Download The Political Economy of Scientific Uncertainty

The Political Economy of Scientific Uncertainty: how
communication campaigns are affected by scientific uncertainty?
February 1, 2013
Abstract
We consider an industry organized as a lobby group whose activity generates pollution.
This pollution may create damages. Scientists are unsure about the level of harm it might
cause, and they can do research to reduce their uncertainty. The government may be benevolent, but populist. The industry wants to avoid being regulated. It can engage in costly
communication efforts to affect public beliefs on the negative outcome. However, the effectiveness of the communication efforts depends on the level of scientific uncertainty. We find
that there exists a certain level of scientific uncertainty above which the lobby communicates
in order to influence the people’s beliefs, and so the government’s regulation. The more uncertain the science, the easier it is for the lobby to affect people’s beliefs. Finally, we discuss
about the possibility of government’s research subvention to decrease this impact.
Keywords: lobby, communication campaign, scientific uncertainty.
JEL Classification: D72, D82, D83, Q58 .
1
Introduction
For contemporary societies, an environmental policy on global warming is an important challenge. This policy depends on public attitudes but also on communication campaign which has an
influence on public’s beliefs. Actually, according to several studies, most people acquires scientific
knowledge through communication campaign coverage (Ader, 1995; Ball-Rokeach and DeFleur,
1976; Cabecinhas, Lazaro and Carvalho, 2008; Corbett and Durfee, 2005; Corner, 2011; Gonzenbach and Hester, 1997; McCombs and Shaw, 1972; Nelkin, 1987). The communication campaigns
then play an important role in the risk perception of global climate change (Kasperson, Pidggon
and Slovic, 2003; Palfreman, 2006). Kahneman (2003) states that under uncertainty individual
reacts differently to the way a message is framed. Dramatic and alarming messages on climate
change, such as those presenting climate change as an extreme threat1 (Pandora’s Box, Polar
bear extinction), a complex problem, or increasing public uncertainty (stressing conflicts between
scientists), may have a distancing effect of public from global warming (Corbett and Durfee, 2004;
Dilling and Moser, 2004; Ereaut and Segnit, 2006; Lowe, 2006; Rogers, 1983; Shanahan, 2007).
On the other hand, a message based on financial aspect or growth of the economy (innovative energy technology, sustainable economic prosperity) may motivate actions (Comby, 2009; Nordhaus
and Schellenberger, 2007).
There is a clear divergence of causes, and so, on recommended actions for global warming
(Boykoff and Boykoff, 2004; Ereault and Segnit, 2006; Shanahan, 2007). Global warming is either
anthropogenic (IPCC, 2007) or is purely caused by natural fluctuations2 (IPSOS/Mori, 2007) implying that voluntary actions would suffice as well as mandatory action would be needed. Hence,
different ideological lines on climate change have appeared (Nisbet, 2009; Painter, 2011; Ward,
2008). For example, in America, a majority of Republicans are sceptics, they refuses climate science and dismisses the urgency of the problem, while a majority of Democrats accept this science
and feels concern about the issue. So, under uncertainty, how communication campaigns will
change people’s beliefs? How these campaigns will influence environmental and research policies?
To address these questions, we consider an economic activity (pollution emissions) with potentially harmful consequences on people’s health and to the environment. Scientists are unsure
about the level of harm it might cause, and they can do research, through experiments to learn
about the truth, to reduce their uncertainty. The industry is organized as a lobby group who
seeks to maximize profit. This lobby group may notably try to influence people’s beliefs about
the issue, through communication efforts. The government may regulate its activity. The gov1
See: ”An Inconvenient Truth”, Gore’s documentary on climate change’s effects, dramatized climate change
as an environmental Frankenstein’s monster; ”Global Warming: Be Worried. Be VERY Worried,” Time, 3 April
2006, cover, http://www.time.com/time/covers/0,16641,20060403,00.html
2
See: ”Weather Wars”, Fox & Friends (2007)
2
ernment may be benevolent, but populist, seeking to maximize median’s voter welfare.3 Lobby
may then be heavily engaged in communication campaigns to affect public perception about the
positive effects of his activity. However, the government may also decide to decrease lobby’s
communication impact on people by giving a subsidize to research.
