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            \begin{large}
    {\bf JUDICIAL LEGITIMACY  AS A REPEATED GAME}\\
             \end{large}
                     
                  
                    \bigskip
                    Eric Rasmusen \\
      
Draft of November 23, 1993. Published in {\it
Journal of Law, Economics, and Organization} (April 1994) 10: 63-83. \\



                    {\it Abstract} 
                    \end{center}
 An independent
judiciary  faces the problem of how to restrain high-court judges
from indulging their personal whims. One restraint is the desire of
judges to influence future judges. To do so, judges may have to
maintain their own or the system's legitimacy by restraining their
own behavior. This situation can be viewed as an equilibrium of
an infinitely repeated game. Such a game has many equilibria, some of which are
Pareto superior to others. In some equilibria,  self-interested judges are
responsible even without the threat of external penalties.

      
\begin{small}
          
 
               \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

 
 \begin{small}
\begin{quotation}
  Use the memory of thy predecessor fairly and tenderly; for if thou
dost not, it is a debt will sure be paid when thou art gone.''\\
  \hspace*{1.7in}---Francis Bacon, Lord Chancellor of
England: 93. 
 \end{quotation}\end{small}  
\parindent 36pt
\bigskip

\noindent
 {\bf 1. Introduction}

  A political system makes laws so that society can commit itself to
rules made in an orderly manner and not retract the rules later when
it appears that particular individuals will be helped or hurt by
them.  For laws to work in this way it is helpful to have judges who
are responsible and independent: responsible, in the sense that they
faithfully interpret the law regardless of their personal policy
preferences, and independent, in the sense that they interpret the
law regardless of the extra-legislative preferences of the
legislature, the executive, or the people.
  The traditional
explanation for the desirability of independence is to provide a
check on  tyranny by the rest of government, as Alexander Hamilton explained in
Federalist Paper number 78.   Another explanation, suggested by Landes and Posner
(1975), is that an  independent judiciary is useful to instill confidence that the
legislature will adhere to its agreements. The case of {\it Fletcher v. Peck}, 6
Cranch 87
(1810), is an early illustration of this:   the Georgia legislature wished to
cancel
a contract that sold state land cheaply to private parties, and the U.S. Supreme
Court ruled that it could not. An independent judiciary is helpful both to
ameliorate agency problems between citizens and elected officials and to allow the
citizens to make binding commitments.


 But how can responsibility be made compatible with independence?  The
decisionmaker in  an independent judiciary, unlike in the executive
branch or a private business,  cannot be removed by his
superiors, rejected in the next election, or abandoned by his customers.$^{1}$
Most  judges  do have
superiors--- the judges of higher courts--- who can overrule them,
but high courts, state and federal, face no such check, and even
lower-court judges have some slack, since the high  courts  
allocate their time to only a limited number of cases.$^{2}$  Some states
exercise control over their   courts by    
elections, but federal courts do not. Judges may be impeached, but
this is a costly procedure which by tradition, if not by
constitutional language, is not invoked against judges who write bad
opinions. 

     Insofar as  disciplinary devices   are used, they  
  undermine the independence of the judiciary.  In the U.S. federal system,
Congress  and the President are  free to increase  the number of justices, a
threat best known  from  Roosevelt's court-packing plan, which  although it
failed to win the approval of Congress may have induced   the ``switch in time
that saved nine''.  In the disputes between the President and Congress over
Reconstruction,  the number of justices on the Supreme Court   fluctuated
depending on the political situation.  In 1865 Congress reduced the number of
justices to seven to prevent President Johnson from making any appointments, and
four years later  the number was increased   to nine   so that newly elected
President Grant could make new appointments (McDowell: 138). Congress also
establishes rules of procedure for the federal court, and the U.S. Constitution
gives the Supreme Court   appellate jurisdiction   ``...with such Exceptions, and
under such Regulations as the Congress shall make'' (U.S. Constitution, III-2).
The Norris-La Guardia Act of 1932, which heavily restricted the power of   federal
courts to issue injunctions in labor disputes,  is an example of Congressional
regulation. More extreme restrictions have been proposed but not passed; in
the 1860's bills were introduced to eliminate  judicial review or to   require  a
unanimous Supreme Court if  federal statutes  were to be overturned (McDowell:
140, 141, 146). More directly,
   statutes and constitutional amendments  can be passed to
overrule  irresponsible judicial rulings, though this is  is problematic if the
irresponsible court has the authority to
interpret the new legislation.$^{3}$  All of these external methods of controlling
judicial excess are costly
and difficult, and   must remain so if the courts are  to
remain a check upon the rest of society.

