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\begin{large}  
 {\bf  Lobbying When the Decisionmaker Can Acquire Independent Information  }\\  
  \end{large}  
         
          
        \bigskip  
 Eric Rasmusen \\  
       

Published: {\it Public Choice} (1993) 77: 899-913.\\

 
        {\it Abstract}   
        \end{center}  
	
   \begin{small}        
 Politicians trade off the cost of acquiring and processing
information   against the benefit  of being re-elected. Lobbyists may    possess
private information upon  which     politicians
would like to   rely    without   the effort of verification. If the politician
does not  try to verify, however, the lobbyist has no incentive to be truthful.
This is modelled as a game in which the lobbyist lobbies to show his conviction
that the electorate is on his side.   In equilibrium,   sometimes the politician
investigates,   and sometimes the information  is  false.  The lobbyists
and the electorate benefit from the possibility of lobbying when
 the politician would otherwise vote in ignorance, but   not when he   would
otherwise   acquire  his own information. The politician benefits in either case.
Lobbying is most socially useful when the politician's investigation costs are
high, when he is more certain of the electorate's views, and when the issue is
less important.

   
  
                
   Original title:  ``Costly Lobbying  as a Signal  of Conviction.'' Draft: 3.6
(Draft 1.1, June 1991).

 I would like to thank Charles Cameron, Jay Choi, David Epstein, Daniel Farber,
and  Paul Johnson for helpful comments.  Much of this work was completed while the
author was Olin Faculty Fellow at Yale Law School and on the faculty of UCLA's
Anderson Graduate School of Management.
 
               \noindent 
\hspace*{20pt} 2000: Eric Rasmusen, 	Professor of Business Economics and Public
Policy and Sanjay Subhedar Faculty Fellow,   Indiana University,
Kelley School of Business, BU 456,   
  1309 E 10th Street,
  Bloomington, Indiana, 47405-1701.
  Office: (812) 855-9219.   Fax: 812-855-3354. Erasmuse@indiana.edu.
Php.indiana.edu/$\sim$erasmuse.
 \end{small}

  
  %---------------------------------------------------------------  
\newpage

\noindent
 {\bf 1. Introduction}
 
   Political persuasion takes many forms. Most directly, someone who
wishes to influence a politician uses  threats or promises.
Less directly,the persuader may communicate information which shows that his
interests and the politician's are the same, although the politician knows that
the information is biased.
Some political action,  seems to avoid rational discourse
altogether and  contains only the message: ``I   want to
change your mind very much!''  Such a message is meaningful if   backed up
by     threats or promises, but  would it have any direct impact? 
  
    An explanation for contentless messages  is that they are made in the hope
of inducing the politician to take the issue more seriously,  under the
belief that  after further study he would 
 change his position. The message is not  informative in
itself, but it attracts  attention and induces the listener to
acquire his own independent information.   The analysis below tries to make sense
of this,  focussing on the relationship between
attention-getting actions and the quality of legislative decisions.
The context will be lobbying, but the results will apply as aptly to
protests  and  demonstrations, or any kind of costly action which    displays
conviction.  It will be seen that the possibility of
attention-getting political action can actually reduce the welfare of
the lobbying group and the electorate, especially when the issue is
important and the politician is undecided about  his position.
Lobbying and protest can also be socially useful, however, especially
on obscure issues and when the politician is wrongly confident that
he knows the opinion of the electorate.



 A number of recent papers have modelled lobbying as signalling. 
 In  Austen-Smith and Wright (1992), the closest of these to the present paper,
a legislator must decide which of two
policies will win him reelection.  Each of two opposing lobbyists
 can acquire information on the extent to which the electorate
supports each policy, and the legislator observes whether they do so.
Each lobbyist then decides whether to lobby.  The legislator
can,  but need not, check on the accuracy of the lobbyists' claims,
and a lobbyist who is caught lying suffers an exogenous penalty.  The
authors conclude that the politician will be helped by the presence
of the lobbyists and that lobbying will, on average, bring the
politician's decisions closer to the tastes of the electorate,
although sometimes it will lead to mistakes.

 In Ainsworth (1991), the  lobbyist knows the electorate's preferences  but does
not necessarily
share them. By assumption, the lobbyist is willing to lobby more
strongly when he agrees with the electorate, so the government may be able to use
lobbying as a signal, even without a cost to being discovered lying.
The government can choose the cost of lobbying, and should choose it
to be above a certain level so that false lobbying claims are
unprofitable. Another paper by the same author,    
 Ainsworth \& Sened (1991), looks at the interaction between the lobbyist, members
of  the interest group he serves, and the  government.  It is assumed that the
lobbyist has superior information, which enable him to raise welfare (and his own
payoff) by helping the members of the interest group  coordinate their   lobbying
efforts.

 Lobbying in these papers  does not benefit the politician directly. In   Ball
(1991),  the  interest group lobbies by making cash transfers to the government---
what are effectively bribes.
The government must choose the level of spending on a  public good, but cannot 
   verify
how much the interest group really values it. 
The government values both the cash transfers and choosing the
socially optimal level of the public good, and the transfers act as a signal of
interest group valuation. Allowing the transfers can
either raise or lower welfare, depending on the parameters, because
it conveys information,    but it may result in overspending to satisfy the
interest group.
 
