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 with reviews (how much or little people are reading) is not a measure of summary quality.
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 ALL signals as independent, if the summary was to be modelled as independent
then reading actual reviews later causes double-counting or extreme belief swings. Here, because the
summary is modeled as a lossless binary compression over a finite evidence pool, opening reviews
simply exhausts the summary budget with learning requiring summary-consistent updating.
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.