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arxiv: 2603.10867 · v2 · submitted 2026-03-11 · 💰 econ.TH

Delegated Information Provision

Francesco Bilotta , Christoph Carnehl , Justus Preusser This is my paper

Pith reviewed 2026-05-15 13:27 UTC · model grok-4.3

classification 💰 econ.TH
keywords delegationinformation provisionpersuasiondouble censorshiprecommender systemsprivacyS-shaped preferencesBayesian persuasion
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The pith

A designer strictly benefits from restricting the set of admissible experiments an experimenter may choose, even though the experimenter can garble them.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

When an experimenter provides information but prefers to persuade the decision maker, the designer can restrict the allowed experiments to improve the outcome. The key is to select experiments that the experimenter has no incentive to garble further, making them maximally informative under the constraint. For S-shaped preferences, this results in double censorship with an intermediate pooling region that reduces extreme pooling. This delegation strictly improves the designer's payoff compared to allowing any experiment. The result applies to settings like recommender systems where privacy rules can limit persuasive distortion.

Core claim

We show that the designer strictly benefits from imposing a nontrivial delegation set that constrains persuasion while retaining information provision. When the experimenter's preferences are S-shaped, we characterize these experiments as double censorship. Relative to the full-delegation benchmark, double censorship features an intermediate pooling region, inducing a smaller pooling region for the highest states. Applying our results to recommender systems, we show that privacy constraints can arise endogenously to protect consumers against persuasion.

What carries the argument

The delegation set of experiments that are maximally informative without giving the experimenter an incentive to garble them.

If this is right

  • Double censorship characterizes the optimal experiments under S-shaped preferences.
  • The designer obtains a strictly higher payoff than under unrestricted delegation.
  • An intermediate pooling region is introduced, shrinking the pooling at the highest states.
  • Privacy constraints emerge endogenously in recommender systems to limit persuasion.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • Similar delegation mechanisms might explain information restrictions in other principal-agent relationships beyond recommender systems.
  • If the experimenter's preferences deviate from S-shape, the form of optimal delegation could change to other censorship patterns.
  • Laboratory tests with induced S-shaped utilities could confirm whether double censorship arises in practice.

Load-bearing premise

The designer is able to commit to the restricted delegation set in advance, and the experimenter cannot be prevented from garbling but will not do so for the selected experiments.

What would settle it

Observing that the designer's payoff decreases when imposing the double-censorship delegation set compared to full delegation would falsify the strict benefit claim.

Figures

Figures reproduced from arXiv: 2603.10867 by Christoph Carnehl, Francesco Bilotta, Justus Preusser.

