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         \begin{center}
\begin{large}
         {\bf  Trivial Bribes and the Corruption Ban: A Coordination
Game Among Rational Legislators} \\
  \end{large}


        \bigskip
 Eric Rasmusen and J. Mark Ramseyer*\\


Published: {\it Public Choice} (1994) 78: 305-327.\\


        {\it Abstract}
        \end{center}

 \begin{small}
  Legislators in modern democracies  (a) accept bribes that are
small compared to value of the statutes they pass and (b) allow bans
against bribery to be enforced.   In our
model of bribery, rational legislators  accept bribes smaller not only
than the benefit the briber receives but  than
the costs the legislators incur in accepting the  bribes.  Rather than
risk
this outcome, the legislators may be willing to suppress
bribery altogether.
The  size of legislatures, the quality of voter information, the
nature of party organization, and the structure of committees will all
influence the frequency and size of bribes.




\noindent
 Ramseyer:  University of Chicago Law School, Chicago, Illinois,
60637. On leave at the University of Tokyo until January, 1993.  \\
 Rasmusen: Indiana University School of Business, Bloomington, Indiana
47405.  Off.:(812) 855-3345.   Fax: (812) 855-8679, Internet:
Erasmuse@ucs.indiana.edu.\\


                \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.\\

 *We gratefully acknowledge the support of the Olin Foundation and the
Center for the Study
of the Economy and the State at the University of Chicago,    the
comments of Jeff Lange, Daniel Lowenstein, George Michaelides, Frances
Rosenbluth,
participants in the Econometric Society 1990 Winter Meetings and the
UCLA Political Economy Lunch Group, and
especially the generous encouragement and comments of  John Wiley.
Much of this work was done while the authors were at the UCLA School
of Law, Harvard Law School,  UCLA's  Anderson Graduate School of
Management,  and Yale Law School.



 \end{small}
 %---------------------------------------------------------------


        \newpage

\noindent
 1. \underline{Introduction}

Bribery is both pervasive and pervasively illegal. But even
where bribes are legal (for by ``bribes'' we will mean payments
to government officials for specific favors,
whether legal or illegal), politicians often sell their votes for
amounts  trivial relative to the value of the favors
bestowed. Where dictators like Ferdinand Marcos sell their favors
dear, democratic
legislators  sell them cheap.  Seldom, it seems, do they
collect aggregate payoffs that even approach the value of
the statutes they sell.  Together with the criminal penalties for
bribery, that value ought to induce legislators to sell high.
Instead, they sell low, and the  public is more often appalled by
bribes's trivial size than by their lavishness.  Consider the ``Grey
Wolves'' of the 1892 Chicago city council:



 \begin{small}
\begin{quotation}
  The irksome aspect of boodling to the civic-minded was not only
that the vicious system corrupted the whole of Chicago politics but
that the city gained from the passage of boodle ordinances hardly a
cent in compensation. Even the grafting aldermen, receiving as little
as \$100 or as much as \$25,000, actually were being paid only a
small fraction of the real worth of the privileges they were selling.
(Wendt \& Kogan, 1943: 35)
 \end{quotation}\end{small}



   At first glance, such behavior hardly seems rational on the part of
the wolves, as
 Gordon Tullock has noted ({\it
e.g.}, Tullock, 1980b: 32;1990: 201).  Indeed, the phenomenon of
profitable rent-seeking is sometimes called the ``Tullock Paradox``
after his observations.  But legislators seem just as irrational when
they ban bribes and thereby restrict their own behavior.  Voting for
bans on bribery may be politically advantageous, but the legislators
could  ban bribes formally while preventing executive enforcement of
the ban.    Nonetheless, they frequently not only ban bribes, but
fund government institutions to  enforce the bans.  If legislators are
truly the rational wealth-maximizers that public-choice analysts have
pictured them to be, an explanation for these enforced bans must be
found.

	Thus, we face two puzzles. Our first puzzle is  the small size
of bribes.  Almost always,  legislators sell their collective services
for less than their value to the buyer.  In many cases, they seem to
sell them for less even  than the expected political and  criminal
costs of providing the services for pay.
The anecdotes
are endless. New York Congressman Mario Biaggi
manipulated the federal government to save from bankruptcy an
enormous Brooklyn dockyard.  For this, he received three Florida
vacations worth \$3000 (Tullock, 1990: 200). The 56 members of
the Senate Finance and House Ways \& Means committees have
jurisdiction over \$400 billion in tax revenues, but ro reeelection
they  raised just
\$20 million  in a recent year(Tullock, 1990: 200-201; Shaviro, 1990:
73).
Alabama state legislators can concurrently hold jobs at local
colleges.  For every $1 they receive in salary from a given college,
they route the school an extra $19 in public funds (Couch, Atkinson \&
Shughart, 1992).  In the 1790s, several Georgia legislators sold 35
million acres of state land at $500,000, a price far below market
value.  For this, they took bribes of about $1000 each.  The incident
became known as the "Yazoo scandal," and for their part in it all but
two of the legislators involved lost their jobs in the next election.
Apparently, they
  sold a valuable asset for a small
amount, and lost office besides (Noonan, 1984: 436-442). From the
1790's to the 1980's,
the vote industry seems sometimes to please its lobbyist customers,
sometimes to ignore them, and perennially to operate at prices below
average cost.  Critics of public choice delight in the puzzle ({\it
e.g.}, Shaviro, 1990: 73).  If legislators are not becoming rich,
they must not be maximizing wealth; the talk of political markets
must be no more than talk.

To be sure, public-choice scholars have suggested several reasons for
these cheap bribes.  Where bribes are illegal, for example, lobbyists
may incur large risks in assembling a bribing coalition.  Where
lobbyists can make take-it-or-leave-it offers, they may place the
legislator in a disadvantageous bargaining position.  Where many
legislators will take bribes, they may compete down the price.  Where
property rights are statutory rather than constitutional, legislators
may receive less because they can renege on any rent-dispensing deal
they make with the bribing lobbyist.  Although each of these factors
suggests bribes should be low, the costs of bribery to the legislator
should nonetheless place a floor on the size of the bribes.  Our model
will suggest a more startling result:  at times, bribes should not
just be low, they should be insignificant.

Our second puzzle is the bribery ban.  Why society as a whole gains
by banning bribes is straightforward: bribes generate a wide variety
of inefficient agency costs and hold-up problems. But bans must be
passed by statute, and policing agencies must be funded.  If
legislators can collect money by accepting bribes, why do they pass
bans and fund enforcement efforts?  To be sure, rational voters might
find it profitable to pay legislators an amount equal to the expected
value of their foregone future bribes in exchange for a ban on such
bribes.\footnote{One simple way to accomplish this would be by paying
them salaries that are high in comparison to present political
salaries but low in comparison to the losses from special-interest
legislation. The high wage would act as an ``efficiency wage,''
making the legislators cautious about any activity that might lose
them their offices. See Rasmusen (forthcoming).  But this does not
address
the enforcement question.} But even if voters made such a deal, they
would find it hard to enforce--- rational legislators ought to pocket
the payment and revoke the ban.  Notwithstanding that logic, most
modern democracies enforce a ban on bribes.


We use a coordination game between wealth-maximizing legislators
to show why cheap bribes are fully consistent with a market analysis:
if self-interested legislators cannot coordinate their
actions, they may supply private-interest statutes for bribes less
than the costs they incur.  Only when they can negotiate agreements
with each other, solving a coordination problem, will they obtain
bribes that equal their costs.  Only when they can {\it enforce}
agreements with each other, solving a prisoner's-dilemma problem, will
they come close to collecting the full benefit of the statutes they
pass.


