Vague lies and lax standards of proof: On the law and economics of advice

• Published date: 01 April 2019
• Author: Mikhail Drugov,Marta Troya‐Martinez
• Date: 01 April 2019
• DOI: http://doi.org/10.1111/jems.12279

298 © 2018 Wiley Periodicals, Inc. wileyonlinelibrary.com/journal/jems J Econ Manage Strat. 2019;28:298–315.

Received: 13 October 2017 Revised: 21 June 2018 Accepted: 22 June 2018

DOI: 10.1111/jems.12279

ORIGINAL ARTICLE

Vague lies and lax standards of proof: On the law and economics

of advice

Mikhail Drugov Marta Troya-Martinez

New Economic Schooland CEPR, Moscow,

Russia

Correspondence

Marta Troya-Martinez,New Economic

Schooland CEPR 121353 Russia Moscow,

SkolkovskoyeShosse, 45.

Email:mtroya@nes.ru

Abstract

This paper analyzes a persuasion game where a seller provides (un)biased and

(im)precise advice and may be fined by an authority for misleading the buyers. In the

equilibrium, biasing the advice and making it noisier are complements. The advice

becomes both more biased and less precise with a stricter standard of proof employed

by the authority, a larger share of credulous consumers, and a higher buyers' hetero-

geneity. The optimal policy of the authority is characterized in terms of a standard of

proof and resources devoted to the investigation.

KEYWORDS

advice, consumer protection, legal procedure, persuasion

JEL CLASSIFICATION

D8, D18, K4, L1

1INTRODUCTION

Sales advice is pervasive in transactions where consumers cannot assess the product's quality or its utility prior to the pur-

chase because of its complexity or number of experience attributes. Consumer electronics, insurance, banking, and medical

care contracts are important examples. In persuading the consumer, the seller can tell an outright lie about the desirability

of the product, for instance, by exaggerating the quality of a financial product with the “hope to gain high commissions, or to

achieve their sales targets for certain product.” But the seller can also choose to give vague advice such as when a financial

advisor does “not clearly define or explain the benchmarks for ‘low-risk,’ ‘mid-risk,’ or ‘high-risk.’ As a result, the client may

not have accurately reflected his or her risk preferences” (see EC, 2011, pp. 49–50).

Giving a misleading sales pitch, although profitable, may come at a cost. Customers complain because the product does

not meet their expectations. These complaints damage the seller's reputation, draw the attention of consumer associations,

and may even trigger an enforcement action by a regulator or result in litigation. Indeed, the types of products and ser-

vices mentioned above consistently top the list of consumers complaints worldwide, which raises the policy relevance of the

problem.1

This paper explores how a seller strategically uses both outright lies and vagueness, when an authority can investigate and

sanction the seller for misleading the consumers. It shows that lies and vagueness are complements in the equilibrium, that is, a

bigger lie is also more vague. It also sheds light on how,given the seller's behavior and consumers' reaction, the authority should

decide on the standard of proof as well as on the resources devoted to the investigation.

In the model, buyers are interested in buying a product that has some attributes whose usefulness will only become fully

known through the use (Nelson, 1970). The seller knows the product's features but does not know how well they fit with the

buyer's needs. As a result, the buyers' valuations for the product, determined by the quality of the match between the product

characteristics and buyers' idiosyncratic preferences, are unknown at the point of sale.

The seller gives advice about the product. It generates an informative signal equal to the sum of the true match quality and

an error term, both normally distributed. The error term represents frictions in the communication as well as the experience

DRUGOV AND TROYA-MARTINEZ 3

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features of the product. The seller secretly chooses its mean (“bias”) and publiclyits variance (“noise” ). The posterior valuation

of the product is the buyer's willingness to pay after the sales pitch. Some consumers are rational and correctly update their

beliefs whereas others are credulous with the posterior equal to the signal realization.2The posterior valuation is shared in a

fixed proportion between the seller and the buyer.