Figure 1
Figure 1. Figure 1: The ICDFs of the prior H, the degenerate experiment δµ, and an experiment F that pools H above a threshold x to a point y, and else coincides with H. CDF F¯ if and only if IF ≤ IF¯ and IF(1) = IF¯(1); analogously, F¯ is a mean-preserving spread (MPS) of F. As is well-known, the set of experiments coincides with the set of MPCs of the prior H, denoted MPC(H). We equip MPC(H) with the L 1 -norm. Let δµ be th… view at source ↗
Figure 2
Figure 2. Figure 2: Equation (2) defines the optimal upper censorship experiment, illustrated by the red dotted line. The tangent to G at y ∗ intersects G at x ∗ . Since x ∗ < r0 , some states in the convex region of the experimenter’s payoff are also pooled into the high atom y ∗ . 4 Maximal Incentive-Compatible Experiments In this section, we first show that it suffices to consider a subset of incentive-compatible experimen… view at source ↗
Figure 3
Figure 3. Figure 3: The ICDF of double censorship F with thresholds (s, t) and atoms (x,y). and depicted in [PITH_FULL_IMAGE:figures/full_fig_p016_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: The order of the set P . For a higher value of y, the slope of G at y is lower, meaning the tangent to G at y intersects G below r0 at a lower point x. more informative at the bottom as well. Finally, note that IF ∗ is affine on [x ∗ ,y∗ ], while IF is convex. Since IF(x ∗ ) ≤ IF ∗(x ∗ ) and IF(y ∗ ) = IF ∗(y ∗ ), we obtain IF(m) ≤ IF ∗(m) for all m ∈ [x ∗ ,y∗ ]. Summarizing, we find that IF lies below IF … view at source ↗
Figure 5
Figure 5. Figure 5: Characterization of MIC experiments. For readability, the horizontal axes are truncated at the top. 5 Optimal Delegation 5.1 Full delegation is not optimal We now revisit the designer’s problem that is at the core of our environment. Anticipating the persuasion motive of the experimenter, can the designer gain from restricting the set of experiments available to the experimenter even though the designer ha… view at source ↗
Figure 6
Figure 6. Figure 6: Examples of M-shaped delegation of information provision. tion outcome reveals some but not all states. We formalize these notions and the claim in Section OB. Here, we give an informal description. First, we formalize locally strict preferences as follows. There is a partition of the state space [0,1] into finitely many intervals on each of which G is either strictly convex or strictly concave, and if G i… view at source ↗
Figure 7
Figure 7. Figure 7: Two tuples and supporting price functions (colored dashed and dotted). The experi￾menter’s payoff G is shown in black. The points y1 and y2 lie on two distinct intervals on which G is concave [PITH_FULL_IMAGE:figures/full_fig_p048_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: Two tuples and supporting price functions (colored dashed and dotted). The exper￾imenter’s payoff G is shown in black. Both tuples admit a single point that lies in an interval where G is concave. (x1 ,y1 ,y2 , x2 ) to meet the differentiability assumptions of Definition 5. We shall use the price function p˜ to construct other IC experiments whose support contains x˜1 , y˜1 , y˜2 , and x˜2 ; the fact that … view at source ↗
read the original abstract

A designer relies on an experimenter to provide information to a decision maker, but the experimenter has incentives to persuade rather than merely transmit information. Anticipating this motive, the designer can restrict the set of admissible experiments, but cannot prevent the experimenter from garbling any admissible experiment. We model this situation as delegation over experiments. The optimal delegation set is obtained by comparing maximally informative experiments among those the experimenter has no incentive to garble. When the experimenter's preferences are $S$-shaped, we characterize these experiments as double censorship. Relative to the full-delegation benchmark, double censorship features an intermediate pooling region, inducing a smaller pooling region for the highest states. We show that the designer strictly benefits from imposing a nontrivial delegation set that constrains persuasion while retaining information provision. Applying our results to recommender systems, we show that privacy constraints can arise endogenously to protect consumers against persuasion.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

0 major / 2 minor

Summary. The paper models delegation over experiments in which a designer commits to a restricted set of admissible experiments that an experimenter may select to inform a decision maker, while the experimenter retains the ability to garble any chosen experiment. The designer chooses the delegation set to maximize her payoff among those experiments for which the experimenter has no strict incentive to garble. When the experimenter's value function is S-shaped, the paper characterizes the optimal non-garbleable experiments as double-censorship signals featuring an intermediate pooling region that induces a smaller pooling region for the highest states. Relative to the full-delegation benchmark, this constrained delegation strictly improves the designer's payoff while preserving information provision. The results are applied to recommender systems to show that privacy constraints can arise endogenously to protect against persuasion.

