Legislative rebellions and impeachments in a neural network society

Inspired by studies of legislative-executive conflict in modern presidential democracies in South America, we present an agent-based statistical mechanics exploration of the collective, coordinated action of strategic political actors in the legislative chamber and the conditions that may result in premature changes in the executive officeholder, such as a president's impeachment or a motion of no confidence in a prime minister. The legislative actors are represented by information processing agents equipped with a neural network, and emit opinions about issues in the presidential agenda. We construct a Hamiltonian which is the sum of the costs for the agents to hold a specific set of political positions. We use replica methods for two types of disorder, in the space of weights and in the network of agents' interactions. We obtain the phase diagram of the model, where the control parameters may be loosely described as indices measuring the strategic legislative support, the presidential polling popularity and the volume of the presidential agenda under discussion. It shows an intermediate phase of coexistence of pro and con strategic behavior. This region is surrounded by pure phases where the strategic vote falls completely in the pro or con camps. Driven by external forces, the change of these indices may lead the system out of the coexistence region into the purely anti-executive phase, triggering a phase transition into a state opposing the executive leader and supporting their removal from office by constitutional means. We use data from Brazil, and show the presidential trajectories that led to impeachment or not during the democratic period which began in 1989. These trajectories ended in the region of the phase diagram in accordance to the president being removed or not from office.