 Our explanation for the  paradox of bribery bans follows from our
explanation for the cheap price of special-interest statutes.  We
show that if bribery is only mildly difficult, then legislators may
find it individually advantageous but collectively disadvantageous to
sell their votes for small bribes.  Were legislators able to take
bribes legally, in short, they would not necessarily obtain large
bribes.  And if legislators would not obtain large bribes even if
bribery were legal, then voters might not find it prohibitively
expensive to convince them to ban the bribes altogether.

	Insignificant bribes do not {\it always} follow in our model.
Instead, the price and quantity of bribery depend on a variety of
factors:  on the penalties convicted legislators face, on the rents
lobbyists earn, on the propensity of voters to reject incumbents
indiscriminately, on the ability of legislators to coordinate their
actions, and on the transaction costs of bribery.  Accordingly, we
explore the implications not only of the size of rents and penalties,
but of party organization, committee structure, and other exogenous
political institutions on the frequency and size of bribes.  We
conclude with several further implications:  the larger the
legislature, the smaller will be the bribes paid and the greater will
be the likelihood of a bribery ban; the more parties involved in
making a political decision, the greater will be the likelihood of
inefficient private-interest statutes; and the better informed the
voters, the larger will be any bribes paid.

 We have organized the paper as follows.
We begin by surveying the public-choice commentary on corruption
(Section 2).  We then turn to the heart of the paper: a game between
bribe-taking legislators and incompletely informed voters (Section
3.1).  We derive the pure-strategy and mixed-strategy equilibria in
simultaneous (Section 3.2) and sequential (Section 3.3) versions of
this game.  Finally, we generalize the model (Section 4) and discuss
its implications (Section 5).




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


 \pagebreak
 \noindent
 2. \underline{Extant Explanations}

Many observers purport to explain patterns of corruption through
moral norms or ideological tastes (Kelman, 1988; Mikva, 1988).  If
legislators fail to earn bribes that capture their marginal product,
such observers imply, they fail because they pursue ideas rather than
money.  To be sure, ideological tastes may explain some Congressional
voting patterns.\footnote{Nelson \& Silberberg (1987); Kalt \& Zupan
(1984); Kau \& Rubin (1979).  Exactly how much ideology does explain
remains unclear.  See Dougan \& Munger (1989); Lott (1987); Peltzman
(1984).} Yet ideology cannot explain why bribes are small.  Suppose
ideologically correct legislators prefer honesty to corruption.  If
so, their scruples simply raise the opportunity costs (foregone moral
satisfaction) of corruption.  As the fraction of legislators with
such scruples increases, the supply curve for private-interest
statutes will shift to the northwest, and two consequences will
follow.  First, legislators will sell fewer private-interest
statutes, but those they sell will command a {\it higher} price.
Second, if the demand for such statutes is sufficiently inelastic
(absent transferrable tax benefits, for example, firms can only use
so many investment tax credits), the {\it total} resources lobbyists
devote to bribery will increase.  Whatever the detail, the basic
point is simple: ideology raises, not lowers, the size of bribes.

   Other scholars propose more promising explanations for the small
size of bribes.  For example, Tullock (1980a) notes that the amounts
a lobbyist will invest in efforts to obtain a statute will depend on
his probability of success, which in turn will depend on what
competing lobbyists do.  Given this uncertainty, some lobbyists will
invest far less (but some far more) than the wealth the statute would
transfer.  Tullock (1990) ascribes the low price of bribes to the
inefficiency of most rent-transferring regulatory arrangements. Snyder
(1991) and Denzau \& Munger (1986) argue that lobbyists will most
often
bribe legislators with policy preferences closest to their own, and
that this will drive down the average size of bribes paid.

Landes \& Posner (1975) and McChesney (1987) note that legislators
cannot always credibly promise that a statute will stay in effect.
Given
this uncertain durability, lobbyists may proffer smaller bribes than
they would otherwise pay.  Finally, Baysinger, Ekelund \& Tollison
(1980) argue that the large size of most democratic legislatures
increases the transaction costs to lobbying, while Browning (1980)
and Rose-Ackerman (1978: 45-48) note that the lobbyists themselves
may sometimes encounter coordination problems.

We take a different approach.  We suppose that
the legislative outcome is certain and durable, and that the lobbying
process is free.  Even here, we show, rational wealth-maximizing
legislators may sell their votes for aggregate amounts less than the
total costs they incur.

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

 \noindent
3. \underline{Coordination and legislative pricing}

 \noindent
3.1. \underline{Legislative production costs.}
 A legislator incurs a variety of costs when he votes for a statute
in exchange for a bribe. If his constituents detect the
bribe, the bribe increases the chance that they will reject him at
the next election. If lobbyists must bribe a legislator to pass
the statute, then presumably his constituents dislike the statute, so
the yes vote (or even just the statute's passage) will hurt his
reelection chances.
Most directly, voters can
unseat legislator $i$ if they dislike the way he votes.  On the issues
that
matter most to them, some constituents  follow their
representative's voting record, and some   others rely on voting
summaries they
obtain from groups they trust (e.g., Americans for Democratic Action
or
the  National Rifle Association).Because voters economize on
information, legislators also incur costs when their party (or
occasionally their legislature) passes statutes that voters do not
like.  Two reasons account for this.  Most simply, voters sometimes
attach ``guilt by association.''  Because they have less than perfect
information, they sometimes vote against a legislator whenever they
think the legislature as a whole has done poorly.

	More realistically, voters rely on the reputational capital
that political parties create.  They vote in candidates from parties
with reputations they like, and vote out those from parties with
reputations they despise.  Because the phenomenon cuts both ways,
party leaders will try to use it strategically:  to choose a portfolio
of policies that will maximize the party's chance of building and
maintaining a legislative majority.  To the extent that they can
enforce party discipline on their members, voters will then simply
vote by party.  And to the extent that voters do, a candidate's
fortunes will depend critically on how {\it other} members of his
party vote.  After Watergate, for example, voters in 1974 cut the
number of Republican Senators they returned to office by 5 and the
number of Representatives by 48. \footnote{xxxx (present f.n. 5) }

	Moreover, because party leaders will instruct legislators to
vote strategically, rational voters sometimes have no choice but to
ignore their representative's voting record.  They will vote instead
on the basis of their representative's party's record.  They do so
because the party leaders may have rigged their representative's
votes--- the leaders may have let him vote as he did because it did
not need his vote.  According to Illinois state senator Judy Topinka,
for example, ``[v]ery often with simple majorities you see structured
votes -- `You put up X number on your side, and we'll put up X number
on our side.'  That way you keep off people in swing districts and let
some people keep a low profile.''\footnote{``Tax Revolt,'' {\it
Chicago Reader}, 20 April 1990, p. 24.}  The Gulf war illustrated this
phenomenon. After George Bush had obtained his vote for  war,
Democratic Representative Torricelli reported that ten more Democrats
were available {\it if needed.}\footnote{{\it New Republic}, 4 Feb.
1991, p. 16.}  All that voters can do in response to such strategic
voting is to vote out all incumbents or all members of the erring
party, regardless of how any one incumbent votes.\footnote{For
empirical evidence of strategic voting against the incumbent majority
members, see Lewis-Beck (1990). Other studies include Cox (1987),
Denzau, Riker and Shepsle (1985),  and Ferejohn \&
Calvert (1984). }

	In short, the the costs of information create reputational
externalities.  When voters do not discriminate perfectly, they will
vote on the basis not just of how a legislator has voted, but also of
how {\it other} legislators have voted.  And when they do, their
``throw the rascals out'' effect can swamp any sympathy they might
otherwise have for their own representative.