Lohmann (1991) has applied the signalling idea to political protest, with
an emphasis on the motivations of individuals along a spectrum of
opinion. The politician cannot acquire his own information, but some
of the individuals are better informed than he is about the value of
a policy change. Protests may occur from both ends of the spectrum,
and may to some extent be futile, occurring only because of what the
politician would read into the absence of protest.  

 
  The present paper will look at a different problem:    the incentive for the
politician to
acquire his own information or to try to verify    the information of
interested parties. Rather than assuming that lying imposes a reputation cost on
the lobbyist or that his willingness to lobby is greater when he is telling the
truth, {\it the incentive for truth will lie in the possibility that the
politician checks up on the information before making his decision, so that  false
statements are wasted effort.} The strategic problem is that the politician would
prefer to avoid the cost of verification, so that  a certain amount of lobbyist
bluffing will succeed.     Section 2 will set out the model, and Sections 3
and 4 will find the equilibrium when lobbying is and is not possible.
Section 5 will compare the quality of the political decisions   in
each case. Section 6 concludes, and  suggests links with advertising, protest, and
influence activities within businesses.

  
 
%---------------------------------------------------------------


\bigskip
\noindent
 {\bf 2. The Model}

  A lobbyist and a politician are two players in a game in which the politician
must make a decision that affects whether the electorate will retain him or not in
the next election.
   The politician can choose either
to retain the status quo or to innovate, knowing from prior information that the
electorate most likely
prefers the status quo.\footnote{Electorate conservatism is just a normalization.
Nothing changes but the labelling if the prior information says that the
electorate favors innovation.} A potential lobbyist exists who knows the
electorate's preference but who favors innovation
regardless of those preferences.   He can lobby the politician and try
to persuade him that the electorate favors innovation, but he bears
no penalty if he lies.\footnote{Lobbyist reputation is an obvious solution to the
problem of credible information transmission. This requires repeated transactions,
and its effectiveness depends on whether the politician eventually learns whether
the lobbyist told the truth (as when the issue is important enough to noticeably
affect an election) or must occasionally verify for himself. See Ainsworth (1991)
for an intertemporal model of lobbying, or Chapters 4 and 5 of Rasmusen (1989) for
a discussion of reputation as a repeated game.}   The politician
can either take the lobbyist's claims on faith  or try to verify them, but
verification is costly.\footnote{The costliness of verification distinguishes this
model from  a different literature in which the interested party can convincingly
present his private  information (or keep silent) without any need for the
listener to incur verification costs.  See, for example, Milgrom and Roberts
(1986).}    If there has been no lobbying, the politician can conduct his own
investigation, which is also costly.
 More formally, the model is a game between lobbyist and
politician with the following order of play: 
 

(1) Nature chooses $T$, the electorate's preference for
innovation.    $T$ equals 0 with probability $\alpha> .5$ and $ \tau $ with
probability $1-\alpha$. The lobbyist observes $T$, but the politician
does not.

(2) The lobbyist chooses  the lobbying level $L$ to equal  0 or $ \lambda$,
observed by the politician.

(3) The politician chooses   $C$, his expenditure on discovering $T$. If there has
been lobbying, $C$ can be set equal to 0 or   the verification cost $c_{ver}$.  If
there has not been   lobbying, $C$ can be set equal to     0 or the independent
investigation cost
$ c_{inv}$, where $c_{inv} \geq c_{ver}>0$.   If $C$ equals $c_{ver}$ or $c_{inv}
$, the politician discovers $T$.

(4) The politician  chooses  the policy $\hat{T} $ to equal    0  (the status quo)
or
$  \tau $ (the innovation).  


  
 \noindent
 The lobbyist's payoff  is 
 \begin{equation} \label{e1}
 \pi_L = \hat{T} \beta - L, 
 \end{equation}
and the  politician's payoff is 
 \begin{equation} \label{e2}
 \pi_P = - (\hat{T}   -T)^2 -C.
 \end{equation}

The politician and lobbyist both   know the values of all the parameters,
$\alpha$, $\tau$, $\lambda$, $c_{ver}$, $c_{inv}$, and  $\beta$.    $\alpha$
represents the politician's certainty about the electorate's views, and     $\tau$
represents the importance   to  him of being correct in his policy decision. $\tau
\beta$ represents the benefit to the lobbyist of obtaining the policy of
innovation, so    $\beta$ is the lobbyist's  interest intensity  relative  to the
politician's.   $c_{ver}$ and $c_{inv}$ are measures of the politician's cost of
verifying the lobbyist's claims and of discovering the electorate's opinion
starting from scratch. In the case of pure attention-getting,   $c_{ver}$ equals
$c_{inv}$ because the lobbying does not reduce the politician's cost of obtaining
information even slightly.
 A final assumption is that 
 \begin{equation} \label{e2a}
    \tau \beta -\lambda >0, 
 \end{equation}
 which says that   if  lobbying persuades the politician to change his policy, it
is worth the cost to the lobbyist.
 
  
 The equilibrium payoffs will be derived for two different  settings which will be
called ``regimes'': a
no-lobbying regime in which   $L=0$ because lobbying is not permitted,
and a lobbying regime in which the lobbyist can choose $L=0$ or $L=\lambda$.


