Information Acquisition Towards Unanimous Consent

TL;DR

The paper investigates how a manager can acquire and communicate information to secure unanimous consent in tasks with unknown difficulty and conflicting incentives. It demonstrates that with a publicly known worker type, a threshold test is optimal and the plan is launched only when the task is hard enough; when the worker's capability is privately known, a simple test menu containing a threshold test plus up to two interval tests can screen for medium-to-high difficulty levels and improve the manager's payoff. A key mechanism is the manager's ability to misreport test results, which constrains the information design to binary tests and yields sharp predictions on when launches occur and how screening should be structured. Extensions to endogenous payments and multi-worker settings show the pivotal role of credibility in collective action and indicate that the main results extend to more complex unanimous-consent environments, preserving the simple threshold-plus-interval-test structure.

Abstract

A manager facing a task of unknown difficulty can propose a plan to let a worker undertake the task; the worker can either accept the proposal or reject it. The plan benefits the worker only when the task is sufficiently easy and benefits the manager only when it is sufficiently hard. The manager can conduct a test at no cost to acquire information about the difficulty of the task; however, she can misreport the test result to the worker. We find that it is optimal for the manager to conduct a threshold test and to propose the plan only when the difficulty of the task exceeds the threshold. Moreover, when the worker privately knows his capability, we find that the manager can benefit from screening the worker by offering up to two additional interval tests.

Figures (5)

• Figure 1: Players' payoffs upon launching the plan as functions of the task's difficulty $\theta$.
• Figure 2: Optimal test for Problem (A) when the worker is ex-ante optimistic. In each panel, the brown curve represents the manager's ex-post payoff function $u(\theta)$, and the blue curve represents the "price function" $p(\theta)$ used to verify the optimality of the characterized test. The optimal test returns a signal $s=0$ if $\theta \in [0, \theta^*)$ and $s=1$ if $\theta \in [\theta^*, 1]$. The red and the green dots represent the induced posterior mean and the corresponding ex-post payoff of the manager under the two signals.
• Figure 3: Optimal test for Problem (A) when the worker is ex-ante pessimistic. The brown curve represents the manager's ex-post payoff function $u(\theta)$. The blue curve represents the "price function" $p(\theta)$ used to verify the optimality of the characterized test. The optimal test returns a signal $s=0$ if $\theta \in (\theta^*, 1]$ and $s=1$ if $\theta \in [0, \theta^*]$. The red and the green dots represent the induced posterior mean and the corresponding ex-post payoff of the manager under the two signals.
• Figure 4: Illustration of \ref{['coro:cstype']}. Panel (a) shows the threshold of task difficulty at which the plan is launched, as a function of $\lambda$. Panel (b) shows the manager's payoff (red curve) and the worker's payoff (green curve). The figure is generated under $G(\theta)=\theta$ and $b=0.4$.
• Figure 5: Illustration of \ref{['coro:cseta']}. Panel (a) shows the threshold of task difficulty at which the plan is launched, as a function of $\eta$. Panel (b) shows the manager's payoff (red curve) and the worker's payoff (green curve). The figure is generated under the parameters $\lambda=1.8$ and $b=0.4$.

Theorems & Definitions (23)

• Definition 1
• Definition 2
• Theorem 1
• proof
• Definition 3
• Definition 4
• Corollary 1
• proof
• Corollary 2
• proof