     The Anglo-American judicial system is   difficult to understand  because it
does not provide its  high courts with the bureaucratic incentives that are
available in the   Continental  judicial  systems.    For most of  Continental
Europe's
history, from Justinian to Hitler, judges have been under the control
of the executive, so  it is not judicial irresonsibility that has been the
problem.$^{4}$   Each system has its advantages: the European system of
bureaucratic judges reduces the agency problem between the judiciary and the
citizens, while the  Anglo-American system of independent judges  reduces the
agency problem between the rest of the government and the  citizens, and allows
government commitments to be made binding.

  Somehow, an independent judiciary must be  self-enforcing, so that even if the
judges are entirely
independent, free from external threats of dismissal or  punishment, 
  they will act as the faithful agents of the legislature
and the constitution. It has long been recognized that the
 system of precedent helps serve this purpose.  The
Anglo-American judicial system is unusual in not one, but  two respects: the
independence of judges and the formal importance of precedent, which
contrast with the bureaucratic judges and free-standing codes of
Continental law.  Continental law puts its emphasis not on individual
cases but on groups of cases that create a practice, so it is unclear
whether a judge is breaking precedent or not, nor does he get so much
credit for creating law. 


  Sir John Salmond (pp. 376, 386), commenting on the connection between precedent
and independence of the judiciary, says of
 precedent that 
 
 
 \begin{small}
\begin{quotation}
 ``It seems clear that we must attribute this feature of English law
to the peculiarly powerful and authoritative position which has been
at all times occupied by English judges.  $\ldots$  The growth of
case law involves the gradual elimination of that judicial liberty to
which it owes its origin.  In any system in which precedents are
authoritative the Courts are engaged in forging fetters for their own
feet.'' 
 \end{quotation}\end{small}  
\parindent 36pt
 But the extent to which precedent should be followed is one of the
longstanding controversies in jurisprudence.  A.L. Goodhart (p. 61),
playing Bentham to Salmond's Blackstone, replies: 
  

 \begin{small}
\begin{quotation}
 ``But why  should it be necessary to forge fetters for judges who
are peculiarly able and powerful? The greater the skill and the
professional reputation of the judges, the less necessary would it
seem to be to bind them by artificial rules. 
$\ldots$ The result is that the English judge is a slave to the past and a
despot for the future, bound by the decisions of his dead
predecessors and binding for generations to come the judgements of
those who will succeed him.'' 
 \end{quotation}\end{small}  
\parindent 36pt


Both parties' arguments are  deficient,  
  Goodhart's, for assuming that a skillful judge is a trustworthy
judge, and Salmond's, for failing to explain why judges forge fetters
for themselves.  But the  two views do suggest two different kinds
of self-enforcing systems, one based on the tastes of judges, and one
based on future rewards for present restraint.

 The first method is to select judges who have a strong taste for
following the law.  One taste that will lead to this result is a
feeling of a duty to responsibly follow the law even if the judge
must thereby violate his own beliefs about good policy.$^{5}$  
  This, of course, is an ideal solution if enough such judges can be
found, or if the state can costlessly mold the preferences of future
judges. If the supply of such judges is limited, however, the state
must accept judges of lower intellectual ability if it wishes to
weight responsibility more heavily.$^{6}$ The supply is
limited, since  talented lawyers make a financial sacrifice
in  becoming judges, which they would   only make for prestige, leisure,
or the ability to put their mark on the law.  Similarly, molding
preferences is not without cost: law schools must teach less law if
they teach more duty.

  Tastes other than duty can lead to the same desirable result. If,
for example, a judge views judging as an intellectual exercise, to be
played as skillfully as possible according to whatever the rules
happen to be, then he is  no more tempted to violate the law
than a card-player is tempted to cheat at
solitaire.$^{7}$    Any taste-based solution, however,  faces the same 
problem  as duty:   it is costly to
discover judges with the appropriate tastes and to exclude other
potential judges. 


 
The  second method, the subject of this article, is based on future
rewards for present restraint, on the desire of today's judges to
influence tomorrow's. The intuition to be examined   is that a judge will
 faithfully follow statute and precedent because he wishes to create
precedents in new areas of law that will be obeyed by other
judges.$^{8}$   Even if he feels he can successfully make policy today against the
will of the legislature and the decisions of past judges, he knows
that the judges who succeed him can change that policy.  Thus, he
shows restraint in most areas of law in the hopes that where he does
innovate, the innovation will be permanent.$^{9}$ 

 

 The idea that the desire for influence constrains judges is not new.
Professor Easterbrook, now a judge himself, said that, ``Each Justice
may find it advantageous to follow rules announced by his
predecessors, so that successors will follow his rules in turn. Stare
decisis thus enhances the power of the Justices'' (Easterbrook, 1982: 817; see
also Posner, 1992: 534, 542).
This fits nicely into the link between precedent and independence.
The less powerful Continental judge, constrained by external forces,
is neither required to obey precedents nor allowed to win fame by
creating them.$^{10}$   But the argument from
future influence is slippery enough to benefit from formal analysis.
Why does a judge's own behavior affect whether his successors will
``follow his rules in turn''?  What if he turns rogue and rejects his
predecessors? How can he possibly punish successors who reject him?
The idea is, in fact, perfectly suited to the theory of repeated
games, and the next section will construct a stylized model of
successive judges, each of whom decides whether to obey his
predecessors or not.  