 Careful analysis of the costs of bribery to the legislator deserves
independent study, but for present purposes
what matters is only how different kinds of costs affect the size of
bribes. For this, what is important is how a cost depends on the
behavior of other legislators, not whether the cost arises from
voters, police, or conscience, or whether it is an expected cost or a
known cost. In the general model analyzed below in Section 4, we
will divide a legislator's costs from bribery into: (1) the cost of
personally voting Yes on a statute that fails ($C_{pf}$); (2) the
cost of personally voting Yes on a statute that succeeds ($C_{ps}$);
and (3) the cost (to oneself) of the legislature having enacted a
private-interest statute ($C_o$).



In Section 3.2, we construct a game in which legislators are
simultaneously bribed and, if the statute passes, voters concern
themselves only with the legislature's general record.  As noted
earlier, in a more realistic model voters may concern themselves with
their incumbent's {\it party}'s general record rather than with the
legislature's record.  We structure the discussion below by the
legislature's record only for expositional simplicity -- the model
would not otherwise change.  The game (an
adaption of the model of exclusive-dealing contracts in Rasmusen,
Ramseyer \& Wiley (1991)) is a simultaneous game with two symmetric
pure-strategy equilibria (Sections 3.2.1 \& 3.2.2).  If legislator
$i$ thinks the other legislators will sell their votes, then $i$ too
will sell.  The legislators will sell, however, at a collective price
both below the value of the wealth transfers involved and below the
costs they incur from voter dissatisfaction.  On the other hand, if
$i$ thinks the others will refuse to sell, $i$ too may refuse.  In
short, both the statute's passing and its failing are Nash
equilibria.  We conclude our discussion of the model by analyzing
mixed strategy equilibria (Section 3.2.4) and sequential games with
full communication (Section 3.3).  The particular payoffs used in
Section 3 will be slightly restricted for simplicity (we will assume
$C_o=0$), and Section 4 will return to greater generality.

 \bigskip
\noindent
 3.2  \underline{The simultaneous game:}\\
  3.2.1 \underline{Pure-strategy equilibria}.  The players are $N$
identical legislators, and one lobbyist $L$.  The lobbyist may offer
a bribe of $X$ in exchange for a positive vote on a statute that
would give him a benefit of $R$.  Legislator $i$ may accept $X$ and
vote ``yes,'' or reject $X$ and vote ``no''. A statute passes if
$\overline{Y}$
legislators vote ``yes,'' where $\overline{Y}$ could be $1/2 N$, $2/3
N$, or
some other margin (including $\overline{Y}=1$---see Section 3.2.3).

As noted above, legislator $i$ can lose office either because of his
own vote (thus generating ``personal costs'' $C_p$) or because of the
statutes his colleagues pass (``outcome costs'' $C_o$).  In this
section
of the article, we assume that the outcome costs overwhelm the
personal costs when voters ``turn the rascals out,'' so that the
legislator incurs a cost of $C_p$ if he votes for a statute that
fails to pass.\footnote{If the legislator's voting for a
successful bill cost him $ C_p + C_o > C_o$, then the general
character
of the equilibrium is unaffected, but (a) the bribes are
positive, though smaller than his total costs $C_o + C_p$ or $R$, and
(b) the
lobbyist  therefore only bribes the minimum number of legislators
needed for passage. We analyze this perhaps more realistic, but
undoubtedly more complex case in Section 4.}

The legislator's payoff  equals his bribe
income minus any costs he incurs. Thus, if he is bribed $X$ and votes
for a successful bill his payoff is $X-C_o$; if he is bribed and
votes for a failed bill his payoff is $X-C_p$; and if he votes
against a successful bill his payoff is $-C_o$. Table 1 summarizes
these payoffs.


\begin{center}

 \begin{tabular}{llrcc}
                    &       &           &\multicolumn{2}{c}{\bf
Other legislators }\\
                    &       &           &  No & Yes      \\
&       &           &             &            \\
                    &       & No&   0       & $-C_o$    \\
         &{\bf Legislator $i$}&           &             &
\\
                    &       &   Yes  &  $X-C_p$      &  $X-C_o$  \\
&       &           &             &            \\
\end{tabular}

{\bf Table 1: Payoffs to Legislator i in the simultaneous game}
\end{center}

The order of play is simple.  First, the lobbyist simultaneously
offers each legislator a bribe $X$, payable if and only if the
legislator votes for the statute.  Second, without communicating with
each other, the legislators each decide whether to accept the bribe.

Proposition 1 states that this game has two pure-strategy Nash
equilibria: one in which the bill succeeds even though the bribe is
$X=0$, and one in which it fails. If the lobbyist's valuation is high
enough, there is just one equilibrium, in which the bill succeeds.
The size of the bribe and the type of equilibrium depend on the
lobbyist's valuation of the bill.

\bigskip

{\it PROPOSITION 1: Let R be the lobbyist's valuation of the bill,
$\overline{Y}$ be the number of votes needed for passage, $X$ be the
bribe and $C_p$ be the legislator's personal cost from voting for the
bill. If $R<\overline{Y}C_p$, there are two pure-strategy Nash
equilibria:

(SUCCESS) $X=0$, all legislators vote ``yes,'' and the statute
succeeds.

(FAILURE) $X < C_p$, all legislators vote ``no'', and the statute
fails.

\noindent
 If $R  \geq \overline{Y}C_p$, then SUCCESS is the only equilibrium.
  }%end of italics.

\bigskip

PROOF: Suppose $i$ believes all other legislators will vote ``yes.''
If so, the statute will pass.  Hence, $i$ will suffer a loss of $C_o$
however $i$ votes, and $i$ will vote ``yes'' for a bribe of $X=0$.
Because all legislators will vote ``yes,'' the lobbyist $L$ has no
incentive to offer more than $X=0$.\footnote{Legislator $  i$ will
vote ``yes,'' in other words, for an arbitrarily small bribe.  We
assume that a legislator who is indifferent between accepting and
rejecting a bribe will accept.  This assumption, customary in
rational-choice modelling, rules out certain weak Nash equilibria and
avoids the open-set existence problem that would arise if the lobbyist
had to offer the legislator an infinitessimally small bribe of $X >
0$.}
  If there were an equilibrium
with $X>0$, the lobbyist could deviate by offering $X=0$ and the
individual legislator, believing that the statute would pass anyway,
would accept $X=0$; deviation would therefore be profitable and such
an equilibrium cannot exist.


