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In the process of collective decision-making, many individual components exchange and process information until reaching a well-defined consensus state. Existing theory suggests two phases to this process. In the first, individual components are relatively free to wander between decision states, remaining highly sensitive to perturbations; in the second, feedback between components brings all or most of the collective to consensus. Here, we extend an existing model of collective neural decision-making by allowing connection strengths between neurons to vary, moving toward a more realistic representation of the large variance in the behavior of groups of neurons. We show that the collective dynamics of such a system can be tuned with just two parameters to be qualitatively similar to a simpler, homogeneous case, developing tools for locating a pitchfork bifurcation that can support both phases of decision-making. We also demonstrate that collective effects cause large and long-lived sensitivity to decision input at the transition, which connects to the concept of phase transitions in statistical physics. We anticipate that this theoretical framework will be useful in building more realistic neuronal-level models for decision-making.

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