Heuristics and optimal solutions to the breadth-depth dilemma

Area of Science:

• Cognitive Science
• Decision Science
• Behavioral Economics

Background:

• Multialternative risky choice involves allocating limited information-gathering capacity across options.
• A fundamental trade-off exists between breadth (sampling many options) and depth (sampling fewer options extensively).
• Optimal strategies for this breadth-depth trade-off in decision-making remain underexplored, despite relevance to foraging and daily choices.

Purpose of the Study:

• To formalize the breadth-depth dilemma in information gathering under bounded capacity.
• To determine the optimal strategy for allocating limited information-gathering resources across multiple alternatives.
• To identify conditions under which breadth or depth sampling is more effective.

Main Methods:

• Development of a finite-sample capacity model to represent the breadth-depth trade-off.
• Mathematical analysis of the model to derive optimal sampling strategies.
• Simulation and theoretical investigation of decision-making under varying capacity constraints.

Main Results:

• For small capacities (approximately 10 samples), optimal strategy favors breadth, sampling each alternative once.
• For larger capacities, a transition occurs, making deep sampling of a few alternatives optimal.
• The number of deeply sampled alternatives decreases with the square root of capacity, indicating a focus on a small subset.

Conclusions:

• Optimal information gathering in multialternative choice is capacity-dependent.
• Ignoring a majority of options can be a signature of optimal behavior, especially with larger information-gathering capacities.
• The findings offer heuristics for metareasoning in complex decisions with limited resources.