Title: 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.