  We present a deliberation model where a group of individuals with
heterogeneous preferences iteratively forms expert committees whose members are
tasked with the updating of an exogenously given status quo change proposal.
Every individual holds some initial voting power that is represented by a
finite amount of indivisible units with some underlying value. Iterations
happen in three stages. In the first stage, everyone decides which units to
keep for themselves and where to distribute the rest. With every ownership
mutation, a unit's underlying value diminishes by some exogenously given
amount. In the second stage, the deliberative committee is formed by the
individuals with the most accumulated voting power. These experts can author
corrections to the proposal which are proportional to their accumulated power.
In the third stage, if an individual outside of the committee disagrees with a
correction, she can vote against it with their remaining voting power. A
correction is discarded if more than half of the total voting power outside of
the committee is against it. If either the committee or the proposal remain
unchanged for two consecutive iterations, the process stops. We show that this
will happen in finite time.