Suppose $i$ believes all other legislators will vote ``no.'' If so,
the statute will fail.  Hence, $i$ will vote ``yes'' if and only if
offered a bribe $X$ larger than the threat to $i$'s career generated
by $i$'s own ``yes'' vote (unless $X \geq C_p$). If $R <
\overline{Y}C_p$, $L$ will not find it profitable to offer
$\overline{Y}$ legislators a bribe of $ X \geq C_p$ and FAILURE will
be a Nash equilibrium.  If $R \geq \overline{Y}C_p$, on the other
hand, $L$ will find it profitable to offer such a bribe to
$\overline{Y}$ legislators, and FAILURE will not be an equilibrium.
Hence, success is the only equilibrium if $R \geq \overline{Y}C_p$.
$\Box$


\bigskip

3.2.2 \underline{A heuristic example.} A simple example comparing an
autocratic government with a democratic one may be useful.  Suppose
that private-interest statute S14 would provide a benefit of 14 for a
lobbyist and would cost an autocratic government 50 because of the
increased probability of revolution.  The autocrat will supply this
statute only if offered at least 50, which the lobbyist is unwilling
to offer, so S14 will fail. Suppose that a second statute, S80, would
cost the autocrat 50 but benefit the lobbyist by 80. The autocrat
will supply this statute if offered 50, and if he is a good bargainer
he may obtain a bribe of up to 80.\footnote{Rose-Ackerman (1978:
45-48) notes that well-organized legislators may be able to extort
larger amounts than disorganized legislators--- a point consistent
with our model.  Our thesis differs from Rose-Ackerman's in the way
we explain how a poorly organized legislature will sell votes for
amounts {\it below} the costs the legislators incur--- for
infinitesimally small amounts.}


Suppose, however, that the state is a democracy with five legislators
who must vote on statutes S14 and S80.  For each statute, each
legislator loses 5 by voting ``yes'' when the others vote ``no,'' but
10 if the statute passes.  The government thus loses a total of 50 if
a statute passes--- the same cost that the autocratic government
incurs.

 Consider first the statute S14.  If each legislator thinks that the
others will vote ``no,'' then all voting ``no'' will be the
equilibrium. The lobbyist could overcome these expectations by
offering a bribe of 5, but that is too costly for him: bribing three
legislators at a total cost of 15 to obtain a statute worth 14 is bad
business.  But if each legislator thinks the others will vote
``yes,'' then each may as well vote ``yes'' and join the crowd.  He
will lose 10 regardless of how he votes, so he will agree to
vote ``yes'' for an infinitesimally small bribe.  Expectations are
crucial, and it is on forming expectations that the lobbyist should
spend his money.

But consider also the statute S80. Here too, there is an equilibrium
in which the statute passes with an infinitesimally small bribe, and,
in fact, this is the only equilibrium.  One might think that there is
also an equilibrium with a successful bribe of 5, but there is not.
If there were, then all five legislators would vote for the bill,
even if only three were bribed, since all of them know the bill will
pass. But then if the lobbyist refrains from paying the bribe to a
legislator, he still might as well vote for the bill---he will lose
the 10 anyway, and voting against the bill does not help him.

 Thus, democratic legislators may refuse to sell a statute at all (a
Nash equilibrium), or they may sell it cheap (another Nash
equilibrium), but they will not sell it dear.  Also, democratic
states may sell private-interest statutes that an autocratic state
would not.  Where autocrats can limit the statutes supplied to those
that generate profits at least as large as the costs they incur,
democratic legislatures cannot without additional institutions.


 3.2.3  \underline{Additional implications.}  At stake is one of the
differences between market
competition and political competition: each legislator's vote
potentially imposes an externality on every other legislator.  Like
firms in a market, legislators may compete the price of their vote
down to marginal cost.  Unlike such firms, they do not control their
marginal cost.  Instead, each legislator's marginal cost depends on
what his colleagues do: each legislator's marginal cost to
voting ``yes'' is 0 if a majority of the others votes ``yes,'' and 5
if a majority votes ``no''. Effectively, that externality can prevent
all legislators from breaking even.  Even when the passage of the
statute costs each legislator 10, each may agree to vote ``yes'' for
a miniscule bribe.

  Because of this coordination problem, wealth-maximizing legislators
may rationally support institutions that make
bribing individual legislators difficult (though lobbyists will
oppose such institutions). One way to do this is to make bribery
illegal and impose heavy penalties on lobbyists who pay the
bribes.\footnote{Putting criminal penalties on the legislator caught
taking the bribe has a slightly more complicated effect, since it
puts a wedge between the payoffs of the legislator who takes the
bribe when the statute passes and the legislator who refuses the
bribe.  We deal with this as Case 3 in Section 4, which generalizes
the model in this section.}

 A second way for legislators to deal with the problem is to
create  institutions which prevent the game from playing out the
Success equilibrium.  Our argument so far has hinged on the inability
of legislators to coordinate their actions.  The lobbyist can succeed
in getting his legislation cheaply if he can create an expectation in
the minds of the legislators that he will succeed. If the legislators
have time and organization enough to reassure each other that they
will vote against the legislation, then the Failure equilibrium
becomes more probable. The simplest institution
for this purpose is the party leader: the legislators delegate their
votes to one of their number who acts as cartel ringmaster, accepting
bribes and deciding which statutes are to pass.

 Note that political organization produces ambiguous results as far
as the total amount of bribery is concerned.  Politicians might
organize to effect a Failure equilibrium; they may also organize to
raise the price of the bribes paid in the Success equilibrium.  In
some legislatures, legislators have apparently centralized bribery.
Japanese legislators, for example, have organized themselves into
disciplined factions that receive enormous pay-offs. Although
competing factions still exist within it, at  least one
observer estimates that from 1966 to 1975, members of the ruling
Liberal Democratic Party received assorted payoffs of \$2.5 billion
(Sasago, 1988: 39).\footnote{xxx Quite tangentially Mark: Has anyone
suggested that one reason  Japanese busienss does so well might be the
corruptness of the politicians? Mayb the way to catch up with the
Japanese is to get rid of ``good governemnt'' in the US A.}

  Alternatively, legislators may be able to avoid unfavorable
equilibria through the committee system.  Were the legislators
to delegate the authority to accept bribes to a single leader, they
would impose on him extraordinary political and legal
risks, and tempt him to withhold the bribery proceeds from his
followers. Under the committee system, the legislators can delegate
the
authority they jointly hold to each other--- by making each
member a leader for one particular kind of statute. Thus, a
committee would exert power not because it set the
agenda, but because each member coordinates the bribe-taking from
particular lobbyists, with a
general understanding that every well-behaved legislator has
a set of captive lobbyists.
Perhaps the most successful of such committees will be the {\it
extra}-legislative groups to which opposition politicians are not
invited.  Japan's Liberal Democratic Party, for example, conducts most
policy-making within its own party's Policy Affairs Research Council
(Inoguchi and Iwai, 1987).  By making policy behind closed doors,
party members can both coordinate any pay-offs and keep the process
invisible.




Consider three other applications  of this model.  First, the crucial
difference between democracies and autocracies does not lie in whether
the
private-interest statute can be authorized by a single person. This
case ($\overline{Y}=1$) is included in the model and in Theorem 1, and
is
quite common in democracies. It occurs where a single legislator can
provide benefits by telephoning an agency, for example, or by
sponsoring an amendment. Having this power, however, does not help the
legislator.  Rather, it hurts him because he shares the power
with all other legislators.  Legislators will still compete with each
other and bid down the bribe price, and
when one accepts a bribe he will cast a cloud over the entire
legislature.




Second, our model does not depend on a formal vote.  Even in an
autocracy, there are many ``legislatures.''  Whenever a group must
make a decision, it acts through implicit votes.  The lobbyist might
be a
dictator, for example, and the group might be the leaders of the armed
forces. If
the dictator can maintain an expectation that he will stay in power,
and the army leaders cannot communicate easily, then even a dictator
unpopular with his generals may be able to remain in power
cheaply. Each general knows that if he deviates unilaterally, he
will lose his ``bribe'' (which might be merely the privilege of
staying alive) without deposing the
dictator.

