Paying for Failure in Expert Advice

Technical Summary: Paying for Failure in Expert Advice

Problem Statement
The paper addresses a design problem in organizational economics: how should an organization compensate a career-concerned adviser whose private confidence determines whether a project reaches the decision margin? The core friction arises from an asymmetry in observability. While the organization observes the adviser's recommendation and the subsequent project outcome (success or failure), it cannot observe the projects the adviser privately declines to propose. Consequently, a failed recommendation creates an observable record damaging to the adviser's reputation, whereas a forgone opportunity (a project not proposed) leaves no trace.

Even if the adviser's material incentives are perfectly aligned with the organization's (i.e., they share the same risk-return trade-off), the adviser will still suppress worthwhile risky projects due to "reputational conservatism." The adviser fears that a failure will lower the market's posterior belief about their ability, while a safe recommendation (which yields no outcome) provides no reputational update, effectively preserving the prior. This creates a wedge where the adviser requires a higher confidence threshold to recommend risk than the organization finds efficient.

Methodology
The authors employ a static delegated-assessment model with the following structure:

• Agents: An organization (principal) and an adviser (agent).
• Information: Project quality is binary ($\omega \in \{1, 0\}$). Ability ($\theta \in \{H, L\}$) is binary and initially unknown to both the adviser and the market. The adviser observes a continuous private signal $x$ regarding project quality. High ability corresponds to a Blackwell-more-informative experiment.
• Actions: The adviser recommends either a safe action ($S$) or a risky action ($R$). The organization commits to implementing $R$ if recommended.
• Outcomes: If $R$ is implemented, it succeeds with probability $p$ (generating $G$) or fails with probability $1-p$ (generating $-L$). Safety yields zero.
• Payoffs: The adviser has a material stake proportional to the organization's ($g, -\ell$) and a linear career payoff ($V(\mu) = \gamma \mu$) based on the market's posterior belief $\mu$ about their ability.
• Contracting: The organization offers nonnegative incremental payments $(t_S, t_+, t_-)$ contingent on safety, success, or failure, respectively.

The analysis proceeds by first characterizing the "laissez-faire" equilibrium (no contract) to identify the reputational distortion. It then solves for the least-cost contract to support a specific confidence threshold, and finally determines the organization's optimal threshold and the role of internal review mechanisms.

Key Contributions and Results

1. The Least-Cost Instrument: Failure Protection
The central theoretical result is that the least-cost instrument to encourage risky advice is protection after failure, not a bonus for success.

• Mechanism: Risky recommendations are selected from the upper tail of the adviser's private confidence distribution. Conditional on a risky recommendation being made, the average confidence is strictly higher than the marginal confidence required to make the recommendation ($E[p | p \ge c] > c$).
• Cost Comparison: A success bonus is paid disproportionately on high-confidence, inframarginal recommendations that would have occurred anyway. In contrast, failure protection is concentrated on the lower-confidence recommendations near the margin, which are the ones most likely to fail.
• Result: For any target confidence threshold $c$ requiring encouragement, the unique least-cost contract sets $t_+ = t_S = 0$ and pays $t_- = D(c)/(1-c)$, where $D(c)$ is the incentive deficit. This is strictly cheaper than a success-only contract because the "price" of delivering a unit of marginal incentive via failure protection is lower due to the selection effect.

2. Implementation and Uniqueness
The paper establishes that this failure-protection schedule induces a unique nonpooling equilibrium (an upper-cutoff rule) among all measurable strategies.

• The authors define a "uniform success dominance" condition ensuring that success remains preferable to safety even under the most unfavorable selection-induced reputation.
• Under this condition, the required failure protection is strictly decreasing in the target confidence threshold, which guarantees that the target is the unique equilibrium cutoff.
• The paper explicitly addresses pooling equilibria, showing that with "upper-tail-consistent" boundary beliefs, both all-safe and all-risk pooling strategies are unstable, leaving the target cutoff as the unique equilibrium.

3. Optimal Organizational Design: Partial Correction
When the organization chooses the target threshold endogenously, the paper finds that exact first-best implementation is never optimal.

• At the first-best threshold, the marginal project surplus loss from increasing caution is zero (by definition of efficiency), but the marginal compensation saving from reducing the failure payment is positive (first-order).
• Therefore, the organization optimally chooses a threshold that is either the laissez-faire level (no intervention) or a level between the first-best and laissez-faire (partial correction). Full correction is too expensive at the margin.

4. Caps and Constraints
The paper analyzes scenarios where failure protection is capped (e.g., by governance rules or pay equity).

• If the cap binds, the organization exhausts the failure protection up to the cap and uses success pay only for the remaining incentive requirement.
• Relaxing the cap weakly lowers the optimal threshold (induces bolder advice).

5. Internal Review and Disclosure
The paper compares transparent review (where a veto is public) with confidential review (where a veto is pooled with safe advice).

• Transparent Review: A veto and a failed launch convey identical information about ability; thus, transparent review does not reduce the reputational wedge.
• Confidential Review: A veto is pooled with safe advice, which is better news about ability than a failure. This shields the adviser from adverse updating, effectively acting as a substitute for explicit career insurance.
• Result: While the organization is trying to encourage risk (i.e., the incentive deficit is positive), confidential review is strictly cheaper than transparent review. The cost advantage of confidentiality increases with the precision of the review.

Significance and Claims
The paper claims to derive the force of the distortion from endogenous career evaluation in delegated advice, rather than assuming it. Its significance lies in:

1. Counterintuitive Policy: It challenges the common intuition that rewarding failure encourages bad projects. Instead, it frames failure payments as insurance against the reputational consequences of reasonable but unlucky decisions.
2. Selection Argument: The cost advantage of failure protection is derived purely from the "upper-tail selection" of risky advice, independent of risk aversion, dynamic learning, or privately known ability.
3. Organizational Substitution: It identifies confidential internal review as a mechanism that can substitute for explicit career insurance, reducing the need for monetary transfers.
4. Design Implications: The paper suggests that organizations should prioritize downside protection over success bonuses and recognize that eliminating all reputational caution is not cost-effective.

The authors explicitly note limitations: the model is static, excludes hidden effort, and assumes ability is commonly unknown. They caution that if ability were privately known, the sign of the distortion could reverse (leading to over-investment), but argue that understanding the common-uncertainty benchmark is a necessary precursor.