GPT 6 Astra Ultra attempt on Econ-644

AI-generated marketplace summaries Information value and interference in marketplace summary experiments

Policy, cohort, and welfare target

The target is the six-month consumer-welfare effect of a specified AI-summary policy, including users who do not buy. Fix eligibility before the summary is displayed, and retain everyone in that cohort. Freeze the model version, prompt, review cutoff, and refresh rule. For user $i$, let $Y_i$ be independently assessed money-valued satisfaction less price and search cost, including returns and disappointing purchases. The no-purchase alternative has zero gross consumption value and price but still incurs any search cost. This attempt establishes a rational-information benchmark, an explicit failure example, and an estimator under an interference model. It does not determine the actual six-month effect or seller response.

A benchmark in which optional summaries cannot reduce welfare

Consider a fixed review corpus, fixed offers, a finite state space $\Omega$, a finite action set including no purchase, and utility $u(a,\omega)$. Let $R$ denote the complete review information and let a summary $S$ be produced by a stochastic kernel depending only on $R$. With correct beliefs and no processing costs, write \[ V(R)={\mathbb{E}}\max_a{\mathbb{E}}[u(a,\omega)\mid R],\qquad V(S)={\mathbb{E}}\max_a{\mathbb{E}}[u(a,\omega)\mid S]. \] Since $\omega,R,S$ form a Markov chain, conditional averaging implies \[ V(R)\ge V(S). \tag{1} \] To prove this, choose an $S$-optimal action for each signal. An observer of $R$ can simulate $S$ from its known kernel and take that action. This achieves $V(S)$, while choosing an optimal action given $R$ does at least as well. Equivalently, apply convexity of the maximum to posterior expected utilities. The summary need not add statistical information to add value when acquiring or interpreting the underlying reviews is costly.

A stronger conclusion applies to the catalogue's optional-access design. Let $\mathcal P_0$ be the feasible information-acquisition and action policies under the old interface, with their full search costs. If every old policy remains available at the same cost after summaries are added, then $\mathcal P_0\subseteq\mathcal P_1$, so \[ \sup_{\pi\in\mathcal P_1}{\mathbb{E}}[u(\pi,\omega)-c(\pi)] \ge\sup_{\pi\in\mathcal P_0}{\mathbb{E}}[u(\pi,\omega)-c(\pi)]. \tag{2} \] No informational ordering between summaries is needed for (2). Its proof is set inclusion, and its assumptions are demanding: correct decision models, free ability to ignore summaries, unchanged old-interface costs, and no price or seller-quality response. Keeping a link to all reviews does not establish those behavioral and institutional conditions.

A checked negative-welfare example

Let product quality be high with probability $1/4$ and low otherwise. Gross values are three and zero, and the price is one, giving purchase surpluses two and minus one. A full review perfectly reveals quality and costs $0.1$ to read. Under the control interface, reading and buying only high-quality products gives expected welfare \[ (1/4)2-0.1=0.4, \] which exceeds both no search/no purchase, with payoff zero, and uninformed purchase, with payoff $-0.25$. The optimal purchase rate is $1/4$.

Suppose a misleading summary causes consumers to believe both that the high-quality probability is $0.8$ and that the full review contains no information beyond the summary. Their perceived immediate purchase surplus is $0.8(2)+0.2(-1)=1.4$. Under these stated beliefs, further inspection leaves that perceived surplus unchanged and adds cost $0.1$, so buying immediately is subjectively optimal. Actual mean welfare becomes \[ (1/4)2+(3/4)(-1)=-0.25, \] a decrease of $0.65$, while purchases rise from $1/4$ to one. Full reviews remain available throughout. This example intentionally violates correct beliefs in (2), through both quality beliefs and beliefs about incremental information. It shows why greater conversion and nominal review access are insufficient welfare evidence. It does not claim that all AI summaries produce these errors.

The control cohort's nonbuyers have paid the review cost. Dropping them would replace $0.4$ by a selected purchaser average and conceal the proper policy comparison. Audits should therefore measure omitted adverse information and consumer interpretation as well as literal falsehoods. A technically true summary can change beliefs about what further search would reveal.