Third, what the lobbyist obtains in exchange for the bribe need not be
a
firm promise to vote for a bill. Some commentators plausibly explain
campaign contributions in the United States as ``access money.''
Through the contributions, the lobbyist obtains not a vote but the
privilege of conveying information to the legislator. The lobbyist
willingly pays for this privilege because he hopes the information
will affect the legislator's vote (see Austen-Smith \& Wright
(1990)).  He thereby obtains not a Yes vote, but the higher
probability of a Yes vote. The question our model answers is why
legislators sell access so cheaply, when lobbyists find it so
valuable.

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

\bigskip

3.2.4 \underline{The mixed strategy equilibrium.} This simultaneous
game has a third equilibrium: a mixed strategy Nash equilibrium in
which the bribe is $X^* < C_p$, and legislators refuse a bribe of $X=
X^*$ with
probability $\theta(X^*)$ and bribes of $X \neq X^*$ with probability
one.\footnote{  The intuition behind the mixed-strategy equilibrium is
that some legislators (the fraction $\omega$ of all legislators) will
take a bribe of $X=X*$ and the rest will refuse, and that those who
would accept the bribe cannot readily be idenfied ex ante.}
To the extent that a mixed strategy describes how legislators act,
Proposition 2 shows that although in a given equilibrium the lobbyist
cannot reduce the bribe without certainly killing his statute, those
equilibria with smaller bribes have {\it greater} likelihoods that
the statute will pass.


\underline{\it PROPOSITION 2:} {\it If $R < \overline{Y}C_p$, then a
continuum of
mixed-strategy equilibria exists, differing in their bribes and the
probabilities the bribes are accepted.  The bribes are positive but
less than the personal cost $C_p$, and the probabilities of the
statute's success are positive but less than one. Equilibria with
greater values of $X^*$ have higher probabilities that the statute
will
fail.}


PROOF: In the proposed equilibrium, the lobbyist offers the same
bribe $X^*< C_p$ to each legislator. Each legislator then rejects
$X^*$ (and votes no) with probability $\theta^*$.

 Legislator $i$ will accept $X$ and vote ``yes'' if $X\geq C_p$, but
if $R < \overline{Y}C_p$ the lobbyist will not offer any $X$ that
large.  If, on the other hand, the bribe is 0 and there is any chance
of the bill failing, the legislator will refuse the bribe.  Hence the
bribes will lie somewhere within $(0, C_p)$ if the equilibrium is in
mixed strategies.

Let $N_y$ represent the number of legislators who accept $X$ and vote
yes. Suppose that every legislator but $i$ votes against the statute
with probability $\theta$. The probability that the statute fails
will be $F_y(\theta) = Prob(N_y < \overline{Y}|\theta, i \; votes\;
yes)$ or
 $F_n(\theta) = Prob(N_y < \overline{Y}|\theta, i \; votes\; no)$,
depending on
how $i$ votes. $F_y(\theta)$ and $F_n(\theta)$ are binomial
distributions, so $ dF_y/d\theta > 0$ and $ dF_n/d\theta > 0$.


 First, consider whether the legislators are willing to follow a
mixed strategy. If $i$ accepts the bribe, he earns the payoff $X -
C_p$ if the
statute fails and $X-C_o$ if it passes, for an expected payoff of
 \begin{equation}
 \pi(yes)= (1-F_y(\theta))(X-C_o) + F_y(\theta)(X-C_p).
 \end{equation}
  If he rejects the bribe, he earns the payoff 0 if the
statute fails and $-C_o$ if it passes, for an expected payoff of
 \begin{equation}
 \pi(no)= (1-F_n(\theta))(-C_o).
 \end{equation}
 In a mixed strategy equilibrium, the mixing player must be
indifferent between the two pure strategies he mixes, so $\theta$ and
$X$ must be chosen so that $\pi(yes) = \pi(no)$. There will exist a
continuum of values of $\theta$ and $X$ such that this is true.

Take $X$ to be fixed. If $\theta$ is sufficiently large, the
legislator will reject the bribe, since $X < C_p$ and the statute
would probably fail even with his vote. If $\theta$ is sufficiently
small, the legislator will accept the bribe, since $X>0$ and the
statue would probably succeed even without his vote. Because the
differential in the payoff is continuous in $\theta$, there must
exist some $\theta$ between these extremes for which the legislator
is indifferent about accepting versus rejecting the bribe. Since he
is indifferent, he is also willing to randomize, and with the same
probability $\theta$ as makes he himself indifferent.

Now consider what happens as $X^*$ increases. If $\theta^*$ remained
fixed at the initial equilibrium level, the payoff from accepting the
bribe would become greater than the payoff from rejecting it. This
would be
true {\it a fortiori} if $\theta^*$ were to decrease, so that the
statute's probability of success would rise. Since the mixed-strategy
equilibrium requires that the payoffs from accepting and rejecting be
equal, $\theta^*$ must therefore decline. As $X^*$ increases,
$\theta^*$, $F_y(\theta^*)$, and $F_n(\theta^*)$ must all decrease.

 $X^*$ is the equilibrium level of X, which is different in different
equilibria.  In a given equilibrium, offering $X < X^*$ results in
being turned down with certainty. But equilibria in which $X^*$ takes
bigger values also have bigger values of $\theta^*$---that is,
smaller probabilities of rejection.

Second, consider whether the lobbyist is willing to offer $X^*$. This
is not immediately obvious, because he must pay the bribes to those
legislators who accept them even if the statute fails, which could
result in a negative expected payoff. He can avoid these costs by
deviating with $X \neq X^*$, in which case the bribes are all
rejected and his payoff is zero, not negative. The lobbyist's
expected payoff from offering $X^*$ is
 $$
  \sum_{t=0}^{y-1} [Prob (N_y= t|\theta^*)N_y(0-X^*)]
 + \sum_{t=y}^{N} [Prob (N_y= t|\theta^*)R -N_yX^*].
 $$
  As $X^*$ approaches 0, the earlier analysis suggests that the
expected number of Yes votes increases  and the left summation will
drop out.  Because $R-N_y X^*$ will be positive as $X^*$ approaches
0, the right summation will be positive and the lobbyist will earn
positive profits.  Hence, he will find some mixed strategy equilibria
profitable. $\Box$

%---------------------------------------------------------------
\bigskip
\noindent
3.3. \underline{The sequential game:}


Even if the lobbyist approaches the legislators sequentially, the
result may still be cheap bribery. The lobbyist could structure such
a sequential game in several ways. One way is to approach the
legislators in order, but so as to require them to respond
independently without knowing what other legislators have decided.
As noted earlier, such a game would be analytically the same as the
simultaneous game.  In the specification of Proposition 3, each
legislator sequentially, permanently, and publicly, decides how to
vote.


{\it PROPOSITION 3}: {\it The sequential game has two possible
equilibrium outcomes for $\overline{Y} \geq 2$:

(SUCCESS) If  $\overline{Y}C_p/2 \leq R$, then $X=0$,
all legislators vote ``yes,'' and the statute passes.

(FAILURE) If $\overline{Y}C_p/2 > R$, then all legislators vote
``no'', and the statute fails.}


PROOF: We deal separately with three parameter ranges.  We call $i$
``crucial'' if enough other legislators have voted ``no'' that the
number of legislators who have voted ``yes'' will be less than
$\overline{Y}$ if $i$ refuses, even if all subsequent legislators
vote ``yes.''

