  Collective estimation is a variant of collective decision-making, where
agents need to achieve consensus on a continuous quantity in a self-organized
fashion via social interactions. A particularly challenging scenario is a fully
distributed collective estimation with strongly constrained, dynamical
interaction networks, for example, encountered in real physical space.
Collectives face several challenges in achieving precise estimation consensus,
particularly due to complex behaviors emerging from the simultaneous evolution
of the agents' opinions and the interaction network.While homophilic networks
may facilitate collective estimation in well-connected networks, we show that
disproportionate interactions with like-minded neighbors lead to the emergence
of echo chambers, preventing collective consensus. Our agent-based simulation
results confirm that, besides a lack of exposure to attitude-challenging
opinions, seeking reaffirming information entraps agents in echo chambers. In a
potential solution, agents can break free from the pull of echo chambers. We
suggest an additional state where stubborn mobile agents (called Messengers)
carry data and connect the disconnected clusters by physically transporting
their opinions to other clusters to inform and direct the other agents.
However, an agent requires a switching mechanism to determine which state to
adopt. We propose a generic, novel approach based on a Dichotomous Markov
Process (DMP). We show that a wide range of collective behaviors arise from the
DMP. We study a continuum between task specialization with no switching
(full-time Messengers), generalization with slow switching (part-time
Messengers), and rapid task switching (short-time Messengers). Our results show
that stubborn agents can, in various ways, help the collective escape local
minima, break the echo chambers, and promote consensus in collective opinion
dynamics.