The bias unambiguously increases the perceived quality of the product and thus the seller's revenues. Because the (biased)

signal is, on average, better than the true match quality, the seller wants rational buyers to pay more attention to the (biased)

advice rather than to the prior. As a result, the seller would like to accompany a largerbias wit h a smaller noise. These incentives

are akin to the ones in Johnson and Myatt (2006) for niche markets.3

However, the bias does not come for free. Misled buyers learn through use the true match quality and complain, which

triggers an action by an authority that might be a consumer protection authority, a sectoral regulator, or the court depending

on the product and the country. The authority investigates the seller by surveying a random sample of customers or sending

mystery shoppers. Based on this information, it estimates the bias and determines whether there is enough evidence that the

seller has misled consumers by biasing his signal. More precisely, the authority presumes the innocence of the seller. That

is, its null hypothesis is that there has been no bias. It then tests whether this null hypothesis can be rejected in favor of the

alternative hypothesis of a positive bias. In doing so, it uses a significance level, which is the standard of proof. If the seller is

found guilty, he has to pay a fine that depends on the estimated bias. A larger bias always increases the expected fine. Noise

affects the expected fine through two channels: It decreases the probability that the seller is found guilty but increases the fine

if the seller is found guilty. The total effect is U-shaped. For a givenbias, t he costsare minimized at some inter mediate level of

noise.

We show that when the choice of the amount of information is endogenously linked to the future fine, two new impor-

tant results emerge.4First, unlike Johnson and Myatt (2006), extreme policies regarding information disclosure are no

longer optimal. Instead, the seller only discloses partial information about the product. Second, bias and noise are com-

plements, that is, the seller “hides” a larger bias with a larger noise. For instance, in a less onerous punishment regime

with a stricter standard of proof, the seller uses a larger bias. As a result, there is more need for noise. This is despite the

fact that rational buyers pay less attention to the signal when the noise is larger and, therefore, are less easily swayed by

bias.

We then characterize the optimal policy of the authority, assuming that some of the sellers are honest and never bias their

advice. The policy of the authority consists of a standard of proof and the amount of resources devoted to the investigation,which

is reflected by the number of sampled consumers. The authority then minimizes a combination of the consumers' harm, the fines

paid by honest sellers, and the costs of investigation.A lower standard of proof reduces the sellers' incentives to bias their advice,

but increases the likelihood of imposing a fine on honest sellers (type I error). The larger the scope of the investigation, the more

precise the authority's test should be. This decreases both the bias and the type I error, but costs more in terms of resources. We

find that the optimal standard of proof is lower and more resources are devoted to the investigation in a market where consumers

are more heterogenous or there are more credulous consumers. A higher share of honest sellers leads to a higher standard of

proof but the effect on the scope of investigation is nonmonotonic.

Biasing the advice can be seen as a form of false advertising, which arises when a low-quality firm advertises itself as

being high quality, that is, when the equilibrium of the signalling game is (semi-)pooling. Although it was discussed by

Nelson (1974), it has received attention only recently (see Renault, 2016, for the latest survey of the advertising literature).

In Corts (2013), Piccolo, Tedeschi, and Ursino (2015), and Rhodes and Wilson (2018), consumers are rational and the firm

uses advertising to signal its quality; a possible fine makes false advertising costly. In Glaeser and Ujhelyi (2010) and Hattori

and Higashida (2012), consumers are credulous and false advertising boosts the demand and hence reduces the quantity dis-

tortion coming from the imperfect competition. Formally, however, our model is quite different because it is a signal-jamming

model à la Holmström (1999) with the specific feature that the seller also chooses the variance of the signal observed by the

buyers.

This paper is also related to the literature on litigation and contributes to it in three important ways.5First, we micro-

found the signal obtained by the court about the behavior of the defendant (seller) although typically the literature assumes

some unspecified process by which the defendant's action generates a signal. Second, we allow the defendant to change the

quality of the signal (variance) about the harmful action (bias). Finally, we let the policy of the court (authority) change the

equilibrium communication between the seller and the buyers rather than just the individual decision problem as in most

papers.

The rest of the paper is organized as follows. Section 2 introduces the model. Section 3 solves for the equilibrium bias and

noise. Section 4 characterizes the optimal policy of the authority. Section 5 considers the scenario when the price is fixed.

Section 6 concludes. The proofs are contained in the Appendix.