We examine the literature on the effects of mass media on public policies (Besley and Burgess,
2001; Sobbrio, 2011). Besley and Burgess (2002) and Stromberg (2003) examine the effects of
mass media on the government responsiveness to the public needs in India and on New Deal relief
program in the U.S. in the 1930s, respectively. While these studies show how the presence of
mass media could affect government policy, the focus of our paper is on how scientific committee
through experiments and lobby’s communication campaigns may influence people beliefs, and so
a popular government’s choices.
Furthermore, our paper also investigate the literature relying political and the environmental
economics.
4
Yu (2005) studies the complementarity and the substitution between ”direct” (lob-
bying the government) and ”indirect” (persuading the public) competition for political influence
on environmental policy. In our paper, we introduce experiments (research) and we focus on
the ”indirect” competition for persuading people between the scientific committee (which may
be subsidized by the government) and the lobby. Yu (2006) finds that when the effectiveness
of anti-smoking campaign increases, the government will increase its effort in campaigns, and
will extract more political contributions from the tobacco lobby. We then propose to study the
impact of the level of uncertainty on the lobby’s contributions, which are, here, communication
campaigns.
In our model, scientists’ beliefs are defined by the results of experiments (research). This
characterization implies that both more research leads to more dispersion in scientists’ beliefs,
and when the number of experiments becomes arbitrarily large, scientists can be sure, ex post,
of which theory is true. In addition, people’s beliefs depends on the interaction between the
scientists’ beliefs and the lobby’s communication campaign. This yields to the more certain the
science the more difficult it is for the lobby to affect people’s beliefs.
Under this characterization, we analyse lobby’s communication efforts and government’s
choices on the pollution regulation with different types of regimes: a benevolent government
who measures the social welfare using scientific committee’s beliefs; a populist government who
only cares about being re-elected by people, and then specifies the social welfare using people’s
beliefs. Moreover, we introduce the possibility that the government decides to subsidizes research
(endogenous science) or not (exogenous science).
First, we present the result under exogenous science. We find that whatever the regimes
3
As in Salanié and Treich (2009), we consider two kinds of regime: benevolent based on scientists’ beliefs, called
paternalist approach in Salanié and Treich, and populist approach.)
4
See Persson and Tabellini (2000) and Mueller (2003) for more details on political economy and public choice.
3
(benevolent or populist) when scientists’ belief on harm increases, the government regulates more,
i.e., reduces emissions more. In contrast, the populist government increases emissions as communication campaign increases. Moreover, we obtain that communication campaign decision
depends on both the scientific belief and the cost of the campaign. The lobby will never make
communication with a cost which leads him to a non profitable profit. However, with a cost of
communication arbitrarily small, the lobby will always make communication. Finally, for some
levels of cost communication, there exists a threshold of scientific committee’s beliefs which leads
people to the highest uncertainty on the dangerousness or not of the industry’s pollution. People
are then more ductile yielding the lobby to act and make communication campaign.
Then, under exogenous science, we show that a populist government benefits from people
being lied to and relieved of their worries. We get that when peoples beliefs for the dangerousness
emerging from the industrys pollution are higher than one half, then the lobby communicates more
for reducing the dispersion in people belief. In addition, when peoples beliefs for the dangerousness
emerging from the industrys pollution are lower than one half, then more dispersion in people
belief increases the lobby’s communication effort. Furthermore, ex-ante, the lobby prefer to
encourage research when the expected scientists’ beliefs are under a certain threshold. Finally,
when the lobby distorts information as much as it can, given the constraint that it cannot fabricate
false information, the lobby prefers to encourage research.
The remainder of paper is organized as follows. Section 1 presents the model. Section 2
investigates the optimal decision-making according to the government’s regime (benevolent and
populist) and the exogenous or endogenous science. Finally, section 3 concludes.
I
The model
We consider an industry organized as a lobby group whose activity generates pollution. This
pollution may create damages to people’s health and to the environment. There are two possible
states of the world, θ̃ = 0 if the activity has no harmful consequences and θ̃ = 1 if it has. Society
(government, industry (lobby), scientific committee and people) has limited initial knowledge on
the dangerousness of pollution, it is unsure about the level of harm it might cause.
