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This study presents a Bayesian spatial voting analysis of the Colombian Senate during the 2006-2010 legislative period, leveraging a newly constructed roll-call dataset comprising 147 senators and 136 plenary votes. We estimate legislators' ideal points under two alternative geometric frameworks: A traditional Euclidean model and a circular model that embeds preferences on the unit circle. Both models are implemented using Markov Chain Monte Carlo methods, with the circular specification capturing geodesic distances and von Mises-distributed latent traits. The results reveal a latent structure in voting behavior best characterized not by a conventional left-right ideological continuum but by an opposition-non-opposition alignment. Using Bayesian logistic regression, we further investigate the association between senators' ideal points and their involvement in the para-politics scandal. Findings indicate a significant and robust relationship between political alignment and para-politics implication, suggesting that extralegal influence was systematically related to senators' legislative behavior during this period.

Politics around the world exhibits increasing polarization, demonstrated in part by rigid voting configurations in institutions like legislatures or courts. A crux of polarization is separation along a unidimensional ideological axis, but voting behavior is in reality more complex, with other signatures of collective order. We extend a foundational, statistical physics framework, restricted Boltzmann machines, to explain the full complexity of voting. The models we propose are minimal, fit strongly correlated voting data, and have parameters that transparently give vote probabilities. The model accounts for multi-dimensional voter preferences and the context in which such preferences are expressed to disentangle individual from collective contributions; for example, legislative bills can negotiate multiple issues, whose appeals add up or compete for individual votes. With the example of the U.S. Senate, we find that senators have multi-dimensional preferences, and, as one consequence, non-polarized coalitions coexist with polarized ones. Increasing polarization is predominantly explained by fewer votes that elicit bipartisan coalitions. We show that these accounts can be consistent

We introduce a new method to identify emerging concepts in large text corpora. By analyzing changes in the heatmaps of the underlying embedding space, we are able to detect these concepts with high accuracy shortly after they originate, in turn outperforming common alternatives. We further demonstrate the utility of our approach by analyzing speeches in the U.S. Senate from 1941 to 2015. Our results suggest that the minority party is more active in introducing new concepts into the Senate discourse. We also identify specific concepts that closely correlate with the Senators' racial, ethnic, and gender identities. An implementation of our method is publicly available.

Representative democracy in the United States relies on election systems that transmit votes into representatives in three key bodies: the two chambers of the federal legislature (House of Representatives and Senate) and the Electoral College, which selects the President and Vice-President. This happens through a process of re-weighting based on geographic units (congressional districts and states) that can introduce substantial distortion. In this paper, I propose quantitative measures of this distortion that can be applied to demographic groups, using Census data, to assess and visualize these distortive effects. These include the absolute weight of votes under these systems and the excess population represented in the bodies through the distortions. Visualizing these metrics from 2000 -- 2020 shows persistent malapportionment in key demographic categories. White (non-Hispanic) residents, residents of rural areas, and owner-occupied households are overrepresented in the Senate and Electoral College; Black and Hispanic people, urban dwellers, and renter-occupied households are underrepresented. For urban residents, this underrepresentation is the equivalent of 25 million fewer res

Large language models (LLMs) have achieved unprecedented performance by leveraging vast pretraining corpora, yet their performance remains suboptimal in knowledge-intensive domains such as medicine and scientific research, where high factual precision is required. While synthetic data provides a promising avenue for augmenting domain knowledge, existing methods frequently generate redundant samples that do not align with the model's true knowledge gaps. To overcome this limitation, we propose a novel Structural Entropy-guided Knowledge Navigator (SENATOR) framework that addresses the intrinsic knowledge deficiencies of LLMs. Our approach employs the Structure Entropy (SE) metric to quantify uncertainty along knowledge graph paths and leverages Monte Carlo Tree Search (MCTS) to selectively explore regions where the model lacks domain-specific knowledge. Guided by these insights, the framework generates targeted synthetic data for supervised fine-tuning, enabling continuous self-improvement. Experimental results on LLaMA-3 and Qwen2 across multiple domain-specific benchmarks show that SENATOR effectively detects and repairs knowledge deficiencies, achieving notable performance improv