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

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

Let there be a infinite sequence of judges.$^{11}$  Each judge
moves in turn and decides $n+1$ cases. In one of these cases, no precedent exists
and the judge   follows his own preferences.    In the  other $n$ cases, the
precedents       set by the   $n$
previous judges are relevant, and the current judge must decide whether to follow
precedent, or flout it and impose his own preferences.  Thus, besides deciding his
one case of first impression, judge   $j$    chooses the values of $n$ indicator
variables
$A^j_{j-n},\ldots A^j_{j-1}$, where $A^j_i = 1$ if precedent $i$ is
followed and $A^j_i=0$ if precedent $i$ is disregarded.$^{12}$  The superscript
refers to the
judge who is taking action, and the subscript refers to the judge who
set the precedent.

The payoff to judge $j$ is a decreasing function
of $A^j_{j-n},\ldots, A^j_{j-1}$ and an increasing function of
$A^{j+1}_j, A^{j+2}_j,\ldots, A^{j+n}_j$. This represents the extreme case of a
judge who wishes  to overturn every one of the $n$ relevant precedents and wants
every one of his own holdings to be followed in the future.  Formally,  the payoff
to judge $j$ is
 \begin{equation} \label{e1}
 \pi^j = -  \sum_{i=1}^n (A^j_{j-i})( x)+ \sum_{i=1}^n \left(
\frac{1}{1+r} \right)^i
(A^{j+i}_j)( y),
 \end{equation}
 where $x$ is the disutility of following a precedent and $y$ is the utility of
being followed. The specification of the discount rate, $r$,  means that although
the   judge  is no unhappier following older precedents than newer precedents, he
derives more utility from his own precedents being followed in the near future
than in the distant future.

We will assume that the payoff to the general public is increasing in
the number of precedents  followed, although this is only relevant to the
normative conclusion's, not the positive conclusions, since the public has no
influence on the judges.
  The variable $n$ represents the fact that old precedents gradually
cease to be relevant to modern cases,  either  because everyone comes to agree
that they are   bad
public policy  or   because the laws they interpret and  the
situations to which they apply disappear.$^{13}$ If $n$ is larger,   judges
come across more cases whose decisions are controlled by existing
precedents. The variable $x$ represents the disutility of obeying
previous judges' precedents, and the variable $y$ represents the
utility of having future judges obey one's own precedents.  If $x<y$,
a judge would be willing to obey one other judge in return for one
judge obeying him.  The discount rate, $r$, represents the declining
utility of obedience to one's precedents by judges further in the
future.$^{14}$ 

 The only reason a judge would follow existing precedents in this
model is to induce future judges to follow his own precedents. It is
possible that a judge dislikes following precedent so much that he
would violate precedent even if that were sure to destroy his own
future influence. If a judge obeys no precedents, and none of his own
precedents are obeyed, his payoff is zero.  If, on the other hand, he
obeys   $m$ past precedents   and the $m$ succeeding judges all obey
his  new precedent, then $A^j_{j-i}=1$ for $ i =1,\ldots m  $, $A^j_{j-i}=0$ for $
i =m+1,\ldots n  $,  and the
judge's payoff is 
 \begin{equation} \label{e2}
  \pi(m)    = -  \sum_{i=1}^m (x) +\sum_{i=1}^m \left(
\frac{1}{1+r}\right)^i (y).
  \end{equation}
The amount  $\pi(m)  $ is a measure of the judge's willingness to obey precedent
in
response to  the  reward  of future influence.  Inspection of (\ref{e2}) shows
that $\pi(m)  $ declines in $x$ and $r$,
and increases in $y$. If $r$ is small enough and $y >x$, then  $\pi(m) >0$  and
$\pi(m)$ is increasing  for small $m$ and decreasing   for large $m$, because
 \begin{equation} \label{e2ab}
 \pi(m)   - \pi(m-1)  = -  x  +   \left(
\frac{1}{1+r}\right)^m (y). 
 \end{equation}
  Denote the value of $m$ that maximizes $\pi(m)$ (subject to $m \leq n$) by
$m^*$.
   We will say that if $\pi(m^*)  
\geq 0$,  {\it the   feasibility condition}  is satisfied.  This means that   the
judge will
be willing to obey $m^*$ precedents if his own precedents thereby command the 
obedience of $m^*$ future judges. Obedience still might not be the equilibrium
outcome, but if the feasibility condition is satisfied,
it becomes possible.$^{15}$  
 