Significance. If the characterization and strict-benefit result hold, the paper contributes to information design and delegation theory by demonstrating how a designer can mitigate an experimenter's persuasion motive through a nontrivial restriction on admissible experiments without eliminating information transmission. The double-censorship form provides a concrete, falsifiable prediction under the S-shaped preference assumption. The recommender-system application supplies a novel mechanism for endogenous privacy that could inform both theory and policy in digital markets.

minor comments (2)
  1. The abstract states that double censorship 'features an intermediate pooling region,' but the main text should include an explicit definition or diagram of this signal structure early (e.g., in the model section) to aid readers who may not be familiar with the term from prior work.
  2. A simple numerical example or figure comparing the designer's payoff under full delegation versus the optimal double-censorship delegation set would strengthen the claim of strict benefit and make the result more accessible.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for the positive and accurate summary of our paper, the recognition of its contribution to information design and delegation theory, and the recommendation for minor revision. We are pleased that the double-censorship characterization, the strict benefit relative to full delegation, and the recommender-systems application are viewed as significant. Since no specific major comments were raised in the report, we have no points requiring substantive response or revision at this stage.

Circularity Check

0 steps flagged

No significant circularity; derivation self-contained from primitives

full rationale

The central claims follow directly from the model's primitives: the designer commits to a delegation set of admissible experiments, the experimenter chooses and may garble any chosen experiment, and the designer selects the set to maximize her value among experiments for which the experimenter has no strict incentive to garble. When the experimenter's value function is S-shaped, the maximal non-garbleable experiments are characterized as double-censorship signals via standard arguments in information design; restricting to these yields strictly higher designer payoff than full delegation. No equation reduces to a self-definition, no parameter is fitted and then relabeled as a prediction, and no load-bearing step relies on a self-citation chain or imported uniqueness theorem. The argument is self-contained against the stated assumptions and the full-delegation benchmark.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The model rests on standard information-design assumptions plus the domain-specific restriction that the designer controls only the admissible set while garbling remains possible.

axioms (2)
  • domain assumption Experimenter has S-shaped preferences over the decision maker's action
    Invoked to obtain the double-censorship characterization of admissible experiments.
  • domain assumption Designer can commit to a set of admissible experiments but cannot prevent garbling of any chosen experiment
    Core modeling choice stated in the setup.

pith-pipeline@v0.9.0 · 5440 in / 1292 out tokens · 50925 ms · 2026-05-15T13:27:31.371310+00:00 · methodology

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Reference graph

Works this paper leans on

13 extracted references · 13 canonical work pages

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    This does not affect the results and for this reason, we suppress this technical detail

    15To ensure that g(0) > 0 and g(1) > 0 to satisfy Assumption 1, we could mix the Beta(2,2) with a uniform distribution and make the uniform component vanishingly small. This does not affect the results and for this reason, we suppress this technical detail. 23 The optimal delegation of information provision induces simple information provision endogenousl...

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    To do so, we relate the objects defining the privacy constraints,δandP, to restrictions on the set of admissible experiments

    6.2 Delegation Sets as Privacy Constraints In the following, we show that the delegation sets we study are closely linked to privacy constraints as introduced above. To do so, we relate the objects defining the privacy constraints,δandP, to restrictions on the set of admissible experiments. First, suppose that the experimenter can pick any signal satisfyi...

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    Conversely, conditional on ω∈ [s, t], the privacy constraint requires any signal to reveal no additional information beyond the state’s falling into [s, t]. Therefore, every conditionally privacy-preserving signal induces an experiment that is a mean-preserving contraction of the experiment that reveals the state whenever the state is outside [s, t], and ...

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    makes the same observation. M-shaped experimenter preferences.Suppose the experimenter’s payoffG is M-shaped as in Figure 6:20 concave on an interval of the lowest states, then convex, and finally concave on an interval of the highest states. In this example, G has locally strict preferences. We now discuss incomplete full revelation, which also involves ...

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    However, transformations of the formm7→aG (m) +bm with a > 0 do not alter the experimenter’s preferences over experiments since all experiments have meanµ

    General experimenter preferences.The preceding examples suggest that profitable restrictions exist when the experimenter has locally strict preferences, and the full delega- 20The depicted G is not a CDF. However, transformations of the formm7→aG (m) +bm with a > 0 do not alter the experimenter’s preferences over experiments since all experiments have mea...