The scientific committee can do research to reduce its uncertainty. The prior beliefs of scientific
committee are p0 on state θ̃ = 1, and 1 − p0 on state θ̃ = 0. It can run n experiments to learn
about the truth. Each experiment provides a noisy signal on the true state of the world. Each
experiment is correct with probability P > 1/2, the same for both states of the world. Denote by
k the number of experiments saying that θ̃ = 1 is the true state of the world, i.e., k experiments
among n showing that environmental damages are real. Bayes’ rule tell us that:
p = p(θ̃ = 1|k) =
p(k|θ̃ = 1)p(θ̃ = 1)
p(k|θ̃ = 1)p(θ̃ = 1) + p(k|θ̃ = 0)p(θ̃ = 0)
4
Here p(θ̃ = 1) = p0 and p(k|θ̃ = 1) = Cnk P k (1 − P )n−k while p(θ̃ = 0) = 1 − p0 and p(k|θ̃ = 0) =
Cnk (1 − P )k P n−k . This yields
p=
p0 P k (1 − P )n−k
p0 P k (1 − P )n−k + (1 − p0 )(1 − P )k P n−k
Introduce α = P/(1 − P ) > 1 the relative precision of any experiment. Scientists’ belief is
p(p0 , k, n) =
p0
p0 + (1 − p0 )αn−2k
(1)
and clearly, p(p0 , k, n) > p0 if k > n/2 while p(p0 , k, n) < p0 if k < n/2. In addition, the ex-ante
probability that p = p(p0 , k, n) is equal to
p(p̃(n) = p(k, n)) = p(k̃ = k)
= p(k̃ = k|θ̃ = 1)p(θ̃ = 1) + p(k̃ = k|θ̃ = 0)p(θ̃ = 0)
= p0 Cnk P k (1 − P )n−k + (1 − p0 )Cnk P n−k (1 − P )k
and we check that E(p̃(n)) = p0 .
We note that equation (1) satisfies the following Bayesian:
p(p0 , k, n) = p(p(p0 , k ′ , n′ ), k − k ′ , n − n′ )
for any k ′ ≤ k and n′ ≤ n. This simply says that the order of experimentations does not matter.
Observe from (1) that p̃(n) dominates in the sense of second order stochastic dominance p̃(n′ )
if n < n′ . In other words, more research leads to more dispersion in scientists’ beliefs. Moreover,
we get that as n tends to +∞, p̃ converges to the following random variable: p = 1 with probability p0 and p = 0 with probability 1 − p0 (both in distribution and in probability). So when the
number of experiments become arbitrarily large, scientists can be sure, ex post, of which theory
is true.
In order to avoid a decrease of consumer’s demand about its products, the industry can engage
in costly communication efforts on the safety of its production, m ≥ 0, to affect people’s beliefs on
the negative outcome. By considering that each scientific experiment corresponds to a different
scientist, industry (lobby) may hire a scientist with experiments signalling θ̃ = 0 at cost c. In
other word, m is the number of experiments showing that there is no damage that the lobby can
present as if they were independently ran. The industry then presents information biased in his
favour in the media. We suppose that media fairly represent all sides in the debate, i.e., they
fairly represent scientific committee’s view as well as the lobby’s view. Hence, according to the
communication effort m and the scientific committee’ beliefs p(p0 , k, n), the beliefs of people are
q on state θ̃ = 1, and 1 − q on state θ̃ = 0.
5
If n experiments are conducted with k signaling θ̃ = 1, and if the lobby cannot directly
lie about evidence but can only present existing evidence as if it were independently drawn,
communication effort m is naturally bounded
m ≤ n − k.
This means that people’s belief is determined as if there were n + m experiments overall, hence
citizen’s belief is
q=
p0
p
=
.
n−2k+m
p0 + (1 − p0 )α
p + (1 − p)αm
(2)
Hence, we can write q = q(p, m). Study how q depends on p and m.
We have
qp =
αm
>0
[p + (1 − p)αm ]2
so q is increasing from q(0, m) = p = 0 to q(1, m) = p = 1. Then
qpp = −
−2αm (1 − αm )
< 0.
