, we seek robust communities by exploring the two-dimensional space of resolution parameter values, examining the numbers of communities at neighboring points in the space, and calculating the mean Jaccard

Conclusions and discussion

We have studied community structure in networks formed by voting on resolutions in individual sessions of the United Nations General Assembly. The UNGA voting record provides a fascinating example of a very general problem: How can one use network methods such as community detection to examine data such as voting records? Accordingly, our focus is not on attempting a sociological or political study of the UNGA but rather on using it as an interesting and potentially valuable example for which

Acknowledgments

We thank Eric Voeten and Adis Merdzanovic for the United Nations voting data [78] and James Fowler, Yonatan Lupu, Mark Newman, and Vincent Traag for useful discussions. We also thank the anonymous referees for their helpful comments on the paper. KTM was funded in part by a Summer Undergraduate Research Fellowship from the UNC Office of Undergraduate Research. PJM & KTM were also funded by the NSF (DMS-0645369). MAP acknowledges a research award (#220020177) from the James S. McDonnell

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