  This article proposes a novel collective decision making scheme to solve the
multi-agent drift-diffusion-model problem with the help of spiking neural
networks. The exponential integrate-and-fire model is used here to capture the
individual dynamics of each agent in the system, and we name this new model as
Exponential Decision Making (EDM) model. We demonstrate analytically and
experimentally that the gating variable for instantaneous activation follows
Boltzmann probability distribution, and the collective system reaches
meta-stable critical states under the Markov chain premises. With mean field
analysis, we derive the global criticality from local dynamics and achieve a
power law distribution. Critical behavior of EDM exhibits the convergence
dynamics of Boltzmann distribution, and we conclude that the EDM model inherits
the property of self-organized criticality, that the system will eventually
evolve toward criticality.