[p + (1 − p)αm ]3
So the scientific belief have an increasing marginal impact on citizen belief.
Moreover, we have
qm = −p(1 − p) ln(α)
αm
<0
[p + (1 − p)αm ]2
so q is decreasing from q(p, 0) = p to q(p, ∞) = 0. Then
qmm = −p(1 − p) (ln(α))2 αm
p − (1 − p)αm
[p + (1 − p)αm ]3
and hence qmm = 0 ⇔ p = (1 − p)αm ⇔ p = αm /(1 + αm ) ⇔ q = 1/2. In addition
qmm > 0 ⇔ q <
1
1
and qmm < 0 ⇔ q > .
2
2
Thus q is everywhere convex if p ≤ 1/2. In that case, any new ”fake” experiment has a decreasing
marginal impact on citizen belief. In contrast, if p > 1/2, q is first concave and then convex. The
first few ”fake” experiments have an increasing marginal impact on citizen belief.
Then, we get that
qpm =
αm ln(α) (p − (1 − p)αm )
[p + (1 − p)αm ]3
and hence qpm = 0 ⇔ p = (1 − p)αm ⇔ p = αm /(1 + αm ) ⇔ q = 1/2. In addition
qpm > 0 ⇔ q >
1
1
and qpm < 0 ⇔ q < .
2
2
Thus, the more certain the science - when scientific committee’s beliefs for the dangerousness
emerging from the industry’s pollution are closer to zero or one - the more difficult it is for the
6
lobby to affect people’s beliefs. So there is no incentive for the lobby to spend money in a failed
communication campaign.
The industry benefits from pollution. Let e be the level of pollution emissions. These benefits
are captured in the function b(e). We define by e0 the level of emissions with business as usual
and assume that for e < e0 then b is an increasing and concave function. Hence e0 solves
maxe≥0 b(e). However, if the activity is harmful, Society suffers from damage d(e) with d defined
as an increasing and linear function.
The industry’s activity being able to generate damages on people health and the environment,
the government may want to regulate the level of emissions, e. The government may be benevolent, but populist, seeking to maximize median’s voter welfare. In other words, if the government
is benevolent, it measures social welfare in using scientific committee’s beliefs, p(k, n); while if
the government is populist, it uses the people’s belief, q(p(k, n), m). So, the expected welfare of
a benevolent and a populist government are recursively:
W (e) = b(e) − p(k, n)d(e) and W (e) = b(e) − q(p(k, n), m)d(e).
Finally, we use quadratic benefits and linear damages:
1
b(e) = be0 e − be2
2
d(e) = de
II
The optimal decision-making
In this section, we present the government’s and the industry (lobby)’s optimal decision-making.
We propose to study four situations in which the government is either benevolent (beliefs depend
on p) or populist (beliefs depend on q), the lobby either engages in a campaign of communication
(m > 0) or not (m = 0), and the government either subsidizes research (endogenous science) or
not (exogenous science). This study allows us to analyse the influence of the level of uncertainty
on the communication campaign. Moreover, this will also tell us whether, ex-ante, the industry
(lobby) prefers to encourage or discourage the research.
We use the backward induction method in order to characterize the government’s and the
industry (lobby)’s optimal decisions.
A
Benevolent government, no lobby and exogenous science.
A government which is benevolent measures the social welfare using scientific committee’s beliefs.
Hence, given scientific committee’s beliefs, p, the government regulates by setting e in order to
maximize welfare. So the government solves the following problem in order to define its optimal
7
decision.
max W (e) = b(e) − pd(e).
e≥0
We easily verify that this problem is concave, so the first order condition is as follows:
b′ (e) = pd′ (e).
(3)
We note eA the optimal level of pollution emissions. From equation (3), we may write that
eA = eA (p). We derive equation (3) with respect to p, this yields
eA
p =
d′ (e)
<0
b′′ (e) − pd′′ (e)
with eA the optimal level of pollution emissions. As scientists’ belief on harm increases, the
government regulates more, i.e., reduces emissions more.
From the form, we get that:
d
eA (p) = e0 − p
b
under the assumption that
d < be0
which guarantees that there is still positive emission in the first best. So effort decreases linearly
with belief. More the scientific committee believes that the pollution creates by the lobby’s
activities is dangerous for people’s health and the environment, more the government will favour
a reduction of emission.
