  There is a paradox in the model of social dynamics determined by voting in a
stochastic environment (the ViSE model) called "pit of losses." It consists in
the fact that a series of democratic decisions may systematically lead the
society to the states unacceptable for all the voters. The paper examines how
this paradox can be neutralized by the presence in society of a group that
votes for its benefit and can regulate the threshold of its claims. We obtain
and analyze analytical results characterizing the welfare of the whole society,
the group, and the other participants as functions of the said claims
threshold.