\bigskip
\noindent
 {\bf 3. Equilibrium in the No-Lobbying Regime}

In the absence of lobbying, the politician must solve the straightforward problem
of
whether to spend $c_{inv}$ to investigate the electorate's opinion.   If
he investigates, his payoff is 
 \begin{equation} \label{e3}
 \pi_p (investigate) = -c_{inv}, 
 \end{equation}
 since he can exactly match his policy to the electorate's preference.   If he
does not investigate, his best move is to set
$\hat{T}  =0$,  and his payoff is
 \begin{equation} \label{e4}
 \begin{array}{ll}
 \pi_p (not \;investigate) & =  -\alpha (0-0) - (1-\alpha)(\tau -0)^2\\
 & = -(1-\alpha)\tau^2.
\end{array}
 \end{equation}
 The politician picks the maximum of these two payoffs,  investigating if
\begin{equation} \label{e5}
 c_{inv}  <(1-\alpha)\tau^2.
 \end{equation}

%---------------------------------------------------------------


\bigskip
 \noindent
 {\bf 4. Equilibrium in the Lobbying Regime}

 
 The lobbying regime has several equilibria, in some of which lobbying will not
occur. The  ``lobbying equilibrium''  in which lobbying does occur   will be the
focus of the analysis.
In the lobbying equilibrium, the lobbyist sometimes lobbies even
if the electorate is conservative, and the politician occasionally checks on the
information and   discovers the deceit. Mixed strategies
are employed,  because if the lobbyist only lobbies when his claims     are true,
the politician has no incentive to
investigate.   But this absence of investigation provides the lobbyist with
an incentive to lie  and claim that the electorate is innovative when
it is actually conservative.  Since the lobbyist with a conservative
electorate wants to lobby only if the politician does not
investigate, and the politician wants to investigate only if the
lobbyist with a conservative electorate lobbies, they are playing a
discoordination game, with no equilibrium in pure strategies.

Instead, if the electorate is innovative ($T=\tau $), the lobbyist lobbies
truthfully, and with probability 1. If the electorate is conservative ($T=0 $),
the lobbyist lobbies deceptively  with probability $\theta$  and not at all  with
probability $(1-\theta)$.   If the lobbyist does not lobby, the politician chooses
$\hat{T}  =0$ and does not investigate. If the lobbyist does lobby, the politician
tries to verify  with probability $\gamma$. If he has tried to verify, he chooses
$\hat{T}   =0$ if $T=0$ and $\hat{T}  =\tau $ if $T=\tau $. If he does not
try to verify, he chooses $\hat{T}  =\tau $ with probability 1.


This equilibrium does not exist for all parameter values, because the
politician must have incentive to choose $\hat{T}  =\tau $ if he does not
try to  verify. It will be shown  that he chooses $\hat{T}  =\tau $ without
verification only if
 \begin{equation} \label{e6}
 c_{ver}\leq .5 \tau^2, 
 \end{equation}
 which is therefore a necessary condition for a lobbying equilibrium.
Solving the game back from the end, the expected value of $T$ from
the point of view of the lobbied politician who   does not verify is 
 \begin{equation} \label{e7}
 E (T) = \frac{ \alpha \theta}{\alpha \theta + (1 - \alpha)} \left(0
\right) + \frac{ (1-\alpha)}{\alpha \theta + (1 - \alpha)} \left(\tau 
\right) 
 \end{equation} 
 For the politician to be willing to choose innovate ($\hat{T}   =
\tau $), it must be that $E (T) \geq .5 \tau $, which is true if $\frac{
(1-\alpha)}{\alpha \theta + (1 - \alpha)} \geq .5$, or 
 \begin{equation} \label{e8}
 \theta \leq \frac{1-\alpha}{\alpha}.
 \end{equation} 
 To show that condition (\ref{e8}) implies condition (\ref{e6}), we
must calculate the probability $\theta$. In a mixed-strategy equilibrium, a
player must be indifferent between the pure strategies he employs.
Equating the politician's two pure-strategy payoffs (calculating the payoffs
starting in the subgame where lobbying occurs) gives
 \begin{equation} \label{e9}
 \pi_p(try\; to\;verify) = -c_{ver} = \pi_p(trust\; lobbyist) = 
 -\frac{ \alpha \theta}{\alpha \theta + (1 - \alpha)} \left(0 -\tau 
\right)^2 - \frac{ (1-\alpha)}{\alpha \theta + (1 - \alpha)} \left(\tau -\tau 
\right)^2. 
 \end{equation} 
 Solving (\ref{e9}) gives the equilibrium probability of    lobbying  when
lobbying is pure bluff,
 \begin{equation} \label{e10}
 \theta = \frac{ (1-\alpha) c_{ver}}{\alpha (\tau^2 -c_{ver})}.
 \end{equation} 
  From (\ref{e8}) and (\ref{e10}),  it is apparent that the condition
for a mixed-strategy equilibrium of this kind to exist 
is   $\frac{ (1-\alpha) c_{ver}}{\alpha (\tau^2 -c_{ver})}
 \leq \frac{1-\alpha}{\alpha}$, or $\frac{c_{ver}}{\tau^2-c_{ver}} \leq 1$,  which
after simplification becomes  condition (\ref{e6}).