B
Populist government, lobby, exogenous science.
A populist government only cares about being re-elected by people. He then specifies the social
welfare using people’s beliefs, q(p, m), rather than the beliefs of scientific committee. Hence,
given people’s beliefs the government regulates by setting e in order to maximize welfare. So the
government solves the following problem in order to define its optimal decision.
max W (e) = b(e) − q(p, m)d(e).
e≥0
We easily verify that this problem is concave, so the first order condition is as follows:
b′ (e) = q(p, m)d′ (e).
(4)
We note eB the best response for the level of pollution emissions. From equation (4), we may
write that eB = eB (p, m). We derive equation (4) with respect to p and m, this yields
eB
p =
qp d′ (e)
qm d′ (e)
B
<
0
and
e
=
> 0.
m
b′′ (e) − q(p, m)d′′ (e)
b′′ (e) − q(p, m)d′′ (e)
8
As scientists’ belief on harm increases, the government regulates more, i.e., reduces emissions
more. In contrast, the government increases emissions as communication campaign increases.
From the form, we get that:
d
eB (p, m) = e0 − q(p, m)
b
under the assumption that
d < be0 .
Next, the lobby then chooses its optimal level of communication, m, in order to maximize its
profit. The lobby’s maximization problem is:
max π(m) = b(eB (p, m)) − cm
m≥0
This problem is not always concave. Let then turn to the form. So industry profit is quadratic
in citizen belief. The lobby’s maximization problem is:
1
1 d2
max π(m) = be20 −
q(p, m)2 − cm.
m≥0
2
2 b
Substituting equation (2) in π(m) and examining the derivatives, we find:
π(m) =
π ′ (m) =
π ′′ (m) =
1 2 1 d2
p2
be0 −
− cm
2
2 b [p + (1 − p)αm ]2
αm
d2 2
p (1 − p) ln(α)
−c
b
[p + (1 − p)αm ]3
d2 p2 (1 − p) (ln(α))2 αm
[p − 2(1 − p)αm ]
b [p + (1 − p)αm ]4
Thus, if p < 2/3, π is concave and the optimal communication effort is given by mB = 0 if
π ′ (0) =
d2 1−p
b p
ln(α) − c < 0 and mB is such that π ′ (mB ) = 0 otherwise.
In contrast, if p > 2/3, π is first convex and then concave. π ′′ = 0 for m∗ such that q = 2/3
implying that
p
p+(1−p)αm
= 32 . This is equivalent to
π ′ (m∗ ) =
1−p m
p α
= 12 . We have:
4d2 ln(α)
−c
27b p
so we easily verify that π ′ (m∗ ) > π ′ (0). Thus, if p > 2/3, the optimal communication effort is
given by mB = 0 if π ′ (m∗ ) ≤ 0; otherwise if π ′ (m∗ ) > 0 then mB is such that π ′ (mB ) = 0.
So the communication campaign decision depends on both the scientific belief and the cost
of the message mB . If c ≥
4d2
ln(α)
27b p
>c≥
d2
1−p
b p
4d2 ln(α)
27b p
then the lobby will never make communication, m = 0; If
ln(α) then there exists a threshold p = 2/3 under which the lobby will not
communicate, while above it, the lobby send a message to the population. Hence, p = 2/3 may
be the level of scientific committee’s beliefs which lead people to the highest uncertainty on the
dangerousness or not of the industry’s pollution. People are then more ductile yielding the lobby
to act. Finally, if
d2 1−p
b p
ln(α) > c then the communication is always profitable for the lobby
which will always communicate.
9
C
Benevolent government, no lobby, endogenous science.
We come back to the case of a benevolent government without lobby and we add that the number
of experiments is not given but it is chosen by the government. Scientific beliefs p then depends
on n and k, so p = p(k, n).
We first analyse the impact of the dispersion of the scientific committee’s belief, p, on the
welfare, W (p) = W (eA (p)) = b(eA (p)) − pd(eA (p)). We get:
W ′ (p) = −d(eA (p)) < 0 and W ′′ (p) = −d′ eA
p > 0.
