Explorando la política: una visión con complejos simpliciales.

Abstract

Simplicial complexes, as a particular example of a topological space, offer a different perspective for understanding the dynamics within political and social structures. These complexes are mathematical constructions that represent sets of elements called simplices, which can be used to model relationships between actors such as political parties, legislators, or voters. By applying the theory of simplicial complexes, contemporary political dynamics can be understood and represented, thus providing a mathematical alternative for their representation. In this work, we represent a political structure composed of five electoral candidates for the 2023 Mayor of Bogotá, evaluating them in four areas of interest (Gender, Transportation, Health, and Education) through natural language processing focused on text analysis and mining. Using this approach, we construct simplicial complexes through the Vietoris-Rips method, generating a mathematical representation that allows us to analyze the relationships between government plans and the potential for collaboration among agents within these political structures. In doing so, we propose a method for constructing simplicial complexes that complements existing methodologies, such that the constructed complexes can explain the interactions between different political structures.