Endogenous Persuasion with Costly Verification

• Published date: 01 July 2019
• Date: 01 July 2019
• DOI: http://doi.org/10.1111/sjoe.12290

Scand. J. of Economics 121(3), 1054–1087, 2019

DOI: 10.1111/sjoe.12290

Endogenous Persuasion with Costly

Verification

Mike Felgenhauer

University of Plymouth, Plymouth PL4 8AA, United Kingdom

mike.felgenhauer@plymouth.ac.uk

Abstract

In this paper, I study a situation in whicha sender tries to persuade a receiver with evidence that is

generated via public or privateexperimentation. Under public experimentation, any experimental

outcome is revealed, and under private experimentation the sender can hide adverse outcomes.

The sender can design the properties of the experiments. The receiver chooses whetherto verify

at a cost the design of the experiment with which the revealed outcome was generated. I find

that communication breaks down under public experimentation if there is no restriction on the

experiment’s design, and that persuasion is possible under private experimentation.

Keywords: Experimentation; information acquisition

JEL classification:D82; D83

I. Introduction

In this paper, I investigate a situation where a sender (e.g., a prosecutor, a

student, or an interested party) tries to persuade a receiver (e.g., a judge, a

teacher, or a politician) to take an action (e.g., the conviction of a defendant,

a better mark, or a policy). For the receiver, the optimal action is in the

sender’s favour in one state and it is against the sender in another state.

There is a threshold belief above which the receiver will take the sender’s

preferred action. Her prior belief is below the threshold.

Evidence (or an argument) used for persuasion usually has an inherent

meaning. In this paper, evidence consists of a recommendation and

reasoning supporting the recommendation. As an illustration, suppose

that a sender provides evidence (or argues) “This is the right decision,

because...”.1The recommendation “This is the right decision” is

straightforward. However, the reasoning following the “because” might be

involved and might require effort to understand. The receiver might not

pay attention to the sender’s reasoning. It can be tedious for the receiver

to grasp its meaning, as for example reading a paper or listening to

1Straightforward recommendations followedby some sort of reasoning are common in practice.

Recent examples are the persuasion attempts of the “Remain” campaign (“Vote Remain,

because...”) and the “Leave”campaign (“Vote Leave,because...”) in the Brexit referendum debate

in the UK. Other examples are “I am innocent, because...”, “TTIP is good, because...”, etc.

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M. Felgenhauer 1055

a presentation. The receiver might just follow the recommendation and

think about something more pleasant instead of trying to understand the

reasoning.2The sender might try to exploit the receiver’s incentive to ignore

the reasoning. Instead of searching for hard-to-find favourable high-quality

evidence, he might search for easy-to-find favourable superficial reasoning

that does not have sufficient persuasive power to convince a receiver who

pays attention.

The evidence used for persuasion in this paper stems from

experimentation. An experimental outcome correctly predicts the decision-

relevant state of the world with endogenous error probabilities. The sender

designs the error probabilities of each experiment that he runs. The outcome

of an experiment is interpreted as a recommendation for a decision. The

experiment’s design determines the quality of the information that the

experiment generates. The design of the experiment (i.e., the probabilities

with which it correctly predicts the states of the world) is viewed as the

reasoning. The evidence of an experiment thus consists of the outcome

of this experiment and the experiment’s design. If the sender uses an

experiment’s outcome for persuasion in his message to the receiver, then

the receiver directly observes the revealed outcome. The receiver then

chooses whether to verify the message. If she verifies the message, then

she learns the design of the experiment with which the presented outcome

was generated.3Verifying the message is costly, whereas no verification is

costless.

Here, I distinguish between public and private experimentation.

Experimentation is public if, starting from a situation without information,

the sender designs one single experiment and then discloses its outcome

to the receiver. For example, a trial can be viewed as a public experiment

in which a prosecutor tries to persuade a jury to convict a defendant. The

prosecutor can, for example, influence the error probabilities by choosing

the structure of the examination of witnesses. Jurors not paying attention

(e.g., by falling asleep, as documented in King, 1996) do not learn these

error probabilities. In contrast, experimentation is private if the sender

secretly runs multiple experiments and selectively reveals an outcome. The

sender’s decision as to whether to run a further experiment with a design

2Not paying attention matters in practice.A drastic example is jurors falling asleep during a trial.

King (1996) finds that 69 percent of 562 judges who returned her survey reported cases (during

the last three years) where jurors had fallen asleep. Another example isWolfgang Sch¨auble, the

German Minister of Finance, playing Sudoku in the Bundestag during a debate on financial aid

worth billions of euros for Greece (Darnst¨adt, 2012). In the context of the recent presidential

election in the United States, I also suspect that many voters did not pay attention to the winner’s

arguments during the electoral campaign.

3For example, by thoroughly reading a paper or by carefully listening to a presentation, the

receiver can assess the quality of the presented argument.

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1056 Endogenous persuasion with costly verification

of his choice is contingent on the experimentation history. For example,

thought experiments that yield logical arguments are run sequentially in

private and the results can be revealed selectively (Felgenhauer and Schulte,

2014). The sender can influence the experiments’ quality by choosing

the conceptual framework from which specific assumptions are drawn.

The receiver under private experimentation does not directly observe the

experimentation history even if she verifies the message, as the sender might

privately have collected additional evidence. Verification of the sender’s

message under private experimentation can be viewed as learning the face

value of the sender’s recommendation.

In this paper, I find that persuasion is impossible under public

experimentation and costly endogenous verification if the design of the

experiments is flexible. This result is in contrast to the findings of Kamenica

and Gentzkow (2011) and Gentzkow and Kamenica (2014), referred to

hereafter as KG and GK, respectively. Both papers analyse persuasion under

public experimentation with complete design flexibility, b ut without costly

endogenous verification. Public experimentation in their papers differs from

that in the present paper, in that there the receiver costlessly observes

the design of the experiment that the sender runs, whereas here she only

observes the design if she pays the verification costs. KG study the best

experimental design from a sender’s perspective with which he can persuade

a receiver, where each experimental design is costless. By being able to

freely design the public experiment the sender has substantial influence over

the decision making, in the sense that his preferred decision is chosen more

often than would be justified by ex ante probabilities. GK show that KG’s

findings are robust to a broad class of cost functions where experimentation

costs depend on the design of the experiment. KG’s and GK’s results also

hold if there is costly exogenous verification (if the receiver has to ask

the sender for advice) or costless endogenous verification. In the current

paper, I show that their results are not robust if verification is both costly

and endogenous in a parsimonious version of their models with costly

experimentation, even if verification costs are arbitrarily small but positive.4

In this case, the design flexibility is the cause of the communication

breakdown and it harms the sender.

The communication breakdown under public experimentation in the

current paper is a result of two commitment problems.5First, the receiver

cannot commit to ignoring the information that she learns: if her belief

4The size of the verification costs depends on the type of argument and the expertise of the

receiver. An example for which verification costs are likely to be very high is where a climate

scientist provides a comprehensivestudy in order to warn a politician about climate change. Park

(2017) models such a situation as a cheap talk game.

5I thank an anonymous referee for suggesting this intuition.

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