  This paper studies the central planner's decision making on behalf of a group
of members with diverse discount rates. In the context of optimal stopping, we
work with a smooth aggregation preference to incorporate all heterogeneous
discount rates with an attitude function that reflects the aggregation rule in
the same spirit of ambiguity aversion in the smooth ambiguity preference
proposed in Klibanoff et al.(2005). The optimal stopping problem renders to be
time inconsistent, for which we develop an iterative approach using consistent
planning and characterize all time-consistent equilibria as fixed points of an
operator in the setting of one-dimensional diffusion processes. We provide some
sufficient conditions on both the underlying models and the attitude function
such that the smallest equilibrium attains the optimal equilibrium in which the
attitude function becomes equivalent to the linear aggregation rule as of
diversity neutral. In addition, we show that the optimal equilibrium is a weak
equilibrium in the existing literature. When the sufficient condition of the
attitude function is violated, we can illustrate by various examples that the
characterization of the optimal equilibrium may differ significantly from some
existing results for an individual agent.