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    In contrast, our characterization of MIC experiments as double censor- ship makes explicit use ofS-shapedness ofGand, hence, does not apply here

    remains applicable given the regularity assumption on G. In contrast, our characterization of MIC experiments as double censor- ship makes explicit use ofS-shapedness ofGand, hence, does not apply here. At first sight, the extreme points of MPC(H) may seem unrelated to MIC experiments. The extreme point characterization reflects the feasibility constraint...

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    Compactness follows if we can show that BR is an upper hemicontinuous, nonempty- and compact-valued correspondence fromMPC(H) to itself

    Existence of an optimal IC experiment follows from Berge’s Maximum Theorem and upper semicontinuity of the designer’s payoffs if we can show that the set of IC experiments is compact. Compactness follows if we can show that BR is an upper hemicontinuous, nonempty- and compact-valued correspondence fromMPC(H) to itself. These properties of BR follow from L...

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    consecutive

    implies there exists ˆx≤r 0 such that (ˆx, ˆy) ∈P and such thatΦ assigns no mass to (ˆx, ˆy)∪( ˆy, 1]. 38 Since ˆy≥y, Lemma 4 implies ˆx≤x. Since Φ assigns no mass to ( ˆx, ˆy), and since [ x, y] ⊆ [ ˆx, ˆy] and t∈ [x, y], we conclude that IΦ is affine on [ˆx, ˆy] and this interval contains t. Now, since F is double censorship, IF is tangential to IH at t...

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    Information Design for Differential Privacy,

    Schmutte, Ian M and Nathan Y oder(2025): “Information Design for Differential Privacy,” Working paper. Song, Doyoung(2025): “Robust Persuasion under Costly Attention,” Working paper. Strack, Philipp and Kai Hao Yang(2024): “Privacy-Preserving Signals,”Econometrica, 92 (6), 1907–1938. Tsakas, Elias and Nikolas Tsakas(2021): “Noisy persuasion,”Games and Eco...

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    Let δ > 0 and [x1, x2] be as in the definition of incomplete full information

    Let F be a DEF with incomplete full information. Let δ > 0 and [x1, x2] be as in the definition of incomplete full information. Let y1 and y2 be the atoms in [x1, x2] (possiblyy 1 =y 2). Find a price functionp as in Corollary 1 of Dworczak and Martini (2019), i.e.p is convex and continuous, and it holds p≥G , suppF⊆ {m∈ [0,1]:p (m) = G(m)} and R p dF = R ...

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    OC Extreme Point Representation In this appendix, we provide a general extreme point representation of IC experiments

    F admits exactly one atom y1 on( x1, x2), the interval[ x2, x2 + δ]is a full revelation interval, and0 =x 1 < x2 <1holds.Analogous to the previous case. OC Extreme Point Representation In this appendix, we provide a general extreme point representation of IC experiments. Let G satisfy part (i) of the regularity condition of Dworczak and Martini (2019), as...

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    Theorem 5.For all IC experiments F there exists a Borel probability measure ν that represents Fand is supported on the set of incentive-compatible extreme points ofMPC(H). 25 25The set of incentive-compatible extreme points of MPC(H) is measurable since IC experiments form a closed set (see Section A.1) while the extreme points form a Gδ-set (Aliprantis a...

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    By Lemma 2, there exists a continuous, convex function p: [0,1] →R such that p≥G and suppF⊆ {m∈ [0,1]:p (m) = G(m)}

    Let F be IC. By Lemma 2, there exists a continuous, convex function p: [0,1] →R such that p≥G and suppF⊆ {m∈ [0,1]:p (m) = G(m)}. By Choquet’s Repre- sentation Theorem (e.g. Kleiner et al. (2021, Proposition 1)), there exists a measure ν that representsFand is supported on the extreme points of MPC(H). We argue that ν-almost all Φ are IC. We use Lemma

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