From (\ref{e5}), the   politician investigates in the no-lobbying regime whenever 
 \begin{equation} \label{e10a}
  c_{inv} \leq (1-\alpha)\tau^2, 
   \end{equation}
a condition which implies,  together with   $\alpha>.5$ and $c_{ver}\leq c_{inv}$,
that
\begin{equation} \label{e10b}
 c_{ver} \leq c_{inv} \leq (1-\alpha)\tau^2 <.5\tau^2.   
   \end{equation}
 Thus, condition (\ref{e6}) holds whenever condition (\ref{e10a}) does, implying
that whenever there would be politician investigation in the no-lobbying regime
there   exists a lobbying  equilibrium in the lobbying regime.
 Sometimes, however,  there  exists a lobbying equilibrium even when the
politician would
not investigate   in the no-lobbying regime.  If $c_{ver}=c_{inv}$, this occurs
if $(1-\alpha)\tau^2 < c_{inv} < \tau^2/2$; if $c_{ver}<c_{inv}$, it occurs over
an even greater parameter range. Thus, the alternative to lobbying  may or may not
be for the politician to investigate on his own.

 
To find $\gamma$, the probability that the politician investigates following
lobbying,  equate the lobbyist's payoffs  from lobbying and not lobbying      when
$T=0$, as must be the case if the lobbyist is willing to adopt a mixed strategy:
 \begin{equation} \label{e11}
 \pi_l(lobby|T=0) = \gamma (0) + (1-\gamma) \beta \tau  - \lambda = \pi_l(not\;
lobby|T=0) =
0.
 \end{equation} 
 Solving equation (\ref{e11}) for $\gamma$ gives
 \begin{equation} \label{e12}
 \gamma = 1 - \frac{\lambda}{\beta\tau }.
 \end{equation} 
 This requires that $  \beta\tau -\lambda  \geq 0$, which was assumption
(\ref{e2a}).
 
   
 Each player's payoff has a pure-strategy component and a mixed
strategy component, depending on events outside his control. The
politician does not investigate if there is no lobbying (which
happens with probability $\alpha(1-\theta)$). His payoff is then    0, because the
absence of lobbying is a sign that $T=0$, and  he can set $\hat{T}  = T=0$. With
probability $(1- \alpha (1-\theta))$   he mixes, and his payoff,   equal to either
of the two pure-strategy payoffs between which he mixes,   equals $-c_{ver}$. His
overall payoff is therefore
    \begin{equation} \label{e13}
    \pi_p   = \alpha(1-\theta) (0) + (1- \alpha (1-\theta))(- c_{ver})
     \end{equation}     
  Substituting for $\theta$ from (\ref{e10}) gives   
         \begin{equation} \label{e13a}
    \pi_p=  \frac{(1-\alpha)   \tau^2 c_{ver}}{\tau^2-c_{ver}}. 
     \end{equation} 
 
 The lobbyist mixes when   $T=0$, which has probability $\alpha$, and his expected
payoff then equals 0,    the payoff from the pure strategy of not lobbying.
  The lobbyist chooses the pure strategy of lobbying when $T=\tau $, which has
probability $(1-\alpha)$, and his payoff then equals $\beta\tau -\lambda$, because
the politician will choose $\hat{T} =\tau $ whether he checks up   or not.
  The lobbyist's  overall payoff is therefore
    \begin{equation} \label{e14}
   \pi_l    =  \alpha (0) + (1-\alpha) (\beta\tau -\lambda).  
  \end{equation} 

 The electorate's payoff is decreasing in the probability that the politician
mistakenly chooses a policy the  electorate dislikes. This probability is the
product of the probabilities that the electorate is conservative, that the
lobbyist lobbies
anyway, and that the politician does not verify, which equals $\alpha \theta (1-
\gamma)$. When the electorate is innovative, lobbying always occurs and the
politician makes no mistakes.  To state the probability in terms
of the parameters instead of the strategies, write it as
 \begin{equation} \label{e14a}
 \begin{array}{ll}
 Prob(mistake) & = (\alpha) \frac{ (1-\alpha) c_{ver}}{\alpha (\tau^2-c_{ver})}
\left(1 -
\left(1 - \frac{\lambda}{\beta\tau } \right) \right)\\
 & \\
  & =  \frac{ (1-\alpha) c_{ver} \lambda }{(\tau^2-c_{ver}) \beta\tau }\\
   & \\
  & = (1-\alpha) \left(\frac{c_{ver}}{(\tau^2-c_{ver})} \right)
\left(\frac{\lambda}{ \beta\tau }
\right)< 1-\alpha,\\
  \end{array}
 \end{equation}
 where the inequality follows because we know  from (\ref{e6}) and (\ref{e2a})
that $c_{ver} <  .5\tau^2$ and $\lambda \leq \beta\tau $ in the mixed-strategy
equilibrium.
  This completes the description of the   equilibrium.