       The feasibility condition is   satisfied if $x$ and  $r$ 
are small enough in magnitude  relative to  $y$--- that is,  if
judges do not dislike following precedent too much, if they do not
discount the future too much,   and if they   enjoy future influence enough.
  Table 1 presents a numerical example   in which 
   $r=.05, x=100$,    $y=200$, and $n=20$.     The payoff of a judge in an
equilibrium in which each judge follows $m$ precedents is greater than the payoff
from following zero precedents (which is zero), and   $m^*=14$.

\begin{center}
 TABLE 1 GOES HERE
 \end{center}




\bigskip
  \noindent
 { 2.1 What the Model Excludes}

 The model is  designed to look specifically at the question of how
judges   motivated by a desire for present and future influence
will behave. It excludes other motivations, which are worth briefly
discussing here before going on to discover what happens when only
influence matters.

 Most importantly, many and perhaps most judges have modest aims. Their 
  opinions on what the law should be are weak enough that  even a
small amount of social conditioning can restrain the temptation to
flout precedent. The typical high-court judge previously served as a
judge on a lower court, where he had little choice but to obey
precedent, so   he has been habituated to following
precedent.$^{16}$    More importantly, judges, like other peoples, are 
averse to effort.    It is easier to follow precedent than to break new ground, so
judges  have incentive to follow precedent when other motives are absent.$^{17}$
The litigant and amicus briefs are helpful, and clerks may do
the actual writing, but the judge still must do some thinking if he
is to sign his name to a novel opinion.$^{18}$  
 

  The model also fails to apply   
 to a Holmes or a Cardozo, a judge who
desires influence but who would achieve it through sheer brilliance even  ina
system without binding  precedent.  Judges with such talent can flout precedent
and still retain their
influence because  their reasoning would be cited even if it was written
in a law review instead of a court reporter.    Cardozo's
judicial influence  is mainly through his state court opinions, which
have no precedential force outside of New York, and   Holmes's  
influence is   through his dissents, which have the {\it
opposite} of precedential force.$^{19}$  But exceptional intellects
are  exceptional.  The model is driven by the assumption that
judges want to influence policy, but it will be a model of the
ordinary judge, whose future influence, if it is to exist, must be
based on the authority of his position rather than the brilliance of
his intellect.$^{20}$ 



 Even limiting ourselves to reputation as a motivation, reputation
might work in a number of different ways. The desire for future
influence is different from 
 three other ways that reputation might discipline
judges.$^{21}$  

First, desire for future influence is different from desire to sell a
high-quality product, although the technical model below will have
features similar to those that economists have used to model product
quality.$^{22}$    The key element in product-quality models is
that consumers can punish a misbehaving seller by boycotting him
after one bad experience. This incentive would apply only if
litigants mutually agreed to let certain judges hear their cases, and
the judges were rewarded for the number of cases they heard. 


 Second, desire for future influence is different from desire for a
good reputation with the public.  To the extent that public opinion
does matter, it undermines judicial independence; so long as the
judge gives way, it makes little difference whether it is to threats
of dismissal or to threats of having his feelings hurt by the
disapproval of his fellow citizens.  But in fact the public does not
seem to mind when judges refuse to obey precedent or statute.
Americans make little distinction between judges and politicians, and
give more credit for desired policy than for judicial integrity, as
one might realize from the emphasis on policy outcomes rather than
judicial craft in the public debates on {\it Roe v.  Wade} and Robert
Bork's nomination to the Supreme Court.$^{23}$  One reason the common man cares so
little about
judicial interpretation is perhaps that he realizes how ignorant he
is on the subject; it requires some sophistication to know that a
judge is brushing aside the law, if he refrains from admitting it
openly.

Third, desire for future influence is different from desire for a
good reputation within the legal profession.  Other lawyers  know better than the
public whether a decision follows
precedent or not, and their opinion of judges might be based on that.
This preserves some of the independence of the judiciary, especially
if judges care only about the goodwill of other judges. It is not 
clear why the legal profession should esteem a judge for following
precedent instead of, for example,   clever substitution of
his personal preferences. It will usually be the case that lawyers will feel
uneasy when precedent is violated, however, since their expertise is based on
their ability to predict judicial outcomes, which becomes easier when precedent is
followed.$^{24}$





\bigskip
\noindent
 {\bf 3. The Model's  Equilibrium}

       An equilibrium  in this model consists of a strategy
for each judge such that no judge could increase his influence by
unilaterally deviating from his strategy to something different.
 The game has an infinite number of equilibria, as is typical of
repeated games with infinite horizons.$^{25}$   What the multiplicity of
equilibria
means is that the actual outcome depends on the expectations of the
players, because there are many self-enforcing outcomes.  This means
that besides the traditional question of how the parameters of the
model affect the equilibrium, we must also ask how expectations
affect it. This will be how the concept of legitimacy can enter a
game in which every player is a cold-bloodedly rational {\it homo
economicus}. 