A design-based result allowing cross-cluster exposure

Let clusters $j=1,\ldots,J$ be independently assigned $Z_j\sim \operatorname{Bernoulli}(p)$, with $0<p<1$. For each baseline user fix a nonempty set $N_i$ of potentially relevant clusters before assignment. Assume the six-month potential outcome is $Y_i(z_{N_i})$: all interference relevant to that user is confined to this set. Define \[ E_i^1=\{Z_j=1\ \forall j\in N_i\},\quad E_i^0=\{Z_j=0\ \forall j\in N_i\}, \] with probabilities $\pi_i^1=p^{|N_i|}$ and $\pi_i^0=(1-p)^{|N_i|}$. The finite-cohort contrast between full exposure to summaries and no exposure is \[ \tau_N=\frac1n\sum_i[Y_i(\mathbf1_{N_i})-Y_i(\mathbf0_{N_i})]. \] Then the Horvitz--Thompson estimator \[ \widehat\tau_N=\frac1n\sum_i\left\{ \frac{\mathbf1(E_i^1)Y_i^{\rm obs}}{\pi_i^1} -\frac{\mathbf1(E_i^0)Y_i^{\rm obs}}{\pi_i^0}\right\} \tag{3} \] is unbiased. On $E_i^a$, consistency and the exposure restriction make the observed outcome equal the corresponding fixed potential outcome; taking expectations cancels the exposure probability in each summand. No independence between users is needed for this expectation calculation.

Exposure overlap can nevertheless make precision poor. Under the extra bound $|Y_i(z)|\le B$, define \[ c_j=\frac{B}{n}\sum_{i:j\in N_i} \left(\frac1{\pi_i^1}+\frac1{\pi_i^0}\right). \] Changing one assignment $Z_j$ can change only summands for users with $j\in N_i$. Each such summand, before division by $n$, takes one of the three values $Y_i(\mathbf1)/\pi_i^1$, zero, or $-Y_i(\mathbf0)/\pi_i^0$; their pairwise distances are bounded by the quantity defining $c_j$. Bounded differences for independent cluster assignments therefore gives \[ {\mathbb{P}}(|\widehat\tau_N-\tau_N|\ge t) \le2\exp\left(-\frac{2t^2}{\sum_jc_j^2}\right). \tag{4} \] This is conservative but fully design-based under the stated assumptions. For one cluster per user, weights are ordinary inverse assignment probabilities. For users linked to many clusters, the exponential growth of inverse exposure probabilities explains why more observations may still leave little useful precision.

The set $N_i$ must include potential exposure routes, not merely products a user actually viewed after treatment. Summary-induced search can change those realized sets. Selecting $N_i$ after observing views would invalidate the assignment-probability calculation and could condition on a treatment mediator. Likewise, market-wide prices or sellers influenced by clusters outside $N_i$ invalidate the assumed outcome mapping.

What remains for the original problem

A frozen-corpus trial estimates a direct interface effect only under its fixed offers and review supply. A market-level six-month trial can include seller adaptation, review manipulation, and changing availability, but its assignment unit must encompass the relevant feedback. One cannot transfer (3) to that ecosystem without expanding its exposure sets or defending a new interference restriction. Broad exposure sets may make (4) vacuous; that is an identification-and-design limitation, not a reason to silently assume individual randomization.

Farronato's 2025 conference paper, Section 1.1, explicitly identifies AI aggregation of textual reviews as a research direction and discusses average/distributional effects and interference. That source motivates this problem; it does not supply the welfare sign. Equations (1)--(4) are restricted decision-theoretic and randomization calculations. Actual monetary satisfaction, search costs, misleading omissions, group heterogeneity, and seller adaptation remain to be measured under a specified policy. The original empirical welfare question is unresolved.

Completion Estimate

40%

This is a post hoc, heuristic estimate for the full catalogue target. The attempt proves optional-information welfare benchmarks, constructs a misleading-summary welfare loss and gives unbiased full-exposure estimation with design-based interference bounds. Actual immediate and six-month group welfare, factual omissions and seller or review adaptation still require measured outcomes and exposure designs spanning the relevant marketplace feedback.

References

• [f] Chiara Farronato (2025), Digital Platforms as Information Aggregators: Implications for their Design and Regulation, conference-paper version, Section 1.1. https://conference.nber.org/confer/2025/DTs25/farronato.pdf.