  In this paper we discuss the problems of modern representative democracy and
we look at the selection of legislators by lot as a way to tame some of the
drawbacks of that system. It is recalled at the beginning that resorting to
sortition for the selection of public officers used to be a popular way of
taming factionalism in public affairs. Factionalism is assumed to be
detrimental to public affairs as public officers may favour their own faction
(a tribe or a party) instead of pursuing the general interest. Moreover they
tend to overinvest in strengthening their power, thus engaging in power
struggles with opposing factions, unlikely to benefit society. In this respect
we present a new mathematical model aiming at describing a more efficient
parliament where sortition is brought to bear. It will be shown that starting
from a parliament working with two parties (or coalitions), where the costs of
representative democracy are quite apparent through the detrimental effects of
party discipline, one can beneficially move towards a parliament where
independent legislators, randomly selected from the population of constituents,
sit alongside elected members who belong to a party and are subjected to party
discipline. The paper shows that increasing the number of independent
legislators up to a point enhances the efficiency of the parliament and puts
into check the factionalism likely to arise from party discipline.