  
 The following six possible equilibrium strategy profiles, of which
only the first four are actual equilibria, 
  will serve as a basis for discussion. Each will be called an
``expectation regime,'' because which one is actually
played out depends on which one the players expect to be played out;
an equilibrium is a set of self-confirming expectations.  Each is described from
the point of view of judge $j$.

\noindent
\underline{Expectation Regime     1 (judicial breakdown)}.\\
 \hspace*{.15in  }  {\it Strategy}: Violate every precedent. \\
\hspace*{.15in  }  {\it Outcome:} Every judge violates every
precedent.

\noindent
\underline{Expectation Regime     2 (breakdown punishment)}.\\
\hspace*{.15in  }  {\it Strategy:} Obey
every precedent unless some previous judge has violated a precedent.
In that case, violate every precedent.\\ 
 \hspace*{.15in  }  {\it Outcome:} Every judge obeys every
precedent.

\noindent
 \underline{Expectation Regime     3 (specific punishment)}.\\ 
 \hspace*{.15in  }
 {\it Strategy:} Obey the precedent of
Judge $j-i$ , for $i=1,\ldots,n$,  if he ``retains legitimacy,'' and violate it
otherwise. Judge
$j-i$ retains legitimacy if he himself followed this strategy.\\
  \hspace*{.15in  }  {\it Outcome:} Every judge obeys every
precedent.

\pagebreak

\noindent\underline{Expectation Regime     4  (lax specific punishment)}.\\ 
 \hspace*{.15in  }  {\it Strategy:} Obey the precedent of
Judge $j-i$ , for $i=1,\ldots,n-1$,  if he ``retains legitimacy,'' and violate it
otherwise.   Violate the precedent of   judge $j-n$.   Judge $j-i$ retains
legitimacy if he himself followed this strategy  or if he obeyed all
$n$ precedents. \\
 \hspace*{.15in  }  {\it Outcome:} Every judge obeys $n-1$ precedents
and violates one precedent.

\noindent
\underline{ Expectation Regime     5 (blind precedent)} (not an equilibrium).\\ 
 \hspace*{.15in  } 
 {\it Strategy:}  Obey the precedent of  every judge.  
  \\ \hspace*{.15in  }  { \it Outcome } (if all judges follow the
strategy):  Every judge obeys every precedent.


\noindent
\underline{Expectation Regime     6 (simple punishment)}  (not an equilibrium).\\ 
 \hspace*{.15in  } {\it Strategy:} Obey the precedents of every
judge   unless the immediately preceding judge violated
any precedents. In that case, violate every precedent.  \\ 
 \hspace*{.15in  }
 { Outcome \it} (if all judges follow  the strategy):  Every judge obeys every
precedent.



\bigskip

 An expectation regime is a Nash equilibrium if   no judge can benefit from
deviating from his expected behavior given that the other judges do not
deviate.$^{26}$  The first four
expectation regimes form Nash equilibrium.  Under Expectation Regime 1, a judge
who
deviates by following precedent reduces his payoff by $x$ for each
precedent that he follows, without any corresponding gain, so he has
no reason to deviate.  Under Expectation Regime 2, a judge who
deviates by violating precedent gains up to $ nx$ (if he violates all
$n$ precedents), but he loses $ \sum_{i=1}^{n} \left( \frac{1}{1+r}
\right)^i y$.  If $\pi(n) \geq 0$, the loss from violating precedent is greater
than the gain.   Under Expectation Regime 3, the same is true.
Under Expectation Regime 4, a judge who deviates by not violating any
precedents reduces his payoff by $x$. A judge who deviates by
violating two or more precedents gains up to $ (n-1)x$, depending on how many
precedents he violates,  but his own precedent is violated in the future, so
unless   $\pi(n-1) \geq 0$,  he has no incentive to violate precedent, and
Expectation Regime 4 also is a Nash equilibrium.

