Compressed Truths: Finite-Slot AI Summaries and Costly Verification
Working Paper, July 2026
Core Takeaways:
Information Design & Search Theory
Separation Theorem (Exact Posteriors)
Finite-Slot Budget Constraint
Abstract & Research Summary
What I do
- Model a consumer who sees a truthful AI summary of a product's reviews and must decide whether reading the underlying reviews is still worth the effort.
- Key modeling choice: the summary and the reviews come from the same finite evidence pool — so each opened review is also information about what remains hidden.
- Prove exact results from this structure: how much a contradicting review should move beliefs (less than an independent signal, by a computable amount), when the summary is fully "spent," and which attributes still justify reading under a limited display.
Why it matters
- AI summaries are the first thing many consumers see; the open design question is when they can replace reading — the model answers precisely: only when hidden evidence can no longer change the decision.
- Showing the most-mentioned topics can be an arbitrarily poor guide to what users actually need to verify.
- A more informative summary can increase reading before decreasing it — so engagement is not a measure of summary quality. Each claim is a testable prediction, not a design opinion.
Interactive Appendix: Summary Content as Compression →
★★★★☆ 4.2 out of 5 stars
| All 10 cards below
come from this exact same pool
AI Summary: "Mostly positive — based on 10 reviews"
Summary Information Budget: 100% Active
(constraining remaining cards)
Requires 6 of 10 positives (
remaining)
This interactive simulation accompanies Theorem 2 (the Separation Theorem). Standard models treat AI summaries as independent signals, implying that reading actual reviews later causes double-counting or extreme belief swings. Here, because the summary is modeled as a lossless budget constraint over a finite evidence pool, opening reviews simply exhausts the summary budget without unearned volatility.
Click face-down cards one at a time to open reviews & update beliefs:
Costly Verification: In real life, reading every review takes time
and cognitive effort. A consumer stops reading and decides whether to buy as soon as they feel
confident enough. Watch how treating the summary as a compression shifts that exact
point where you stop reading!
Opened:
0 / 10
Posterior Quality Belief: P(Quality = Good | Evidence)
Initial
state
Step-by-Step Belief Path across Flips
Blue: Compression | Gray: Independent Signal | Dashed: No Summary
Remaining Evidence Pool (Unopened Cards)
Remaining Hidden Cards ()
At least (+) required
Before opening any cards, the summary guarantees that at least 6 of the 10 cards in the pool
are positive (+).
Click any card above to flip a review. Try finding a negative one — watch
what happens to the two belief lines. The blue line (this paper's model) will drop less than
the gray line (standard model). That gap is the paper's main prediction.
Figure 1: Post-Compression Verification Mechanism & Finite Evidence Pool (𝓡)
Exact replication of Figure 1 from the theoretical manuscript. The AI summary and any later opened
reviews are generated from the same finite evidence pool 𝓡. Observing the summary changes
both beliefs about product quality and what raw evidence remains hidden.