Hence W is convex, by Jensen welfare is then always higher when facing a more dispersed
repartition of beliefs (in the sense of second order stochastic dominance).
Now, we introduce the possibility the government can subsidize scientists at cost C per experiment. The government’s best response for the level of emission, eC , is characterize by equation
(3) with p = p(k, n). The government seeks to maximizes
W (n) = Ek̃ W (eC (p(k̃, n))) − Cn
with respect to n. We easily verify that this problem is concave, so the first order condition is as
follows:
−Ek̃ pn d(eC (p(k̃, n))) = C.
(5)
With p = p(k, n) and from equation (3) we obtain that
eC
n =
pn d′ (eC (p(k̃, n)))
> 0.
b′′ (eC (p(k̃, n))) − p(k, n)d′′ (eC (p(k̃, n)))
(6)
We derive pn d(eC (p(k̃, n))) with respect to n, we obtain
pnn d(eC ) + pn d′ (eC )eC
n
which is negative if p0 ≤
αn
α2k +αn
and otherwise the sign is ambiguous. So if p0 ≤
αn
α2k +αn
then
more dispersion in scientists’ belief leads the government to make lower number of experiments.
On the other hand, more dispersion on scientists’ belief leads the government to regulates less,
i.e., increases emissions more.
From the form, we get that the best response for the level of emission is:
d
eC (p(k, n)) = e0 − p(k, n)
b
under the assumption that d < be0 . Then the optimal number of experiment chosen by the
government is such that:
dp0 (1 − p0 )lnααn−2k
Ek̃
(p0 + (1 − p0 )αn−2k )2
(
dp0
e0 −
p0 + (1 − p0 )αn−2k
10
)
= C.
D
Populist government, lobby, endogenous science.
We turn to the case of a populist government which only cares about the social welfare using
people’s beliefs, q(p, m), rather than the beliefs of scientific committee. We add that the number
of experiments is chosen by the government. Scientific beliefs p then depends on n and k, so
p = p(k, n). Hence, people’s beliefs q(p, m) = q(p(k, n), m). Moreover, we introduce the possibility
the government can subsidize scientists at cost C per experiment. The government’s best response
for the level of emission, eD , is characterize by equation (4) with p = p(k, n).
Remark that any distribution of scientists’ beliefs p̃ gets transformed by lobbies’ actions into
a distribution of people’s beliefs q̃. We know that E(q̃) < E(p̃) since the lobby can only lead to a
lowering of belief. This then increases welfare for a populist government: a populist government
benefits from people being lied to and relieved of their worries.
Observe from (2) that q̃(n) dominates in the sense of second order stochastic dominance q̃(n′ )
if n < n′ . In other words, more research leads to more dispersion in people’s beliefs.
If the government anticipates the distortion of scientific beliefs generated by the lobby’s efforts,
how does this affect his incentives to subsidize research? The government seeks to maximizes
W (n) = Ek̃ W (eD (q(p(k̃, n)), m)) − Cn
with respect to n. We easily verify that this problem is concave, so the first order condition is as
follows:
−Ek̃ qp pn d(eD (q(p(k̃, n)), m)) = C.
From the derivation of equation (7) with respect to m, we get that if q ≥
(7)
1
2
then the communi-
cation effort reduces the number of experiments. On the other hand, the effect is ambiguous. So
when peoples beliefs for the dangerousness emerging from the industrys pollution are higher than
one half, then the lobby communicates more for reducing the dispersion in people belief. This
tells us that in this situation, more communication efforts reduces the government’s incentives to
subsidize research.
Now, we are looking for the optimal effort of communication. The lobby’s maximization
problem is:
max π(m) = Ek̃ b(eD (q(p(k̃, n)), m)) − cm
m≥0
This problem is not always concave. Let then turn to the form. So industry profit is quadratic
in citizen belief. The lobby’s maximization problem is:
1
1 d2
max π(m) = be20 −
E q(p(k̃, n)), m)2 − cm.
