Statistical mechanical model in legislative networks

Abstract

Looking for ways to quantify political polarization on parliaments, we have built a statistical mechanics model for the specific case of a legislative networks from roll-call votes. For this we have considered a network of legislators that is fully connected and whose links have assigned values of 1 or -1 accordingly if a pair representatives have vote the same or not. Then, we have taken links a triangles in the networks as spins, and from there we developed a mathematical formalism which led us to derive expression for magnetizations, entropies, energy and temperature for the system.

En busca de cuantificar la polarizaci´on pol´ıtica en parlamentos, hemos construido un modelo de mec´anica estad´ıstica para el caso espec´ıfico de una red legislativa creada a partir de votos en sala. Para esto hemos considerado una red the parlamentarios completamente conectada, a cuyas conexiones se les han asignado los valores de 1 o -1 seg´un cada par de parlamentarios vot´o lo mismo o no. Luego, he considerado las conexiones y tri´angulos presentes en la red como espines, y a partir de esto hemos elaborado un formalismo matem´atico que nos condujo a obtener expresiones para magnetizaciones, entropies, energ´ıa y temperatura del sistema.