The United Nations Security Council (UNSC) is the foremost international body responsible for the maintenance of international peace and security. Members vote on issues of global importance and consequently receive perkselection to the UNSC predicts, for instance, World Bank and IMF loans. But who gets elected to the UNSC? Addressing this question empirically is not straightforward as it requires a model that allows for discrete choices at the regional and international levels; the former nominates candidates while the latter ratifies them. Using an original multiple discrete choice model to analyze a dataset of 180 elections from 1970 to 2005, we find that UNSC election appears to derive from a compromise between the demands of populous countries to win election more frequently and a norm of giving each country its turn. We do find evidence that richer countries from the developing world win election more often, while involvement in warfare lowers election probability. By contrast, development aid does not predict election.
Phylogenetic trees are a central tool in many areas of life science and medicine. They demonstrate evolutionary patterns among species, genes, and patterns of ancestry among sets of individuals. The tree shapes and branch lengths of phylogenetic trees encode evolutionary and epidemiological information. To extract information from tree shapes and branch lengths, representation and comparison methods for phylogenetic trees are needed. Representing and comparing tree shapes and branch lengths of phylogenetic trees are challenging, for a tree shape is unlabelled and can be displayed in numerous different forms, and branch lengths of a tree shape are specific to edges whose positions vary with respect to the displayed forms of the tree shape. In this paper, we introduce representation and comparison methods for rooted unlabelled phylogenetic trees based on a tree lattice that serves as a coordinate system for rooted binary trees with branch lengths and a graph polynomial that fully characterizes tree shapes. We show that the introduced tree representations and metrics provide distance-based likelihood-free methods for tree clustering, parameter estimation and model selection, and apply the methods to analyze phylogenies reconstructed from virus sequences.
We analyze democratic equity in council voting games (CVGs). In a CVG, a voting body containing all members delegates decision-making to a (time-varying) subset of its members, as describes, e.g., the relationship between the United Nations General Assembly and the United Nations Security Council (UNSC). We develop a theoretical framework for analyzing democratic equitability in CVGs at both the country and region levels, and for different assumptions regarding preference correlation. We apply the framework to evaluate the equitability of the UNSC, and the claims of those who seek to reform it. We find that the individual permanent members are overrepresented by between 21.3 times (United Kingdom) and 3.8 times (China) from a country-level perspective, while from a region perspective Eastern Europe is the most heavily overrepresented region with more than twice its equitable representation, and Africa the most heavily underrepresented. Our equity measures do not preclude some UNSC members from exercising veto rights, however.
Phylogenetic trees are a central tool in evolutionary biology. They demonstrate evolutionary patterns among species, genes, and with modern sequencing technologies, patterns of ancestry among sets of individuals. Phylogenetic trees usually consist of tree shapes, branch lengths and partial labels. Comparing tree shapes is a main challenge in comparing phylogenetic trees as there are few tools to describe tree shapes in a quantitative, accurate, comprehensive and easy-to-interpret way. Current methods to compare tree shapes are often based on scalar indices reflecting tree imbalance, and on frequencies of small subtrees. Polynomials are important tools to describe discrete structures and have been used to study various objects including graphs and knots. There exist polynomials that describe rooted trees. In this paper, we present methods based on a polynomial that fully characterizes trees. These methods include tree metrics and machine learning tools. We use these methods to compare tree shapes randomly generated by simulations and tree shapes reconstructed from data. Moreover, we also show that the methods can be used to estimate parameters for tree shapes and select the best-fit model that generates the tree shapes.
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