📈 economics

Selective Peer Disclosure and Reputational Forecasting

This paper demonstrates that in a setting where career-concerned experts can observe peers' locked forecasts, a unique classification-optimal policy exists within the reveal-or-silence class that selectively discloses approximately 71% of agreements while never revealing disagreements, thereby maximizing forecast accuracy by eliminating low-type inertia more effectively than full disclosure or complete concealment.

Original authors: Georgy Lukyanov

Published 2026-07-21

📖 7 min read🧠 Deep dive

CC BY 4.0

Original authors: Georgy Lukyanov

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

The Science of Secrets and Second Guesses

Imagine you are trying to solve a mystery, but you have a team of detectives. In the world of economics and decision-making, this is often how organizations work: they hire experts to predict the future, like a bank asking analysts to guess if a company will succeed, or a hospital asking doctors to diagnose a patient. But here is the tricky part: experts care deeply about their reputations. If they look smart, they get hired; if they look foolish, they get fired. This is called "career concern."

Usually, we think that if experts can talk to each other, they will share all their clues and get the best answer. But sometimes, sharing too much information can backfire. If an expert knows exactly what their partner thinks, they might be afraid to change their own mind, even if they get new evidence, because they don't want to look like they were wrong before. This paper explores a fascinating middle ground: What happens if a boss (or a "platform") controls when and if experts see each other's work? It turns out that sometimes, hiding information on purpose—specifically, hiding it in a random, unpredictable way—can actually make the final prediction more accurate. It's a bit like a coach deciding whether to show a player the opponent's playbook: showing it all the time might make the player freeze up, but showing it never might leave them guessing. This paper asks: Is there a perfect "secret recipe" for sharing just enough to keep everyone sharp?

The Game of Locked Forecasts

Let's dive into the story the paper tells. Imagine two experts, let's call them Alex and Blake, working for a big organization. They both have a job to do: predict whether a hidden state is "0" or "1" (think of it as guessing if a coin will land on Heads or Tails, but they have special glasses that give them clues).

Here is the game they play:

The First Move: Both Alex and Blake get a private clue and write down their first guess. They "lock" these guesses in a digital safe. No one can see them yet.
The Second Move: Blake gets a new clue. Before Blake writes their final answer, the organization (the "platform") decides whether to show Blake what Alex wrote.
The Twist: The platform doesn't just say "Yes" or "No." It follows a strict rule it promised in advance. Sometimes, if Alex and Blake agreed, the platform shows the note. Sometimes, if they disagreed, it shows the note. But here is the secret sauce: the platform can also choose to randomly stay silent. It can hide the note even when they agreed, or even when they disagreed.

The goal of the platform is to get the most accurate final prediction possible. But the experts are playing their own game: they want to look smart to the "evaluator" who will judge them later.

The Problem with Being Too Honest (or Too Silent)

The paper finds that there are two bad extremes.

The "Sealing" Extreme: If the platform never shows Blake Alex's note, Blake is flying blind. Blake might stick with their first guess even if the new clue says otherwise, just to avoid looking inconsistent. This is called "inertia."
The "Full Disclosure" Extreme: If the platform always shows Blake Alex's note, Blake knows exactly what Alex thinks. If Alex and Blake disagree, Blake knows Alex thinks the opposite. If Blake changes their mind, they look like they are just copying Alex or admitting they were wrong. This pressure can make Blake stick to their old, wrong guess just to save face.

The paper argues that the solution isn't to pick one of these extremes. Instead, the best strategy is a randomized mix of silence and revelation.

The "Disciplinary Silence" Discovery

The authors discovered a specific, somewhat surprising rule that works best in their model. They call it "Disciplinary Silence."

Here is how it works in plain English:

Never reveal a disagreement: If Alex and Blake have different locked guesses, the platform never tells Blake what Alex wrote. This keeps the "disagreement" pool mysterious.
Randomly reveal agreements: If Alex and Blake have the same locked guess, the platform flips a coin. About 71.08% of the time, it shows Blake the note. The other 28.92% of the time, it stays silent.

Why does this work?
When the platform stays silent, Blake has to guess: "Did Alex agree with me, or did Alex disagree?"