Signed networks capture the polarity of relationships between nodes, providing valuable insights into complex systems where both supportive and antagonistic interactions play a critical role in shaping the network dynamics. We propose a separable temporal generative framework based on multi-layer exponential random graph models, characterised by the assumption of conditional independence between the sign and interaction effects. This structure preserves the flexibly and explanatory power inherent in the binary network specification while adhering to consistent balance theory assumptions. Using a fully probabilistic Bayesian paradigm, we infer the doubly intractable posterior distribution of model parameters via an adaptive Metropolis-Hastings approximate exchange algorithm. We illustrate the interpretability of our model by analysing signed relations among U.S. Senators during Ronald Reagan's second term (1985-1989). Specifically, we aim to understand whether these relations are consistent and balanced or reflect patterns of supportive or antagonistic alliances.

This study introduces a novel approach to simulating legislative processes using LLM-driven virtual agents, focusing on the U.S. Senate Intelligence Committee. We developed agents representing individual senators and placed them in simulated committee discussions. The agents demonstrated the ability to engage in realistic debate, provide thoughtful reflections, and find bipartisan solutions under certain conditions. Notably, the simulation also showed promise in modeling shifts towards bipartisanship in response to external perturbations. Our results indicate that this LLM-driven approach could become a valuable tool for understanding and potentially improving legislative processes, supporting a broader pattern of findings highlighting how LLM-based agents can usefully model real-world phenomena. Future works will focus on enhancing agent complexity, expanding the simulation scope, and exploring applications in policy testing and negotiation.

Complex time-varying networks are prominent models for a wide variety of spatiotemporal phenomena. The functioning of networks depends crucially on their connectivity, yet reliable techniques for learning communities in time-evolving networks remain elusive. We adapt successful spectral techniques from continuous-time dynamics on manifolds to the graph setting to fill this gap. We consider the supra-Laplacian for graphs and develop a spectral theory to underpin the corresponding algorithmic realisations. We develop spectral clustering approaches for both multiplex and non-multiplex networks, based on the eigenvectors of the supra-Laplacian and specialised Sparse EigenBasis Approximation (SEBA) post-processing of these eigenvectors. We demonstrate that our approach can outperform the Leiden algorithm applied both in spacetime and layer-by-layer, and we analyse voting data from the US senate (where senators come and go as congresses evolve) to quantify increasing polarisation in time.

Understanding the dependence structure between response variables is an important component in the analysis of correlated multivariate data. This article focuses on modeling dependence structures in multivariate binary data, motivated by a study aiming to understand how patterns in different U.S. senators' votes are determined by similarities (or lack thereof) in their attributes, e.g., political parties and social network profiles. To address such a research question, we propose a new Ising similarity regression model which regresses pairwise interaction coefficients in the Ising model against a set of similarity measures available/constructed from covariates. Model selection approaches are further developed through regularizing the pseudo-likelihood function with an adaptive lasso penalty to enable the selection of relevant similarity measures. We establish estimation and selection consistency of the proposed estimator under a general setting where the number of similarity measures and responses tend to infinity. Simulation study demonstrates the strong finite sample performance of the proposed estimator, particularly compared with several existing Ising model estimators in estim

The shift towards increased remote work and digital communication, driven by recent global developments, has led to the widespread adoption of i-voting systems, including in academic institutions. This paper critically evaluates the use of i-voting platforms for elections to academic senates at Czech public universities, focusing on the democratic and technical challenges they present. A total of 18 out of 26 Czech public universities have implemented remote electronic voting for these elections. Yet, the systems often lack the necessary transparency, raising significant concerns regarding their adherence to democratic norms, such as election security, voter privacy, and the integrity of the process. Through interviews with system developers and administrators, along with a survey of potential voters, the study underscores the critical need for transparency. Without it, a comprehensive assessment of the technical standards and the overall legitimacy of the i-voting systems remains unattainable, potentially undermining the credibility of the electoral outcomes.

We find striking correlations between the presidential election outcome probability and major financial indicators, including USD currency pairs, bond prices, stock index futures, and a market volatility measure. The correlations are consistent with 'risk-on' behavior in markets, a term which describes investors moving toward riskier asset classes, as the election results became clearer. Further, we decompose the market reaction into a 'reduction in uncertainty' component and a 'probability of a Democratic party presidency' component. This decomposition reveals how markets reacted to the increasing certainty of the outcome as election results came in. Finally, we analyze the differing market reactions to the presidential election and the Senate election, including data from the unique Georgia runoffs, and demonstrate that bond prices were particularly sensitive to the probability of a combined Democratic Senate and Presidency.

