Ask fewer questions. Show fewer products. Match better.
The solicit-then-suggest model (arXiv:2603.20972) formalizes what an AI shopping agent should do: ask m questions to refine its belief about what the customer wants, then recommend k products. The economics reveal a clean asymmetry.
Deepening the conversation (more questions) reduces expected mismatch proportionally to 1/m. Broadening the assortment (more recommendations) reduces it proportionally to k^{−2/d}, where d is the dimensionality of the product space. As the product space gets more complex — more features, more axes of variation — adding recommendations becomes exponentially less effective. Adding questions stays linear.
The optimal recommendation structure is a Voronoi partition of the belief space. Each recommended product “owns” a region of posterior uncertainty. The customer's revealed preferences place them in a region, and the product assigned to that region is the recommendation. For a single recommendation, the agent should equalize posterior uncertainty across dimensions — a “water-filling” rule that ensures no dimension of the product space is wildly uncertain relative to the others.
The structural insight is about the economics of information in high-dimensional spaces. When the product is simple (low d), breadth works: show many options and the customer will find what they want. When the product is complex (high d), breadth fails: the curse of dimensionality means each additional option covers exponentially less of the space. Depth — targeted questions that collapse the dimensions one by one — doesn't suffer from this curse.
This generalizes beyond shopping. Any system that must match a high-dimensional preference to a high-dimensional offering — job matching, content recommendation, medical treatment selection — faces the same asymmetry. Asking the right question is always more efficient than showing another option.