\underline{Range A:} SUCCESS.  Suppose that $C_p \overline{Y} < R$.
Legislator $i$ will accept $X$ = 0 and vote ``yes'' unless enough
colleagues have refused so that all remaining legislators are crucial.
In that case, $L$ will offer $X =C_p$ to each remaining legislator,
each will accept the bribe, and the statute will pass.  Yet that
situation will not occur.  Each $i$ will accept $X=0$ and vote
``yes'' unless $i$ is crucial.  As the first legislators are never
crucial, they will vote ``yes'' for $X$ = 0.  Because all non-crucial
legislators vote ``yes,'' $L$ never encounters a crucial legislator,
and thereby signs up all legislators at $X=0$.

In Range A, $L$ can sign up all legislators for free because $L$ is
willing to pay each of $\overline{Y}$ legislators $X=C_p$ if he ever
did become
crucial.  Non-crucial legislators receive only $X=0$, but are willing
to vote ``yes'' because they know that $L$ can successfully obtain
$\overline{Y}$ ``yes'' votes regardless of what they do.  $L$'s
willingness to
pay $\overline{Y}$ legislators, in short, induces all to vote ``yes''
at $X=0$.

\underline{Range B:} SUCCESS:  Suppose that $C_p \overline{Y}/2\leq R
< C_p \overline{Y}.$
The lobbyist
now is unwilling to pay $C_p$ to $\overline{Y}$ legislators, and the
argument
above collapses.  Suppose $i$ expects every other legislators to vote
``no''. If so, $i$ will vote ``yes'' only when $X \geq C_p$, unless
(off the equilibrium path) $\overline{Y}$ legislators have already
voted ``yes.``
As $L$ will not pay $C_p$ to $\overline{Y}$ legislators, the statute
apparently
fails.

In fact, however, the statute passes.  To
see why, assume the contrary: that an equilibrium exists where the
majority votes ``no''. We show below that $L$ can successfully induce
$\overline{Y}$
legislators to deviate from the equilibrium and vote ``yes.`` We
start at the end of the deviation subgame.

(B1) Suppose that $L$ needs
each of the legislators he can still approach.  If so, then each
remaining legislator is crucial and $L$ must pay each
$C_p$.\footnote{We assume $L$ can make take-it-or-leave-it
offers.  Relaxing this assumption raises the danger of extortion by
crucial consumers who could demand the whole of the rents the
lobbyist expects to gain from the statute.  On hold-up problems in
sequential models, see, e.g., Rasmusen (1988).}


(B2) Suppose that $\overline{Y}-1$ legislators have voted ``yes,'' and
that $L$
has not yet approached two legislators.  If the first of the
remaining two legislators refuses, the second will vote ``yes'' for
$C_p$ which (because $R \geq C_p\overline{Y}/2$) $L$ will pay.
Knowing that, the first will vote ``yes'' for $X=0$.  Because
$\overline{Y}$
legislators have now voted ``yes,'' the last legislator is not
crucial and will vote ``yes'' for $X=0$ as well.

 (B3) Suppose that $\overline{Y}-2$ legislators have voted ``yes,''
and that
three legislators remain.  The first of the three will vote ``yes''
for $X=0$, because his vote is not crucial; if he refuses, the last
two legislators will vote ``yes'' for $C_p$ (we
address what happens if $R < 2C_p$ in [B5]).  Accordingly, the
first legislator votes ``yes'' at $X=0$.  From (B2), we know that the
other two will also vote ``yes'' at $X=0$.

(B4) Suppose that $\overline{Y}/2$
legislators have voted ``yes,'' and that $\overline{Y}/2 + 1$
legislators remain.
By induction from (B2) and (B3), all legislators will vote ``yes''
for $X$ = 0.

  (B5) This induction does not hold indefinitely.  Suppose that
$R=C_p\overline{Y}/2$, that $L$ needs $\overline{Y}/2 + 1$ more votes,
and that $\overline{Y}/2 + 2$ legislators remain.  The first
legislator in this
subsequence knows that if he refuses, $L$ will need $\overline{Y}/2 +
1$ more
votes, yet only $\overline{Y}/2 + 1$ legislators will remain.  Because
$R= C_p\overline{Y}/2$, $L$ cannot bribe all remaining
legislators ($\overline{Y}$/2 + 1 of them).  Therefore, the first
legislator is crucial,
and will hold out for $C_p$. This amount $L$ willingly pays,
however, because he foresees that in the remaining subgame all
$\overline{Y}$/2 + 1
will vote ``yes'' for $X$ = 0.  The statute thus passes, but $L$ must
pay
the first legislator $X =C_p$.

  (B6) Last, suppose that $\overline{Y}$ votes are needed and that
$\overline{Y}$ + 1 legislators
are left.  By the logic of (B5), $L$ must pay $C_p$ to the first
$\overline{Y}$/2 of
these legislators, and $X$ = 0 to the remaining $\overline{Y}$/2 + 1.
Because $L$ is
willing to pay $C_p\overline{Y}/2$, the statute passes.  If $R >
C_p\overline{Y}/2$, then
(by the same logic) $L$ will be able to sign up $R/C_p$ legislators
for
free.

  (B7) Suppose that $N$ = $\overline{Y}$ + 1.  The first legislator
knows that if he refuses to vote ``yes,'' all others will be crucial.
Hence the logic above would suggest that $L$ will need to pay $X
=C_p$ to all legislators.  The point is misleading: if $N$ =
$\overline{Y}$ + 1 and statutes pass by majority vote, there are only
2 or 3 legislators--- not generally the case in modern democracies.

 (B8) If (more realistically) $N > \overline{Y} + 1$, the only
equilibrium is
where everyone votes ``yes'' and {\it no one} receives more than
$X=0$.  By the induction argument, the first $N - (\overline{Y} + 1)$
legislators will foresee that the statute will SUCCEED.  Hence, each
will vote ``yes'' for $X$ = 0.  $L$ thus never reaches the situation
where he needs $\overline{Y}/2 + 1$ more legislators and only
$\overline{Y}/2 + 2$ remain.
Never encountering a crucial legislator, the lobbyist never pays $X >
0$.

\underline{Range C:} FAILURE.
Suppose that $R <C_p \overline{Y} /2$. Now the statute
cannot pass.  The argument in Range B crucially depended on the
lobbyist's
willingness to pay $C_p$ to the last $\overline{Y}/2$ legislators.  If
the
lobbyist cannot do so, then any equilibrium in which all legislators
vote
``yes'' at $X=0$ is unstable.  If all but $\overline{Y} + 2$
legislators have
refused, the next legislator knows that if he refuses, so will
enough future legislators that the statute will fail.  Therefore, if
all but $\overline{Y}$ + 3 legislators have refused, the next
legislator knows
that if he refuses, the statute will fail.  The argument
continues back to the initial legislator. $\Box$


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

\bigskip
\noindent
4. \underline{Extending the Model.}

 In this section we will extend the model in two directions: to
general assumptions on the legislators' costs, and to the case where
only a single legislator  can grant the desired favor.