 \bigskip

 Table 1 summarizes the 
 comparative statics for the payoffs, with (+) indicating variables that raise
payoffs and $(-)$ indicating variables that reduce them.   Using equation
(\ref{e14a}),  the  probability of a mistake is  falling in  the politician's
certainty about the electorate ($\alpha$), the   lobbyist's benefit ($\beta$), and
the importance of the issue  ($\tau $).  It is increasing in the verification cost
($c_{ver}$) and the lobbying cost ($\lambda$).
    
     
    The politician's payoff, given in equation (\ref{e13}),  is    decreasing in
the verification cost,\footnote{
    $    \frac{d\pi_p}{dc_{ver}} =  -\frac{(1-\alpha)\tau^2}{\tau^2-c_{ver}} -
\frac{ (1-\alpha) \tau^2 c_{ver}}{(\tau^2-c_{ver})^2} = \frac{(1-\alpha)\tau^2}
{(\tau^2-c_{ver})^2} (-(\tau^2-c_{ver}) - c_{ver}) <0$.} ($c_{ver}$)
    and increasing in the  importance of the issue\footnote{  $  \frac{d\pi_p}
{d\tau^2} =  -\frac{ (1-\alpha)c_{ver}}{\tau^2-c_{ver}}  + \frac{ (1-\alpha)
\tau^2 c_{ver}}{(\tau^2-c_{ver})^2} = \frac{(1-\alpha) \tau^2}{(\tau^2-c_{ver})^2}
(-(\tau^2-c_{ver}) - c_{ver} ) < 0$.}
  ($\tau$)  and the certainty about the electorate ($\alpha$).  It is independent
of the lobbying cost ($\lambda$) and
      lobbyist preference intensity ($\beta$).
  
   The lobbyist's payoff, given in equation (\ref{e14}), is  decreasing in the
politician's certainty about the electorate, because this is also a measure of the
certainty that the  electorate has different preferences from the lobbyist. His
payoff is increasing in the importance of the issue and the intensity of his
preferences, is independent of the verification cost, and is falling in the
lobbyist cost.

\begin{center}
\begin{tabular}{|l|cccccc |} 
 \hline 
      Payoff to: & $\alpha$ & $\tau $ & $\beta$ & $c_{ver}$ &$c_{inv}$  &
$\lambda$\\
     \hline
  Politician  & + &  +  & 0& $-$& 0 &0 \\
  Lobbyist &  $-$ &  + & + & 0 & 0 & $-$ \\ 
 Electorate & +  & + & + &  $-$ &0 & $-$ \\ 
  \hline
   \multicolumn{7}{c}{ } \\
   \multicolumn{7}{c}{TABLE 1: Comparative Statics}
 \end{tabular}
 \end{center}
$\alpha$ =  certainty about the electorate.
 $\tau $ = importance  of the issue. $c_{ver}$ =  verification cost. 
  $\beta$ =  lobbyist benefit. 
   $\lambda$ =  lobbying cost.   
   
 A curious feature   is that the politician's and electorate's payoffs are
increasing in   the importance of the issue. This is particularly puzzling for the
politician, since his ideal payoff is 0, and the bigger is $\tau $  the bigger is
his possible loss. The explanation    is that a large $\tau$ discourages false
lobbying; $\theta$ is decreasing in $\tau$. It does this indirectly. If $\tau $
increases,   the politician would verify more often unless the lobbyist were
deceptive less often.
     
 

\bigskip
Two
other equilibria, somewhat degenerate, exist in the lobbying regime. The
first   is  a pooling equilibrium in which  (a) the lobbyist
 never lobbies,    regardless of the electorate's opinion, and  (b) if
he did lobby, the politician would ignore  him and vote for
the status quo. This is rational for each player if  
the politician has the out-of-equilibrium belief that while potential lobbyists
generally  do not  lobby,  the electorate is as likely to be conservative as
 innovative on the rare occasions when they do.   Given that belief, the
politician will not
change his vote or bother to incur the cost of verification after
being lobbied, so the lobbyist never has incentive to lobby.  This is degenerate,
but not implausible;  if attention-getting lobbying is not traditional in the
political system,   that it would be ignored when tried seems reasonable. When the
parameters are such that the politician investigates for himself in the absence of
a lobbying equilibrium, this equilibrium is especially attractive,   because the
lobbyist prefers that the politician, not himself, investigate. No lobbyist has
any incentive to try to break out of the pooling equilibrium, and the various
equilibrium refinements proposed by game theorists have no bite.

In  another degenerate equilibrium, possible only if $c_{ver} \geq
.5\tau^2$, lobbying occurs  but the politician never verifies. Instead,  he
responds  randomly to lobbying in a different way, sometimes innovating and
sometimes retaining the status quo.  The lobbyist lobbies with
probability 1 if $T=\tau $ and with probability $\theta =
\frac{1-\alpha}{\alpha}$ if $T=0$. If the lobbyist does not lobby, the
politician chooses $\hat{T}  =0$ and does not verify or investigate. If the
lobbyist does lobby, the politician  still does not verify or investigate, but he
chooses $\hat{T}   =\tau $ with probability $ \frac{\lambda}{\beta\tau }$. The
lobbyist is willing to randomize because he is indifferent about
lobbying or not, given the politician's random response. The
politician is willing to randomize because just enough lobbyists of
each type lobby to make him indifferent about the policy he chooses.
This  equilibrium is implausible   because there is no real reason
why the   lobbyist's actions should depend on the electorate's
opinion.   His incentives are exactly the
same whether the electorate is conservative or innovative, yet the equilibrium
requires him to lobby more often when  it is innovative.

