How do you know you won't like it if you've (never) tried it? Preference discovery and data design

1. Problem Statement

The paper addresses a fundamental gap in the literature on consumer learning: how the structure of consumption data, designed by firms or platforms, influences the speed and accuracy of preference discovery.

While traditional models assume consumers learn preferences through independent experience, real-world consumption is often structured via bundling (e.g., product bundles, streaming playlists, policy reforms). The authors argue that the sequence and composition of these experiences create a specific covariance structure in the data. This structure dictates how "utility surprises" (the difference between expected and realized utility) propagate across goods, potentially accelerating learning, slowing it down, or amplifying biases. The core question is: How can a provider design exposure to manipulate the consumer's belief dynamics, and what are the welfare implications?

2. Methodology and Model Framework

The Consumer Learning Model

• Setup: A consumer (she) has linear preferences over a set of $n$ goods, represented by a true vector $\beta$. She does not know $\beta$ and faces taste uncertainty.
• Experience: At each time $t$, a provider (he) offers a bundle $x_t \in \mathbb{R}^n$. The consumer realizes utility $u_t = \alpha + x_t'\beta + \varepsilon_t$, where $\varepsilon_t$ is noise.
• Estimation: The consumer updates her estimate $\hat{\beta}_t$ using Ordinary Least Squares (OLS) on the history of bundles $X_t$ and utilities $u_t$.
• Key Object: The Information Matrix $Z_t = X_t'X_t$ (the co-occurrence matrix) and its inverse, the Variance-Covariance Matrix $W_t = Z_t^{-1}$.
  • $Z_t$ captures how often goods are consumed together.
  • $W_t$ captures the uncertainty and the correlation externalities: how learning about one good affects the estimate of another.

The Updating Mechanism

The consumer updates beliefs based on the consumption surprise $\Delta u_t = u_t - x_t'\hat{\beta}_{t-1}$.
The update rule is:
$$\hat{\beta}_t = \hat{\beta}_{t-1} + \omega_t W_{t-1} x_t \Delta u_t$$
Crucially, the matrix $W_{t-1}$ acts as a propagation mechanism. A surprise in one bundle affects the estimated values of all goods connected in the co-occurrence network, not just those in the bundle. This creates informational externalities.

The Provider's Role

The provider chooses the sequence of bundles $x_t$ to influence the consumer's learning path. The provider may have objectives such as maximizing current profits, sustaining biased demand, or accelerating the discovery of undervalued products.

3. Key Contributions

1. Data-Design Framework: The paper introduces "data design" as a distinct mechanism from signal design (persuasion). Instead of choosing a signal, the provider chooses the structure of experiences (bundles), which determines the correlation structure of the data driving belief updates.
2. Spectral Analysis of Learning: The authors utilize spectral graph theory to characterize learning dynamics. They show that the speed of learning is governed by the condition number ($\kappa_t = \lambda_{max}/\lambda_{min}$) of the information matrix $Z_t$.
3. Correlation Externalities: They formalize how bundling creates "correlated externalities," where a positive surprise for an underestimated good can inadvertently increase the estimated value of an already overestimated good if they are positively correlated in the data.
4. Robust vs. Targeted Strategies: The paper distinguishes between strategies that require knowledge of the consumer's current bias (targeted) and those that rely only on the geometry of past data (robust).

4. Key Results

A. Local Dynamics: Bias-Targeted Bundling

• Halting Learning: If a provider offers a bundle $x_t$ orthogonal to the current estimation error vector ($\Delta \beta_t$), the expected consumption surprise is zero. The consumer receives no new information, and beliefs remain frozen ($E[\hat{\beta}_{t+1}] = \hat{\beta}_t$). This allows a firm to monetize current misperceptions without correcting them.
• Amplifying Bias: Bundles can be designed such that a positive surprise for an underestimated good also increases the estimated value of an overestimated good (if they are positively correlated). This can "lock in" biases.

B. Long-Run Dynamics: Speed of Learning

• Fastest Learning: Single-good exposure (isolating goods) minimizes the Mean Squared Error (MSE) and maximizes learning speed because it eliminates cross-covariance.
• Slowest Learning: Bundles that reinforce existing correlations slow learning.
• Spectral Strategies (Robust Design): Even without knowing the consumer's true preferences or current errors, a provider can control learning speed using the eigenvectors of $Z_t$:
  • Popularity-Biased Bundles ($v^N_t$): Aligning bundles with the leading eigenvector (eigenvector centrality) of the co-occurrence network reinforces the most frequent consumption patterns. This maximizes the condition number, increases redundancy, and slows learning (traps consumers in correlated environments).
  • Correlation-Breaking Bundles ($v^C_t$): Aligning bundles with the correlation centrality vector (associated with the smallest eigenvalue) introduces variation in the least explored direction. This minimizes the condition number and accelerates learning.

C. Monopolistic Application

• Complete Information: If the monopolist knows the consumer's bias, they can choose between "Manipulation Bundles" (to preserve a favored but overvalued product) or "Discovery Bundles" (to accelerate the valuation of a truly profitable but undervalued product).
• Incomplete Information: If the monopolist does not know the bias but has a prior on the consumer's surprise:
  • Pessimistic Priors: The monopolist prefers Popularity Bias ($v^N$) to minimize the risk of negative surprises and maintain stable demand.
  • Optimistic Priors: The monopolist prefers Correlation-Breaking ($v^C$) to accelerate discovery and capture future profits from undervalued goods.

D. Welfare Implications

• Decomposition: Welfare changes are decomposed into a Price Effect (pure transfer) and a Bundle Effect (allocative distortion).
• Result: Misguided data design leads to allocative inefficiencies. Even if prices are optimal for the monopolist's perceived preferences, the resulting bundle selection may deviate from the true welfare-maximizing allocation. In some cases, both consumer surplus and profits can decrease simultaneously due to the distortion in the bundle effect.

5. Significance and Policy Implications

• Mechanism for Platform Power: The paper provides a micro-foundation for why dominant platforms (e.g., Netflix, Amazon) sustain biased demand. By algorithmically recommending "Top 10" or "Trending" items (Popularity Bias), they reinforce the leading eigenvector of the consumption network, slowing the discovery of diverse or high-quality alternatives.
• Regulatory Insight: Effective regulation may need to intervene on the structure of exposure rather than just prices or market shares. Policies could mandate "correlation-breaking" variations in algorithms (e.g., requiring diversity in recommendations) to accelerate preference discovery and reduce allocative inefficiencies.
• Beyond Price Discrimination: The paper redefines bundling. It is not just a tool for price discrimination or entry deterrence; it is a tool for information design that shapes the very data consumers use to learn what they value.

6. Empirical Illustration

The authors apply the model to a dataset of IMDb movies and actors.

• Network: Actors are nodes; co-starring in a movie creates edges.
• Findings: The "Popularity Bias" vector ($v^N$) highlights actors in major franchises (e.g., Star Trek, X-Men). The "Correlation-Breaking" vector ($v^C$) splits actors into groups with opposing signs (e.g., separating Star Trek actors from X-Men actors), effectively breaking the dominant correlation structure.
• Dynamic Updates: The simulation shows how a surprise in one movie (e.g., Thor: Ragnarok) updates the estimated value of actors not in that movie but connected in the network, demonstrating the propagation of information through the co-occurrence structure.

Conclusion

The paper establishes that preference discovery is a function of data geometry. By designing the covariance structure of consumption experiences, providers can strategically control the speed and direction of learning. This creates a tension between discovery (which improves welfare) and control (which preserves market power), suggesting that data design is a critical frontier for competition policy.