\noindent
4.1 \underline{General Payoff Functions.}

In the model above, voters did not discriminate among legislators
when a statute passed.  A more general model would allow some voters
to respond in different ways that might be more appropriate to some
situations. As before, the legislator's benefit from voting for a
statute will be the bribe $X$. Now, however, we will split the
legislator's costs into the three categories shown in Table 2: (1)
the cost of being part of a legislature which passes a corrupt
statute ($C_o$), (2) the cost of personally voting Yes on a statute
that fails ($C_{pf}$), and (3) the cost of personally voting Yes on a
statute that succeeds ($C_{ps}$).  For example, if (as is generally
true) a politician who accepts a bribe faces a positive risk of a
criminal conviction regardless of whether the statute passes, then
both $C_{ps}$ and $C_{pf}$ will be positive.  The earlier model is a
special case with $C_o>0$, $C_{pf}>0$, and $C_{ps}=0$.


\begin{center}

 \begin{tabular}{llrcc}
                    &       &           &\multicolumn{2}{c}{\bf
Other legislators }\\
                    &       &           &  No & Yes      \\
&       &           &             &            \\
                    &       & No&   0       & $-C_o$    \\
         &{\bf Legislator i}&           &             &            \\
                    &       &   Yes  &  $X-C_{pf}$      &  $X-C_{ps}-
C_o$  \\
&       &           &             &            \\
\end{tabular}

{\bf Table 2: Payoffs to Legislator $i$ in the general model}
\end{center}


  The  game consists of the lobbyist choosing the bribe $X$ and
deciding which legislators are to be offered it, followed by a
subgame consisting of simultaneous offers and votes. The size of the
bribe that the lobbyist offers depends on his benefit from a
successful statute ($R$) and the equilibrium he  expects in the
voting subgame.  Depending on the size of the bribe $X$ relative to
the
cost of personally voting Yes on a failed bill ($C_{pf}$) and the
cost of personally voting Yes on a bill that succeeds ($C_{ps}$), the
subgame falls into one of four categories:

{\it (CASE 1) The only equilibrium is passage of the bill.  This
happens if the bribe is large enough so that $X \geq C_{pf}> C_{ps}$
or $X > C_{ps}> C_{pf}$.}\footnote{xxx Eric, I don't see why one
inequality is absolute and one isn't. Mark: if $X=C_{pf} > C_{ps}$,
then one equilibrium is for the legislators to turn down the bill.
They are willing to do that, because they are indifferent about voting
for the bill or against it given that the other legislators will vote
against it.  Eric:  But that CONTRADICTS the statement in the text!
MARK: What statement? Does this still apply?}

Case 1 bears some resemblance to the prisoner's dilemma. The
legislators hope that the statute fails, so they can avoid the
coat-tails cost, $C_o$, but the bribe is great enough that taking the
bribe and voting for the statute is a dominant strategy.  In a
one-shot game the legislators would not be able to trust each other,
because even if they all agreed not to accept bribes, any individual
legislator would wish to break the agreement and accept the bribe
anyway.


{\it (CASE 2) The only equilibrium is failure of the bill.  This
happens if $X < Min(C_{pf}, C_{ps})$.}

 Case 2 applies if the briber is not willing to offer even a bribe of
$C_{ps}$, much less one equal to $C_o + C_{ps}$. If, for example,
$X=0$ and both $C_{pf}$ and $C_{ps}$ are positive, then the bill will
certainly fail.

{\it (CASE 3) There are two pure-strategy equilibria (one with
success; one with failure), and, if $X < C_{pf}$, a continuum of
mixed-strategy equilibria.  This happens if $C_{ps} \leq X \leq
C_{pf}$.}

 If $C_{ps} < C_{pf}$, the legislator's loss from voting for a failed
bill is greater than the difference between his voting for a
successful bill and voting against a successful bill. Note that this
inequality does {\it not} imply that his loss is greater for a failed
bill than from voting for a successful bill.  If, for example, $X=0$,
$C_o=5, C_{ps}=1$ and $C_{pf}=3$, then the legislator's ranking of
outcomes is (a) Vote No and the bill fails (payoff 0), (b) Vote Yes
and the bill fails (payoff $-3$), (c) Vote No and the bill succeeds
(payoff $-5$), and (d) Vote Yes and the bill succeeds (payoff $-6$).

If $C_{ps}$=0, a zero bribe will allow multiple equilibria, as in the
model of Section 3, where $C_o >0$, $C_{ps}=0$, and $C_{pf} >0$.
Otherwise, a positive bribe equal to $C_{ps}$ is required.

Case 3 differs from Case 1 in that accepting the bribe and voting for
the statute is not a dominant strategy. Rather, a legislator will
vote for the statute if he thinks it will pass and against it if he
thinks it will fail. If the legislators could communicate and
coordinate with each other, they would give each other assurances
that each would turn down the bribe; and once these assurances were
given and believed, each individual would have no incentive to
deviate from them. This points to an important role for party
leaders: they not only lead in positive actions, but they can prevent
stampedes to vote for statutes that no legislator really wants.


{\it (CASE 4) There is no pure-strategy equilibrium.  This happens if
$C_{pf} \leq X < C_{ps}$.}

 In Case 4, there is a positive personal cost of voting for a bill,
even beyond the coattail cost, a cost that is greater if the bill
succeeds than if it fails. Each legislator is willing and eager to
take the bribe and vote for the statute, but only if he thinks it is
going to fail.

\bigskip

 The four cases above were all contingent on the value of the bribe,
$X$, which is endogenous. What value of $X$ will the lobbyist choose?
Effectively, he can choose which of the four cases he prefers.

If $R$ is small enough relative to the costs, the lobbyist will
choose not to offer a large enough bribe to allow success, and Case 2
applies. The statute fails and no bribes are paid.

If $R$ is larger, then the lobbyist has a choice of subgames. If
$C_{pf} < C_{ps}$, then he chooses between a pure-strategy
equilibrium in which the statute passes but the bribe is $X=C_{ps}$
and a mixed-strategy equilibrium in which $C_{pf} < X <
C_{ps}$ and the statute
sometimes fails. With specific parameter values, it is a
straightforward problem for the lobbyist to choose between these
alternatives.

If $C_{ps} \leq C_{pf}$, then the lobbyist chooses between a
pure-strategy equilibrium in which the statute passes but the bribe
is $X=C_{pf}$ and a subgame with multiple equilibria and a smaller
bribe.  Which option is preferable depends on which of the multiple
equilibria would be played out, which in turn depends on the
expectations of the legislators. To make a prediction, we would have
to move outside of the model. If the lobbyist can manipulate
expectations, then we would expect him to choose $X=C_{ps}$ and
succeed with the statute. Indeed, the act of offering a bribe as low
as $X=C_{ps}$ might persuade legislators that the statute was going
to pass, since they know the lobbyist will offer no more than he has
to.  On the other hand, if the legislators can credibly communicate
with each other, even if they cannot make binding agreements with
each other, then they will agree to turn down very cheap bribes, and
the lobbyist would offer the merely cheap bribe of $X=C_{pf}$, which
could still be less than his benefit of $R/Y$ and the legislator's
cost of
$C_o+ C_{ps}$.

 Note that $C_o$ does not enter into these parameter ranges, a
curious feature of the model.  If other legislators have decided to
vote for a bad bill and impose cost $C_o$ on our representative
legislator, then his own actions do not depend on that cost, which he
cannot possibly avoid.