%---------------------------------------------------------------
\bigskip
\noindent
 {\bf  5. Comparing Welfare With and Without Lobbying}


 
{\it \underline{ Proposition 1:} 
 If the politician would investigate in the no-lobbying regime,  allowing
lobbying hurts the electorate and the lobbyist  by increasing the number of
mistaken innovations. If the politician would not investigate in the no-lobbying
regime,  allowing
lobbying helps the electorate and the lobbyist  by increasing the
number of correct innovations. Lobbying helps the
politician in either case.}

\noindent
{\it Proof:}
 The lobbyist's payoff under the no-lobbying regime if
the politician would investigate is $ (1-\alpha) \beta\tau $, compared
with $(1-\alpha)(\beta\tau -\lambda)$ from lobbying, so the lobbyist prefers the
no-lobbying regime.   

 The electorate's payoff  is falling in the probability with which the  politician
mistakes
its preferences. In the no-lobbying regime, if the politician
investigates, he makes zero mistakes.  In the lobbying regime, the
probability of a mistake is  given by equation (\ref{e14a}) and is
positive, so the electorate prefers the no-lobbying regime.
Furthermore, these mistakes are always towards too much innovation,
since when the lobbyist is silent, the politician can be completely
sure that the electorate is conservative.

 
The lobbyist's payoff under the no-lobbying regime if the politician
would {\it not} investigate is $ 0$, compared with $(1-\alpha)(\beta\tau -\lambda)
$
from lobbying. Thus, the lobbyist prefers the lobbying regime.

 The electorate's payoff under the no-lobbying regime if the
politician does not investigate  increases in the probability that he is
mistaken, which is $1-\alpha$. With lobbying, the probability of
mistake, given by (\ref{e14a}), is less than $1-\alpha$, so the
electorate prefers lobbying. In addition, the nature of the mistakes
changes: in the no-lobbying regime, there are not enough
innovations, while in the lobbying regime there are too many.

If the politician would investigate under the no-lobbying regime, his
payoff would be $\pi_p=-c_{inv}$, from equation (\ref{e3}). His  lobbying payoff
from equation
(\ref{e13})  is $-\frac{(1-\alpha)\tau^2 c_{ver}}{\tau^2-c_{ver}}$. We know that
$(1-\alpha)\tau^2 < \tau^2-c_{ver}$, because $\alpha >.5$ by assumption  and
condition (\ref{e6}) says that $\tau^2 \geq .5 c_{ver}$.   Hence, the lobbying
payoff of   $-(\frac{(1-\alpha)\tau^2  }{\tau^2-c_{ver}})(c_{ver})$ is more
positive than $-c_{ver}$, which is more positive than $-c_{inv}$, showing that the
politician's payoff is greater in the lobbying regime. More intuitively, the
politician still has the option to investigate independently, so the presence of
lobbying cannot hurt him if he optimizes.

  If the politician would not investigate under the no-lobbying regime,
his payoff would be $  -(1-\alpha)\tau^2$, from equation (\ref{e4}).
Given his payoff from equation (\ref{e13}) and the value of $\theta$
from equation (\ref{e10}), he weakly  prefers the lobbying regime if 
 \begin{equation} \label{e15}
  -(1-\alpha) \tau^2  \leq -\frac{(1-\alpha)\tau^2 c_{ver}}{\tau^2-c_{ver}}, 
   \end{equation}
  which is equivalent to $-(\tau^2-c_{ver}) \leq -c_{ver}$, which is true from
equation (\ref{e6}) if lobbying would occur in the lobbying regime. Hence, the
politician prefers the lobbying regime.  $\Box$


\bigskip

 The key to Proposition 1 is that lobbying is a
substitute for the politician's own investigation. Since he bears the
entire cost of his own investigation, but he  shares the benefit with the
electorate and the lobbyist, his investigation generates    positive
externalities. If he is at the corner solution of zero investigation,
both the lobbyist and the electorate benefit from the
lobbyist's contributing information to the politician. If the
politician would investigate anyway, however, only the politician
benefits from substitution towards acquiring   information from
lobbying. Lobbying is less accurate as a means of information
collection,  because sometimes the lobbyist is trying to deceive the
politician. Moreover, it   is costly to the lobbyist, and has no benefit for him
overall, since the politician knows he is sometimes being
bluffed  and takes action accordingly. It is also harmful to the
electorate, since the politician is willing to be occasionally deceived
in exchange for shifting some of the information cost onto the
lobbyist.

