  In this article, we analyse a two-tier voting system in which the overall
population is split into several different groups and the democracy deficit,
the expected quadratic deviation of the council vote from the referendum
involving the entire population. The proposals voted on fall in the category of
yes/no voting. The voting behaviour is described by a probabilistic model in
which there is a central influence or bias that affects the voters' decision.
We study different versions of the model and the correlation between voters
belonging to different groups is allowed to be weaker than within groups. The
two main questions we analyse are the asymptotic behaviour of the (normalised)
democracy deficit and the optimal voting weights the groups receive in the
council vote chosen to minimise the democracy deficit.