m≥0
2
2 b k̃
We then summarize the solutions: If c ≥
munication, mD = 0; If
4d2 ln(α)
27b E p(k̃,n)
k̃
> c ≥
4d2 ln(α)
27b E p(k̃,n) then the lobby will never make comk̃
d2 1−Ek̃ p(k̃,n)
b E p(k̃,n) ln(α) then there exists a threshold
k̃
11
Ek̃ p(k̃, n) = 2/3 under which the lobby will not communicate, while above it, the lobby sends a
message to the population, mD which is defined such that π ′ (mD ) = 0. Hence, Ek̃ p(k̃, n) = 2/3
may be the level of scientific committee’s beliefs which lead people to the highest uncertainty on
the dangerousness or not of the industry’s pollution. People are then more ductile yielding the
lobby to act. Finally, if
d2 1−Ek̃ p(k̃,n)
b E p(k̃,n)
k̃
ln(α) > c then the communication is always profitable for
the lobby which will always communicate, mD which is defined such that π ′ (mD ) = 0.
So now we analyse the impact of the number of experiments on the optimal communication
effort. When mD = 0 then there is no impact, so we focus on mD defined such that π ′ (mD ) = 0.
We then get mD > 0 such that:
Ek̃ b′ (eD (q(p(k̃, n)), m))eD
q qm = c.
From the derivation of equation (8) with respect to m, we get that if Ek̃ q ≤
(8)
1
2
then the number
of experiments increases the lobby’s communication effort. On the other hand, the effect is
ambiguous. So when peoples beliefs for the dangerousness emerging from the industrys pollution
are lower than one half, then more dispersion in people belief increases the lobby’s communication
effort.
We now study how q̃(n) vary with n, under the assumption that the lobby exerts the optimal
amount of communication effort. We rewrite q̃(n) = q(p(k̃, n)), m(n)) and we derive it with
respect to n. We obtain
qp pn + qm mn
which is negative if Ek̃ p ≤
threshold, Ek̃ p =
αm
1+αm ,
αm
1+αm ,
and its sign is ambiguous otherwise. Hence, there exists a
under which the number of experiments decreases the people’s beliefs.
This tells us, ex-ante, the lobby prefer to encourage research when the expected scientists’ beliefs
are under this threshold.
Finally, we propose to analyse the impact of the number of experiments on the people’s
beliefs when the lobby make the maximum communication effort. We characterize the maximum
12
communication effort as follows:
1−p =
p
1−p
=
αn−2k =
n − 2k =
k =
n−k =
(1 − p0 )αn−2k
p0 + (1 − p0 )αn−2k
p0
α−(n−2k)
1 − p0
p0 1 − p
1 − p0 p
p0 1−p
ln[ 1−p
]
0 p
ln[α]
ln(p0 ) − ln(1 − p0 ) − [ln(p) − ln(1 − p)]
1
[n −
2
ln(α)
1
ln(p0 ) − ln(1 − p0 ) − [ln(p) − ln(1 − p)]
[n +
2
ln(α)
In this case, the maximum communication effort is
1
ln(p0 ) − ln(1 − p0 ) − [ln(p) − ln(1 − p)]
mmax = [n +
2
ln(α)
In that case, we get
q(mmax ) =
q(mmax ) =
p
p + (1 −
p0 1−p 1/2 n/2
p)[ 1−p
] α
0 p
3/2
p (1 − p0 )1/2
1/2
p3/2 (1 − p0 )1/2 + (1 − p)3/2 p0 αn/2
So when the lobby makes the maximum communication effort, the number of experiments decreases the people’s beliefs. This tells us, when the lobby distorts information as much as it
can, given the constraint that it cannot fabricate false information, the lobby prefer to encourage
research.
III
Conclusion
In this paper, we wonder how communication campaigns are affected by scientific uncertainty.
We find that there exists a certain level of scientific uncertainty above which the lobby communicates in order to influence the people’s beliefs, and so the government’s regulation.
Moreover, we get that more dispersion in people belief increases the lobby’s communication
effort. Then we also show that when the lobby distorts information as much as it can, given the
constraint that it cannot fabricate false information, the lobby prefer to encourage research.
Nevertheless, the linearity of the damage function is a restrictive simplification. It is applied
for the sake of mathematical simplicity. However, Germain, Tulkens, and Zeeuw (1998), Tol
(1996) and Tahvonen (1995) have also used this form to study global warming and pollution
issues.
13
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