 Expectation Regimes 5 and 6 are included to show that although many
equilibria exist for this game, not every  pattern of behavior  forms an
equilibrium.  It is easy to see why   Regime 5 does not. If
every future judge is going to obey precedents regardless of what
happens, judge $j$ can increase his payoff by deviating and violating
every previous precedent. His own precedent will be obeyed despite
his misbehavior, so the  expectations are   not self-sustaining. The failure of
  Regime 6 is more subtle. If every judge did follow the
behavior specified, no judge would have an incentive to deviate by violating
precedent, because his immediate successor would violate his
precedent and the judges further into the future would also violate
precedent, in a chain reaction in which judge $j$ violates precedent
because judge $j-1$ had violated precedent.  Consider, however, the
incentives of judge $j+1$ after judge $j$ violates precedent. If
judge $j+1$ follows   Regime 6, he will violate precedent
himself, as will all future judges, and his payoff will be 0.  If he
deviates by obeying $j$'s precedent, and that of his other
predecessors, then his successors will obey precedent and judge
$(j+1)$'s payoff will be $\pi(n)  $, from equation (\ref{e2}). If 
 $\pi(n)  >0$, 
  Regime 6 is not an equilibrium.$^{27}$ This shows that
punishments must be carefully arranged; if they cost the punisher too
much, they are not effective.  Expectation Regime 2  appears  
similar to  Regime 6 but it is more effective because
under   Regime 2, unlike  Regime 6, no
individual judge has the power to stop the  destructive consequences
of judge $j$'s deviation.  

  Which equilibrium is  actually played out depends on the expectations of the
players in the game. The considerations which enter into this s will be discussed
below in Section 4.2, but first let us look into the welfare properties of the
different equilibria.
 
%---------------------------------------------------------------

\bigskip  
\noindent
 {\bf 4. Implications}

What has been shown so far is that different equilibria exist  and
the effectiveness of a system of precedent depends very much on the
expectations of the judges.  The argument that judges do not need
external monitoring because they will follow precedent in order to
increase their influence can be true, but it  is not necessarily true
even within the confines of a simple model. This section will
discuss the attractiveness and feasibility of the different equilibria
and link them with exogenous variables such as the degree of
discounting of future influence.  


 If the feasibility condition is satisfied, there exist both
equilibria in which courts follow precedent and equilibria in which
they do not.  Let us divide the implications of the model into those
relating to the feasibility condition and those relating to
differences in the equilibria.

 First, consider the feasibility condition. If it is not satisfied,
then Expectation Regimes 2 and 3 are not equilibria,  and if it is
strongly violated (if, for example, $x>y$), there is only a single
equilibrium: judicial failure. This is bad for the public because
every judge violates precedent and the law is inconsistent, and it is
bad for judges because their influence ends with their tenures on the
bench. Hence, if society can change the parameter values $x$, $y$,
$r$, and $n$ so that the feasibility condition is satisfied, it
should do so. 

 The disutility of following precedent, $x$, should be made as small
as possible. Choosing $x$ to
be small was one of the methods of judicial control discussed
earlier, where it was noted that it is costly, whether it takes the
form of selecting judges with small $x$'s or of teaching judicial
restraint in law schools.  As with any choice variable, however, it
should be used up to where the marginal cost exceeds the marginal
benefit.$^{28}$ 

 The utility of having one's precedents followed, $y$, should be made
as large as possible. The desire to have an impact on the law is is
not bad in itself; it is only bad because breaking precedent and
misinterpreting statutes are its byproducts. To the extent that
judges can be made desirous of having future influence, however, it
is easier to induce them to follow precedents they dislike. 

  

 The number of old precedents, $n$, is not a matter of
the judge's taste, like $x$ or $y$, but of how long old law remains
relevant. It really represents the maximum amount of old law that judge must
follow relative to the amount of new law he can create, which is
normalized to a value of one.  If old law does not depreciate, but
instead accumulates until it decides almost  every case a judge
will hear in his lifetime, it follows that $n$ is very large and   $\pi(n)   <0$,
so no equilibrium can induce the judge to follow every relevant precedent.  The
value of $n$ is
determined partly by the pace of social change, as whaling law
becomes obsolete and software law becomes necessary. It is also
partly determined by the activism of the legislature, which can
forestall judge-made law by passing detailed statutes in new areas.
The model suggests that the legislature might find more of its
statutes faithfully interpreted if it left more legal territory
empty, because judges need scope for their policymaking urges if they
are to be kept responsible.$^{29}$ 

 The distinction between {\it ratio decidendi} and {\it dictum}
limits the rate at which new law can be created, which is  useful
with regard to maintaining a precedent-obeying equilibrium. Judges
must wait to create law until appropriate cases arrive at their
benches, and only the {\it ratio decidendi} or {\it holding}, the
case's essential and decisive point of law, is binding precedent.
{\it Dicta},   rulings irrelevant to the case's outcome, are,
by convention, not binding on future judges, although, like anyone's
writings they may be considered as arguments.  If {\it dicta} were
binding, a judge could create an unlimited amount of new law. His
six-hundred-page decision on a bankruptcy case could also control the
law on abortion, copyright, and criminal evidence. Such an
equilibrium could not be maintained in this model, because even if
the {\it dicta} carefully avoided violating existing precedent, very
little new law would be left to future judges to create.
 
