Best-of-N Collective Decisions on a Hierarchy

The best-of-N problem in collective decision making is complex especially when the number of available alternatives is larger than a few, and no alternative distinctly shines over the others. Additionally, if the quality of the available alternatives is not a priori known and noisy, errors in the quality estimation may lead to the premature selection of sub-optimal alternatives. A typical speed-accuracy trade-off must be faced, which is hardened by the presence of several alternatives to be analyzed in parallel. In this study, we transform a one-shot best-of-N decision problem in a sequence of simpler decisions between a small number of alternatives, by organizing the decision problem in a hierarchy of choices. To this end, we construct an m-ary tree where the leaves represent the available alternatives, and high-level nodes group the low-level ones to present a low-dimension decision problem. Results from multi-agent simulations in both a fully-connected topology and in a spatial decision problem demonstrate that the sequential collective decisions can be parameterized to maximize speed and accuracy against different decision problems. A further improvement relies on an adaptive approach that automatically tunes the system parameters.