  The tradeoff between accuracy and speed is considered fundamental to
individual and collective decision-making. In this paper, we focus on
collective estimation as an example of collective decision-making. The task is
to estimate the average scalar intensity of a desired feature in the
environment. The solution we propose consists of exploration and exploitation
phases, where the switching time is a factor dictating the balance between the
two phases. By decomposing the total accuracy into bias and variance, we
explain that diversity and social interactions could promote the accuracy of
the collective decision. We also show how the exploration-vs-exploitation
tradeoff relates to the speed-vs-accuracy tradeoff. One significant finding of
our work is that there is an optimal duration for exploration to compromise
between speed and accuracy. This duration cannot be determined offline for an
unknown environment. Hence, we propose an adaptive, distributed mechanism
enabling individual agents to decide in a decentralized manner when to switch.
Moreover, the spatial consequence of the exploitation phase is an emergent
collective movement, leading to the aggregation of the collective at the
iso-contours of the mean intensity of the environmental field in the spatial
domain. Examples of potential applications for such a fully distributed
collective estimation model are spillage capturing and source localization.