 An interesting feature of the game  is  that the relative costs of different ways
of acquiring information   have little effect on how the information is actually
acquired. Four costs  arise in discovering and communicating   information. The
direct costs  are the politician's investigation cost, $c_{inv}$, and a cost so
far unmentioned in the model,  the lobbyist's cost  of discovering the
information, which we will call $C_L$.  The lobbyist must   decide to incur $C_L$
before he knows whether the electorate is  as innovative as he hopes, so in the
lobbying equilibrium, where his alternative to acquiring information is   a payoff
of zero, he is willing to incur $C_L$ so long as it does not exceed the total
expected payoff from equation (\ref{e14}). Thus, the  condition for    a lobbying
equilibrium  is
     \begin{equation} \label{e17}
   C_L \leq  (1-\alpha) (\beta\tau-\lambda).  
   \end{equation}
    If $\beta$ and $\tau$ are large, $C_L$ can be substantially greater than
$c_{inv}$ and it will still be an equilibrium for the lobbyist, not the
politician, to collect the information. Thus, lobbying can occur even when its
direct costs are higher than those of independent investigation.
 But lobbying also incurs two indirect  costs:  
   the lobbying cost $\lambda$ and the verification cost $c_{ver}$.  Whether the
lobbying equilibrium exists   depends   on $\lambda$ being low enough to satisfy
assumption (\ref{e2a}) that lobbying is worth the cost to the lobbyist  and on
$c_{ver}$ not being so high as to violate equation (\ref{e6}).\footnote{Austen-
Smith \& Wright (1992) also note that the politician  can prefer   lobbying and
occasional verification to direct investigation (their Proposition 5).  This  can
even be true if the cost of verification is greater than the cost of
investigation, a result which would also obtain in the present model if  $c_{ver}>
c_{inv}$ and lobbying somehow precluded direct investigation.}
 
 
 Proposition 1 is stated in terms of whether the politician
investigates or not. Another way to  think about the conditions under which
attention-getting lobbying is desirable is in terms of the model's primitive
parameters.    The condition under which the politician investigates in
the no-lobbying regime is given by equation (\ref{e5}): 
 $$
(6) \;\;\;\;\;\;\;\;\;\;\; c_{inv} < (1-\alpha)\tau^2.
 $$
  When (\ref{e5}) is false,   all parties benefit from lobbying, giving the
results in Proposition 2.
 
 {\it \underline{ Proposition 2:}  Lobbying raises welfare when the
politician's investigation costs are higher, the politician is  more certain of
the electorate's views,  and the issue is less important; that is, if
 $c_{inv}$ and $\alpha$ are large  and $\tau $ is small. The politician's
verification cost, $c_{ver}$,  is irrelevant to whether lobbying raises welfare. }
 
 Proposition 2 suggests that 
attention-getting  lobbying should   be encouraged by public policy when it
concerns    minor
technical issues on which the politician is  satisfied with his uninformed
position and finds independent investigation too costly.  This would not be
surprising in a model of lobbying as the direct provision of
information, and it is the implication of the   ``service
bureau'' view of lobbying as the provision of services to politicians
whose minds are already decided (see Bauer, Pool and Dexter [1963] or  Gilligan
and Krehbiel
[1989]).  The same result is true  here, however, where lobbying is
purely a way for the lobbyist to claim that if
the politician investigated himself he would agree with the lobbyist,   
and where the public benefit  is not improved technical
crafting of legislation, but changing the mind of the confident but wrong
politician.

 The comparative statics results in Table 1   have welfare implications when the
question is not whether lobbying should be discouraged, but how it might be
regulated.    The probability of a mistake rises in
the lobbying cost   and the verification cost  and falls in
the importance of making a correct decision,  the intensity of
lobbyist preferences,  and the  politician's certainty about the electorate's
position.      Thus, given that lobbying is going to occur, public policy
should be directed at reducing the cost of both lobbying and  verification, and at
increasing the
intensity of lobbyist preferences. This last point   implies that   bills  that
both strongly redistribute resources to special interest groups  and are
attractive to the electorate at large,  will
be more often correctly passed, because the special interests will
have more incentive to lobby.    The channel through which lobbyist intensity
reduces
mistakes is the politician's probability of investigation, given by
(\ref{e12}); the politician, knowing that   the lobbyist's preferences are
intense,    verifies their information    more often to deter false claims.
Lobbying as bribery or as provision of technical information may have quite
different implications, but  in the case of   attention-getting lobbying the best
policy is either to ban it entirely, or   make sure that   lobbyists  have such
strong   incentives  that the
politicians will not trust them  too far. 

\bigskip
\noindent
{\bf 6. Extensions and Conclusions}

 
 The lobbying game can be usefully compared with another class of games  in which
investigation takes place:     signalling
models of advertising in the tradition of Nelson (1974). In such models,
sellers do not advertise to provide direct information
to the customer, but to signal   that the seller is
willing to bet his profits on the customer liking the product if he buys
it. If the quality is actually low, the customer will not make
repeat purchases, and the seller will incur losses, given the high cost
of   advertising.  The  investigation and
voting decisions in the lobbying game are    combined in the purchase decision in
the advertising model, so in equilibrium the customer always investigates.  This
need not be
the case, however, and the lobbying game can easily be adapted to become
  an advertising model with one-time purchase and the possibility of
the customer engaging in costly pre-purchase quality investigation.
  
  A difference between advertising and lobbying   lies in the agency problem
between politician and electorate. In my  discussion, I  implicitly assume that
public policy should respond solely to the
electorate's desire and that the politician's payoff is trivial by
comparison. This is not exactly correct, since investigation and verification do
incur real costs.   Ideally, the electorate would construct  a payoff function for
their agent, the politician, setting his disutility from
voting against them    so that he   
will investigate efficiently, refraining from investigation only when       his
personal  cost   is greater than the electorate's benefit.
 The world is unlikely to be in the first-best,
however, and in the  likely case that the politician has insufficient
incentive to match the electorate, public policy should look to the
electorate's welfare, not the politicians.