Single Transferable Vote (STV) is used to elect candidates to the 76 seat Australian Senate across six states and two territories. These eight STV contests are counted using a combination of ballot scanners, manual data entry and tabulation software. On election night, some properties of the set of cast ballots are determined by hand. This includes the first preference tallies of each party. This technical report considers whether there are some properties, such as individual candidates' first preference tallies, that, if assumed to be accurate, imply a portion of the election outcome. The paper also presents an interesting example showing that the rules of STV tabulation used for the Australian Senate can allow bizarre behaviour, such as votes increasing in value over time.

The reconstruction of interaction networks between random events is a critical problem arising from statistical physics and politics, sociology, biology, psychology, and beyond. The Ising model lays the foundation for this reconstruction process, but finding the underlying Ising model from the least amount of observed samples in a computationally efficient manner has been historically challenging for half a century. Using sparsity learning, we present an approach named SLIDE whose sample complexity is globally optimal. Furthermore, an algorithm is developed to give a statistically consistent solution of SLIDE in polynomial time with high probability. On extensive benchmarked cases, the SLIDE approach demonstrates dominant performance in reconstructing underlying Ising models, confirming its superior statistical properties. The application on the U.S. senators voting in the six congresses reveals that both the Republicans and Democrats noticeably assemble in each congress; interestingly, the assembling of Democrats is particularly pronounced in the latest congress.

In this paper, a Bayesian spatial voting model is applied for the first time to characterize the legislative behavior of the Senate of the Republic of Colombia for the period 2006-2010. The analysis is carried out based on the plenary nominal votes of the Senate. The estimation of the model is done using Markov Monte Carlo chain algorithms. The estimated ideal points provide empirical evidence supporting a latent non-ideological feature (opposition--non-opposition) underlying senators' voting. Additionally, the relationship between the parapolitics scandal and the legislative behavior of senators is analyzed through a logistic model, both Bayesian and frequentist. The results indicate a significant relationship between being or having been involved with the parapolitics scandal and the legislative behavior of the senators from the period 2006-2010.

Our question is ``What is the probability that at least three members of the senate share the same birthday?'' Before the pandemic, I asked this question in several popular math talks I gave at universities across the country. Inspired by ChatGPT's abysmal failure to answer the question, I have recently come back to this problem and now have a more satisfactory answer, thanks in no small part to what I learned form a page of Wolfram's Math World, which I located by a Google search.

We use instruction-tuned Large Language Models (LLMs) like GPT-4, Llama 3, MiXtral, or Aya to position political texts within policy and ideological spaces. We ask an LLM where a tweet or a sentence of a political text stands on the focal dimension and take the average of the LLM responses to position political actors such as US Senators, or longer texts such as UK party manifestos or EU policy speeches given in 10 different languages. The correlations between the position estimates obtained with the best LLMs and benchmarks based on text coding by experts, crowdworkers, or roll call votes exceed .90. This approach is generally more accurate than the positions obtained with supervised classifiers trained on large amounts of research data. Using instruction-tuned LLMs to position texts in policy and ideological spaces is fast, cost-efficient, reliable, and reproducible (in the case of open LLMs) even if the texts are short and written in different languages. We conclude with cautionary notes about the need for empirical validation.

In legislative redistricting, most states draw their House and Senate maps separately. Ohio and Wisconsin require that their Senate districts be made with a 3:1 nesting rule, i.e., out of triplets of adjacent House districts. We seek to study the impact of this requirement on redistricting, specifically on the number of seats won by a particular political party. We compare two ensembles generated using Markov Chain Monte Carlo methods; one which uses the ReCom chain to generate Senate maps without a nesting requirement, and the other which uses a chain that generates Senate maps with a 3:1 nesting requirement. We find that requiring a 3:1 nesting rule has minimal impact on the distribution of seats won. Moreover, we study the impact the chosen House map has on the distribution of nested Senate maps, and find that an extreme seat bias at the House level does not significantly impact the distribution of seats won at the Senate level.