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

\noindent
4.2 \underline{Monopoly Provision of Legislative Favors.}

 So far we have assumed that a single lobbyist faces a legislature of
independent individuals who suffer from a coordination problem.
Another case occurs when the single lobbyist faces either a
coordinated
legislature that delegates its votes to a single leader, or when only
one individual---more likely a bureaucrat than a legislator---is in a
position to grant the desired favor.\footnote{Still another case is
when multiple lobbyists compete for a limited stock of government
favors.  We will not explore that case here; see Peltzman (1976) or
Hillman \& Riley (1989).}

This is a case of bilateral monopoly, of bargaining over the surplus
$S=R-C_o-C_p$. The legislator will receive at least $X=C_o+C_p$ and
the lobbyist will pay no more than $X=R/Y$, but without further
information it is difficult to say
more.  One's first thought is that the lobbyist and the legislator
are symmetrically situated, so that we might reasonably guess that
each would receive a net benefit of $S/2$ from the transaction.  This
would be the outcome in the axiomatic model of Nash (1950) and in the
shrinking-pie model of Rubinstein (1982), and it seems intuitive.

An even split between the briber and the bribed may indeed occur.
Consider the case of Judge Manton, who frequently accepted large sums
of
money from litigants from 1932 to 1938 (see Noonan [1984] p. 568-70).
Manton  was the only one of three judges on a panel
to accept bribes, and in some of the cases the bribes turned out
perhaps to
be unnecessary, since the decisions were unanimous.  In one
case, a stockholder sought a return of \$10 million in bonuses
paid to American Tobacco Company executives. A few days before
argument, Manton asked a high-ranking partner of the law firm
representing American for a \$250,000 loan.  This partner, Louis
Levy, was Manton's mentor at law school and helped push his
appointment.  Levy gave Manton the loan, and took in return  a demand
note he never actually demanded.

 Whether or not the split of the surplus was 50-50, Manton's bribe
certainly
was not cheap.  But what  is special about this example is
that (a) Manton approached Levy, (b) Manton and Levy had longterm
ties, and (c) Levy's costs from discovery were substantial because of
the risk of disbarment (which actually occurred).  Thus, Manton could
make an initial offer and bargaining costs were sizeable for both
sides.

 Even if there is bilateral monopoly, however, it is not always the
case that the two
 bargainers are symmetric and will
split the surplus evenly. If the briber and the bribed
have different bargaining costs, the split will not be even.  A
reasonable way to model the bargaining in bilateral monopoly is for
one bargainer to make an initial offer, for the other to reply with a
counter-offer, and for them to alternate offers until one of them
accepts. Each time an offer is made, the offeror incurs a cost, which
in this context would be the expected cost of being discovered. But
this expected cost will normally be much higher for the legislator
than for the lobbyist.  Both may be subject to criminal prosecution,
but only the legislator needs to maintain a reputation for honesty in
order to be re-elected.  Thus, if the legislator makes a
counteroffer, he may risk much more than does the lobbyist. If the
bargaining costs are $B_p$ for the legislator and $B_l < B_p$ for the
lobbyist, then the model just described is the fixed-bargaining-cost
model of Rubinstein (1982).  The equilibrium outcome is that the
lobbyist gets all or almost all of the surplus; if the lobbyist moves
first, the equilibrium bribe is $X = C_p+C_o$, and if the legislator
moves first it is is $X=C_p+C_o+B_l$. For proof, see Rubinstein;
roughly, the legislator knows that the lobbyist has lower bargaining
costs, and after any offer by the legislator the lobbyist would be
willing to make a counter-offer if he could reduce the bribe by
$B_l$.  Hence, the legislator ends the
bargaining immediately by accepting the cheap bribe.  In ABSCAM,
Congressman Thompson told the lobbyist ``I'm not looking for any
money'' in the morning, but returned in the evening for his briefcase
to which \$50,000 had been added. He was more ready to accept the
money than to talk about its amount (Noonan, 1984: 609-614).

 The lobbyist would ordinarily have the first move in this game,
further improving his position. By moving first, the lobbyist is in a
much better position to make a take-it-or-leave-it offer to the
legislator. He could purposely make it difficult for the legislator
to reply by, for example, not revealing his identity. Or, he could
wait until the last possible moment when the favor might be granted,
and then make an offer without leaving the legislator time to make a
counteroffer. In either case, the lobbyist will succeed with a cheap
bribe.  The legislator might try to respond by refusing bribes
until they are bid up high enough, but the briber's costs rise
significantly with successive offers to a legislator who claims to be
honest---for he might actually be honest. In one of the ABSCAM cases,
Judge Bryant held that: ``Anyone other than an agent [of the
government]...  would have given up at the first refusal by the
congressman for fear of being reported and prosecuted.  Only the
knowledge that he was safe from any charge let the agent press his
offer. Without realistic restraint, the government's conduct was
fundamentally unfair'' (Noonan, 1984: xxx).

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

\bigskip
   \noindent \underline{5. Implications.}

Our model suggests why legislators in democratic societies sell their
votes so cheaply--- and thus also why they are willing to ban bribes:
when legislators vote for private-interest statutes, they impose an
externality on every other legislator, yet they cannot coordinate
their votes to demand a bribe which compensates them for that
externality.

 Our model yields the following additional hypotheses.  First, the
average price of bribes paid will correlate with the
ease with which legislators can coordinate.  Because coordination
problems generally increase as the number of people involved rises,
pay-offs should be larger where the number of people involved in a
political decision is smaller -- a point corroborated by Parker (1992:
177).\footnote{
Committees, disciplined factions, and political machines serve in
part to reduce the coordination problems of large legislatures.  See,
e.g., Crain \& Tollison, 1980.} Accordingly, our model predicts that
the greater the number of legislators, the greater the likelihood
that they will receive only very small bribes and therefore decide to
ban corruption.

 Second, again all else equal, \footnote{ Autocrats often incur lower
political costs for dispensing private-interest statutes--- in which
case all else will not be equal.} decision-making {\it groups} will
supply more private-interest statutes than decision-making {\it
individuals}.\footnote{ Empirical evidence consistent with this
hypothesis appears in, e.g., McCormick \& Tollison, 1980.  } The
difficulty of coordination can lead groups to supply statutes even
when they earn a collective pay-off less than the collective cost the
statute imposes.  An individual--- whether an autocrat or a
democratically elected president--- would not do so.
 This second hypothesis contradicts the implications of
transaction-costs analysis.  Baysinger, Ekelund \& Tollison (1980)
argue that the transaction costs of purchasing a statute increase
with the size of the political control group.  They then suggest that
private-interest statutes should be most common where the
decision-making group is small.  Our model predicts the opposite: the
greater the number of legislators, the more acute the coordination
problems, and the greater the probability that legislators will
supply legislation that costs them more than the wealth it transfers.

Third, the better the information voters possess, the larger will be
the average bribe paid.  The greater the percentage of informed
voters, the greater the
percentage who respond to the actions their legislator has personally
taken, the larger $C_{ps}$, and the smaller $C_o$.  As $C_o$ falls
and $C_{ps}$ rises, the size of the bribes paid also rises.


When legislators pass private-interest statutes, they irritate voters
and hurt efficiency.  Effectively, they impose an externality on
their colleagues--- on those who opposed the statute as well as on
those who supported it.  Were they able to coordinate their actions,
they could demand bribes that compensated themselves for those costs.
Yet coordination must often be public and most modern democracies
contain voters who resent bribes.  As a result, legislators often
cannot coordinate their bribe-taking with each other.  Unable to
coordinate, they each agree to support private-interest statutes for
bribes far smaller than the costs they thereby incur.  In the
process, they also become more amenable to efforts to ban bribes.
Unable to capture the high bribes in a legalized regime anyway,
legislators more readily accept pressure from voters to ban bribes
and fund the necessary enforcement machinery.

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

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