 The discount rate, $r$, is like $x$ in being influenced by the taste
of the judge and like $n$ in being influenced by external factors.
If $r$ is too large, given the other parameters, judicial breakdown
is the only equilibrium, because judges care too little about the
future. As with the disutility of following precedent, $r$ might be
controlled by molding the tastes of future judges or by selecting
judges carefully to find those that look to history. But it too is
affected by legislative activism. If the legislature increases the
probability with which it replaces judicial decisions by statutes,
especially if the statutes reverse instead of codifying the
decisions, then $r$, like $n$, will increase as the expected lifetime
of the precedent declines. 

 \bigskip
\noindent
 {4.1 Comparing Equilibrium Expectation Regimes   }

Having discussed what makes precedent-following  expectation regimes feasible,
let us now compare  them.  The payoffs
for the judges are 0 under Expectation Regime 1 and $\pi(n)$ under
Expectation Regimes 2 and 3. The payoff  under Expectation Regime 4 is $\pi(n-1)$,
which might be either greater or smaller than $\pi(n)$, depending on the value of
$m^*$.
 The public simply wants the greatest number of precedents upheld, so
it likes Expectation Regimes 2 and 3 best, then Expectation Regime 4,
and lastly Expectation Regime 1. 
Judges and public both prefer  Expectation Regimes 2 and
3   to Expectation Regime
1.  In addition, if $m^*=n$, then both the judges and the public both rank
Expectation Regime 4 between Regimes 3 and 1, because everyone prefers an
equilibrium in which more precedents are followed.$^{30}$  If $m^*< n$,  then
judges have slightly different interests from the public, because the public
favors equilibria in which all $n$ precedents are followed, but the judges prefer
equilibria in which only $m^*$ equilibria are followed.

 Expectation Regimes 2 and 3 achieve exactly the same outcome: every
judge obeys every precedent.  Where they differ is in the sanctions
they would impose if a judge deviated and violated precedent.
Expectation Regime 2 uses a sanction similar to the grim strategy in
the repeated prisoner's dilemma: if there is a deviation, the game
instantly and permanently drops into the worst possible equilibrium.
Expectation Regime 3 uses a narrower sanction, punishing only the
deviant judge. The effect on the deviant judge is the same  in either equilibrium,
but Expectation Regime 2 has adverse side effects on all
other judges too.  This makes Expectation Regime 3 superior if there
are a few judges who break precedent out of confusion or because they
do not care about future influence. If such judges exist, Expectation
Regime 2 sooner or later brings the system to judicial breakdown.

Expectation Regimes 2 and 3 can be interpreted as depending on the
legitimacies of the judicial system and of individual judges
respectively.  One can interpret Expectation Regime 2 as saying that
misbehavior by a judge destroys the legitimacy of the judicial system
as a whole. Judges no longer expect each other to obey precedent once
the triggering event occurs, and their beliefs are self confirming.
One can interpret Expectation Regime 3 as saying that misbehavior by
a judge destroys that judge's legitimacy but not the legitimacy of
the system. Future judges reject his precedents, but obey those of
well-behaved, legitimate judges. Note also that loss of legitimacy
can take more than one form under Expectation Regime 3. Not only does
a judge who breaks precedent without reason lose his legitimacy, but
also the judge who obeys the precedent of a precedent-breaker.
Failure to punish is as deviant as the initial offense.
 
 Expectation Regime 4 shows that Expectation Regimes 2 and 3 are not
fragile in the sense that a slightly greater reluctance to punish
would induce complete judicial breakdown.  Expectation Regime 4
allows each judge to disregard one previous precedent without
punishment, which he will thereupon do.  Other equilibria may exist 
 in which two, three, or some other number   of
unpunished precedent violations are allowed.  The difficulty with
these equilibria is in the unmodelled formation of expectations: it
may be difficult for the judges to maintain common expectations that
the equilibrium is one in which each of them is, for example,  limited to exactly
seven violations before he becomes illegitimate. 