If they did agree, and the platform stayed silent, Blake knows the platform is hiding a "good" match.
If they disagreed, and the platform stayed silent, Blake knows the platform is hiding a "bad" match.

By revealing some agreements but hiding all disagreements, the platform makes "silence" feel like a bad sign. It becomes a "disciplinary" tool. If Blake gets a new clue that contradicts their first guess, and the platform stays silent, Blake thinks, "Oh no, maybe Alex actually disagreed with me, and the platform is hiding it! I better change my mind to be safe."

This fear of being "caught" in a bad spot forces the less confident expert (the "low type") to actually listen to their new clues, rather than stubbornly sticking to their old guess.

The Numbers and the Results

The paper uses a computer to check this idea with very specific, exact numbers (rational fractions, not just estimates). They found that this "Disciplinary Silence" rule is the unique best strategy for their specific setup.

The Magic Number: The platform should reveal agreements about 71.08% of the time.
The Gain: This rule improves the accuracy of the final prediction by about 1.37 percentage points compared to never showing anything (sealing).
The Comparison: It also improves accuracy by 0.30 percentage points compared to showing everything (full disclosure).

While these numbers might seem small, in the world of high-stakes forecasting, they are significant. The paper proves that this specific mix of hiding and showing is mathematically the best way to get the experts to do their jobs right.

What the Paper Rules Out

It is important to note what this paper says doesn't work.

Deterministic Rules Don't Work: You can't just say "We will only show notes when they agree" or "We will only show notes when they disagree." If you do that, the experts can figure out the pattern. If you only show agreements, silence automatically means "disagreement," so the experts know the answer anyway. The paper shows that randomization is essential. You must be unpredictable to make the silence informative.
No "One Size Fits All": The paper also warns that this specific 71% rule depends on the exact details of the experts' skills and the type of decision being made. If the goal changes (for example, if the experts are trying to make a different kind of choice), the perfect rule might change too. The "best" policy depends on what you are trying to achieve.

The Bottom Line

This paper tells us that in a world where experts care about their reputations, hiding information can be a powerful tool for truth. By carefully controlling when experts see each other's work—specifically by hiding disagreements and randomly hiding some agreements—a boss can create an environment where experts are forced to think critically and update their beliefs, rather than just stubbornly sticking to their first guess to look consistent. It's a counter-intuitive lesson: sometimes, to get the full picture, you have to leave a few pieces of the puzzle hidden.

Technical Summary: Selective Peer Disclosure and Reputational Forecasting

Problem Statement
The paper investigates the optimal design of feedback mechanisms in organizations where experts provide forecasts. Specifically, it addresses a setting where two career-concerned experts (A and B) lodge initial, locked binary forecasts regarding a fixed state. After these initial reports are submitted, a platform commits to a stochastic rule determining whether Expert B observes Expert A's locked report before submitting a final, terminal forecast. Expert A receives no peer feedback. The platform's objective is to maximize the accuracy of the public information available to a downstream decision maker, subject to the strategic incentives of the experts, who seek to maximize their posterior reputation (probability of being perceived as high-ability) after the state is revealed.

The core tension lies in the trade-off between information aggregation and reputational incentives. While revealing peer reports provides information, it also alters the reputational incentives for the receiving expert (B). If B observes agreement, she may be incentivized to stick to her initial forecast to appear consistent; if she observes disagreement, she may revise. However, the paper notes that deterministic disclosure rules (e.g., revealing only agreements or only disagreements) are not truly selective in a binary setting, as the receiver can infer the hidden report. Genuine selectivity requires randomization (silence), which pools agreement and disagreement cases.