  The reader should recall that the model also applies to political demonstrations
when the aim   is not to threaten but to  persuade. The model's implication
becomes that protests increase welfare if the politician would not investigate the
issue in their absence.\footnote{    A difference from lobbying is that  protests
may serve as a means to attract the attention of other citizens  who on
verifying the protestor's claims might discover that their own opinions were more
popular than they had believed. This  could lead to equilibrium shifts of the kind
discussed in Kuran (1989).}  Protests are most useful when they concern issues
that are mistakenly thought to be uncontroversial or  are difficult  for the
politician or citizens outside the protest group to investigate directly.
 Protests are harmful when they concern issues that   would be investigated even
without the protests,    because trust in the protestors, who are sometimes
bluffing, is substituted for independent discovery.
  
  
   The model might also be applied to influence activities within the private
sector. Middle managers lobby top managers for shares of the budget, promotions,
and salary increases,  and in a certain number of these cases, when the desired
actions are efficient business decisions,  the interests of the shareholders will
be aligned with those of the middle managers.  The top managers have a choice
between collecting their own information, relying on the middle managers' reports,
or checking on the reports, and they may  sometimes sacrifice shareholder
interests to avoid personal costs. Political science applies in this context just
as in the case of governments.    Milgrom \& Roberts (1988) have modelled
influence activities formally, analyzing whether employers should allow employees
to spend part of their time lobbying for promotions. They conclude that the
employer  should restrict the amount of lobbying, but not eliminate it altogether.
The present model suggests that the business should encourage influence activities
when it is difficult for the employer to discover the information himself and
where the employer is certain enough of the truth that he would not try to  verify
it without the stimulus of lobbying, but that the business should discourage
influence activities when they displace direct investigation of the top managers.
   
   
   Decisionmakers, whether they be politicians or top managers, always have the
option of collecting their own information about the best policy to undertake, but
information collection is costly. Lobbyists and protestors serve the useful
function of providing the information  at no direct cost to the decisionmaker.
These interested parties are not entirely reliable, however, and unless the
politician is willing to expend resources on verifying the information, he may
well make the wrong decision.  If politicians never checked on lobbyist reports,
lobbyists would never be truthful and would never affect political decisions. If
politicians always checked, then lobbyists would always be truthful but this would
deprive the politicians of any motive to check on them.  The equilibrium consists
of a careful balance between   politician trustfulness and the lobbyist
trustworthiness, in which lobbyists are never sure whether their information will
be trusted  and politicians are never sure whether it should be trusted. From the
point of view of the voters, such an equilibrium is desirable if the politician
would otherwise decide not to investigate independently, but it is undesirable if
it displaces independent investigation.   Lobbying is most desirable when it is
concerns   issues on which the politician is  falsely  confident, especially if
the issue is minor or technical,  since it is in these cases that the politician
would not   investigate himself.
   
   
   

%---------------------------------------------------------------
\newpage

\noindent
{\bf References}

Ainsworth, Scott (1991) ``Regulating Lobbyists and Interest Group
Influence,'' working paper, Department of Political Science,
University of Georgia.


Ainsworth, Scott  and Itai Sened (1991) ``The Role of Lobbyists:
Entrepreneurs with Two Audiences,'' working paper, 
 Department of Political Science,
University of Georgia.

 Austen-Smith, David and John Wright (1992) ``Competitive Lobbying for
Legislators' Votes,''  {\it Social Choice and Welfare},  9: 229-257. 

 
Ball, Richard
(1991) ``Political Lobbying as Welfare Improving Signalling,''
working paper, Dept. of Agricultural and Resource Economics,
University of California, Berkeley, July 1991.


Bauer, Raymond, Ithiel Pool, and Lewis Dexter (1963), {\it American
Business and Public Policy}, New York: Atherton.


Gilligan, Thomas and Keith Krehbiel (1989) ``Asymmetric Information
and Legislative Rules with  a Heterogeneous Committee,'' {\it
American Journal of Political Science}, 31: 459-490.

Kuran, Timur (1989) ``Sparks and  Prairie Fires: A Theory of Unanticipated
Political Revolution,'' {\it Public Choice}, April 1989, 61: 41-74.

Lohmann, Susanne (1991)  ``Information Versus Manipulation: A
Signaling Theory of Political Action,'' Stanford Graduate School of
Business Research Paper Number 1131. March 1991.

Milgrom, Paul and John Roberts (1986) ``Relying on the Information of Interested
Parties,'' {\it Rand Journal of Economics}, Spring 1986, 17: 18-32.

Milgrom, Paul and John Roberts (1988) ``An Economic Approach to Influence
Activities in Organizations,'' {\it American Journal of Sociology}, 94: S154-S179.

  Nelson, Philip  (1974) ``Advertising as Information''  {\it Journal
of Political Economy.} July/August 1974.  84, 4: 729-54.

Rasmusen, Eric (1989) {\it Games and Information}. Oxford: Basil Blackwell, 1989.

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