Geometric vulnerability of democratic institutions against lobbying: a sociophysics approach

Abstract

An alternative voting scheme is proposed to fill the democratic gap between a president elected democratically via universal suffrage (deterministic outcome, the actual majority decides), and a president elected by one person randomly selected from the population (probabilistic outcome depending on respective supports). Moving from one voting agent to a group of r randomly selected voting agents reduces the probabilistic character of the outcome. Building r such groups, each one electing its president, to constitute a group of the groups with the r local presidents electing a higher-level president, does reduce further the outcome probabilistic aspect. Repeating the process n times leads to a n-level bottom-up pyramidal structure. The hierarchy top president is still elected with a probability but the distance from a deterministic outcome reduces quickly with increasing n. At a critical value n_{c,r} the outcome turns deterministic recovering the same result a universal suffrage would yield. The scheme yields several social advantages like the distribution of local power to the competing minority making the structure more resilient, yet preserving the presidency allocation to the actual majority. An area is produced around fifty percent for which the president is elected with an almost equiprobability slightly biased in favor of the actual majority. However, our results reveal the existence of a severe geometric vulnerability to lobbying. A tiny lobbying group is able to kill the democratic balance by seizing the presidency democratically. It is sufficient to complete a correlated distribution of a few agents at the hierarchy bottom. Moreover, at the present stage, identifying an actual killing distribution is not feasible, which sheds a disturbing light on the devastating effect geometric lobbying can have on democratic hierarchical institutions.