Methodology
The analysis employs a game-theoretic framework with the following structure:

Environment: Two experts with private types (High or Low ability) and private binary signals. The state is binary with a symmetric prior.
Timing: Experts lodge initial reports simultaneously. Expert B receives a second signal and a message from the platform (revealing A's report or silence). Both submit terminal reports. A downstream decision maker acts, and an evaluator updates beliefs about expert ability.
Equilibrium Concept: The paper acknowledges that the unrestricted game admits a "babbling" equilibrium (where reports are uninformative) for any policy, rendering strict policy ranking impossible without selection. Consequently, the analysis conditions on a regular-monotone sequential equilibrium. This selection requires:
- Truthful reporting of initial signals.
- High-ability types following new conflicting evidence.
- Low-ability types potentially mixing between their initial report and new evidence (forecast inertia).
- Consistency of beliefs with these behaviors.
Design Approach: The platform chooses a policy $\pi = (\alpha, \delta)$ , where $\alpha$ is the probability of revealing agreement and $\delta$ is the probability of revealing disagreement. The analysis focuses on the "concealment ray" defined by the probabilities of concealing agreement ( $c_A$ ) and disagreement ( $c_D$ ).

Key Contributions and Theoretical Results

The Concealment-Ray Theorem:
The paper establishes that the two-dimensional design problem reduces to a one-dimensional search along "rays" from full disclosure.
- Along any ray where the ratio of concealment probabilities ( $c_A/c_D$ ) is constant, the likelihood ratio conveyed by silence remains constant.
- Consequently, the experts' continuation strategies and the resulting wage schedules are fixed along the ray.
- The value of any finite downstream decision problem and the incentive constraints for locked reporting are affine functions of the scale parameter $t$ (the frequency of silence).
- Implication: The optimal policy must lie on the boundaries of the policy space (either never revealing disagreement, never revealing agreement) or at full disclosure. The search space is reduced to these three candidates.
Disciplinary Silence:
The analysis identifies a specific non-polar policy on the boundary where disagreement is never revealed ( $\delta = 0$ ), but agreement is revealed with a specific probability $\alpha_{DS}$ .
- This policy creates a "disciplinary" effect: by revealing some agreements, the platform removes favorable observations from the silent pool.
- This makes silence sufficiently unfavorable evidence regarding the expert's initial forecast to eliminate the low-type's incentive to retain an old forecast when new evidence contradicts it.
- At the threshold $\alpha_{DS}$ , the low-type expert is indifferent between revising and sticking to the old forecast, effectively eliminating "inertia" in the silent branch.
Exact Optimality and Computer-Assisted Certification:
Using a specific rational profile of parameters (signal precisions and prior ability), the paper provides a computer-assisted proof of a unique global optimum within the regular-monotone class.
- Optimal Policy: Never reveal disagreement; reveal approximately 71.08% of agreements.
- Performance: This policy increases the probability of correct state classification by approximately 1.37 percentage points compared to sealing (no feedback) and 0.30 percentage points compared to full disclosure.
- Robustness: The strict feasibility and unique optimality persist on an open set of parameters after recalibrating the threshold.
Objective Dependence:
The paper emphasizes that the ranking of policies is objective-specific. The experiments generated by sealing and full disclosure are Blackwell incomparable; neither dominates the other for all downstream decision problems. The "disciplinary silence" policy is optimal for symmetric state classification but the identity of the optimal boundary depends on the specific downstream decision problem.

Significance and Claims
The paper claims to provide a mechanism for improving information aggregation in settings with career concerns, distinct from standard Bayesian persuasion or information design.

Mechanism: It demonstrates that randomized silence is not merely a lack of information but an active design tool. By carefully calibrating the likelihood ratio of silence, a platform can discipline low-ability experts into updating their beliefs, thereby improving the quality of the final public forecast.
Modesty: The authors are modest about the quantitative magnitude of the gains (e.g., the gain over full disclosure is small). The primary contribution is theoretical: establishing the existence of a strict, non-polar optimal policy and isolating the mechanism (disciplinary silence) rather than providing a broadly calibrated policy recommendation for all contexts.
Limitations: The results are conditional on the maintained selection of regular-monotone equilibria. The paper does not claim to eliminate the babbling equilibrium or provide a general implementation theorem for all equilibria. Furthermore, the policy conclusion is not universally preferred for all downstream objectives due to Blackwell incomparability.

In summary, the paper argues that in environments where experts care about their reputation, a platform can improve forecast accuracy not by maximizing transparency, but by strategically withholding information (silence) in a randomized manner that alters the reputational cost of consistency, thereby forcing experts to rely more heavily on their private signals.