In multialternative risky choice, we are often faced with the opportunity to allocate our limited information-gathering capacity between several options before receiving feedback. In such cases, we face a natural trade-off between breadth—spreading our capacity across many options—and depth—gaining more information about a smaller number of options. Despite its broad relevance to daily life, including in many naturalistic foraging situations, the optimal strategy in the breadth–depth trade-off has not been delineated. Here, we formalize the breadth–depth dilemma through a finite-sample capacity model. We find that, if capacity is small (∼10 samples), it is optimal to draw one sample per alternative, favoring breadth. However, for larger capacities, a sharp transition is observed, and it becomes best to deeply sample a very small fraction of alternatives, which roughly decreases with the square root of capacity. Thus, ignoring most options, even when capacity is large enough to shallowly sample all of them, is a signature of optimal behavior. Our results also provide a rich casuistic for metareasoning in multialternative decisions with bounded capacity using close-to-optimal heuristics.

在多重选择的风险选择中，我们经常面临着在收到反馈之前在几个选项之间分配我们有限的信息收集能力的机会。在这种情况下，我们面临着广度（将我们的能力扩展到许多选项）和深度（获得有关较少数量的选项的更多信息）之间的自然权衡。尽管它与日常生活广泛相关，包括在许多自然觅食情况下，但广度与深度权衡的最佳策略尚未被描绘出来。在这里，我们通过有限样本容量模型形式化了广度-深度困境。我们发现，如果容量较小（∼10 个样本），则最佳方案是每个备选方案抽取一个样本，从而有利于广度。然而，对于较大的容量，会观察到急剧的转变，并且最好对一小部分替代品进行深度采样，该比例大致随容量的平方根而减小。因此，忽略大多数选项，即使容量足够大，可以对所有选项进行浅层采样，也是最佳行为的标志。我们的结果还为使用接近最优启发式的有限容量的多元决策中的元推理提供了丰富的推理。