Where a lax equilibrium such as Expectation Regime 4 makes social sense is if (a)
it is not
always clear if a judge is obeying precedent or not, or (b) it is
socially important to allow some precedents to be broken.  Judges
will try to push against precedent as far as they can under any
system, wherever the line is drawn, so condition (a) will certainly
apply. Allowing   one distortion of precedent so gross as to be
called a violation will of course encourage them to distort all
precedents more, and would require a more complicated model to
analyze. But this may be a reason to allow some apparent
violations.$^{31}$   Reason (b)
will also usually apply: the social optimum will rarely be to follow
precedent always, and even if judges' policy tastes did not match
those of the people exactly, they would match for the most extreme
cases.$^{32}$  

 
 
Another advantage of ``lax equilibria'' which allow some violation of
precedent is that they may have weaker feasibility conditions, and
hence be possible to maintain when Expectation Regimes 2 and 3 are
not.   If the number of precedents to be followed is   $m^* < n$, it is  possible
to sustain an equilibrium even when judges cannot be induced to follow all $n$
precedents.   Note, however, that it does not necessarily become easier to sustain
an equilibrium as the number of precedents to be followed declines, because this
also reduces the influence of the precedent-following judge: he is less
constrained today, but influences fewer future generations of judges.


  

 If no feasibility condition is satisfied, and Expectation Regime 1
is the only equilibrium, the result is not necessarily a system in
which judges always violate precedent and interpret statutes
capriciously. Rather, one would expect society to arrive at some
other solution to the problem of judicial control. The obvious
solution is to give up on independence of the judiciary and subject
judges to external sanctions: if the equilibrium is bad, change the rules of the 
game. If expectations fail to result in a desirable
equilibrium, one might expect the state to move to a civil law system
in which judges are more closely constrained. 



 \bigskip
\noindent
 {4.2  Which Equilibrium Will be Played Out?   }
 
 
When the feasibility condition is
satisfied but the current equilibrium is undesirable,  is  it possible
to move to a better equilibrium, rather than abandoning hope of an independent and
responsible judiciary?   Expectations determine what behavior is in an
individual's   self-interest.  Under Expectation Regime 2,
for example, each judge expects that if he were to break precedent,
future judges would disregard his precedent, and this is a correct prediction. A
player in a game cannot create his own expectations,
even though this might be to his advantage. Game theory takes
expectations as part of the primitive assumptions of the model; it
is, indeed, one of game theory's weaknesses that it must do so. More
informally, however, we might hope that public policy could be
directed towards creating the expectations that lead to the
equilibrium with the highest payoffs.
 The origins of expectations are unclear, but game theorists commonly
refer to    pareto optimality, simplicity,  tradition,  and communication as three
ways that expectations can be formed.  An equilibrium that is pareto optimal,
that uses simple strategies,  that has  been played  out in the past, and that is
publicly announced to be the equilibrium is a ``focal point,'' an equilibrium
attractive for psychological reasons.

 Pareto optimality is perhaps the most unreliable  of these  focal
characteristics, especially in this game. If $m^*=n$, then an equilibrium with all
$n$ precedents followed is best for both judges and public, but if $m^* <n$,   an
equilibrium with only $m^*$ of the precedents followed is pareto optimal from the
viewpoint of the judges.  Adapting the game to the real world, where it is often
unclear whether precedent has been violated or not, makes it even less clear what
equilibrium is Pareto optimal, since, as discussed in the previous section, a lax
equilibrium is less likely to result in judicial breakdown when judges make
mistakes about the behavior of previous judges.   Thus, even the identity of the
pareto optimal equilibrium is ambiguous.

 Simplicity is also a difficult characteristic to determine. It seems plausible
that judges would have a difficult time coordinating on a complex equilibrium such
as one in which every judge violates only the precedent of the judge six times
removed from himself, but it is less clear whether Expectation Regime 4 in the
list above is significantly more complex than Regime 1.
   
Tradition is a more plausible source of expectations. 
  If Expectation Regime 4 has been the equilibrium
in previous repetitions of the game, that makes it focal for the game
presently being played out. The  expectations that
sustain a good equilibrium are a form of social capital  (see Coleman),
a valuable asset which may be
 difficult to recover if it is  ever  destroyed.

  The influence of tradition may provide a tool for changing the equilibrium. One
problem that arises in macroeconomics is self-confirming inflationary
expectations.  People expect prices to rise, and they therefore behave in ways
that make prices rise. One justification for temporary price controls is that they
will change expectations, so that even after the price controls are removed,
prices will not rise. Here, similarly, if judges consistently break with
precedent, removing the independence of the judiciary for a period of time by
punishing judges who break precedents  might change the expectation of how judges
will behave, so that if independence is restored, the judges will be more
responsible.  Thus, if the legislature intervenes occasionally using external
incentives such as those discussed in the introduction to this article---
impeachment, changes in the number of justices, and changes in procedural rules---
it may be able to change expectations in such a way that judges continue to behave
responsibly even after the external threat is removed.  The lack of success of
price controls in stopping inflation, however, should  prevent us from  putting
too much   hope in this solution to judicial misbehavior.
 
 

 Announcements may also determine expectations. 
If all the
judges tell each other that Expectation Regime 2 is the equilibrium
to be played out, it seems  plausible that they would
believe each other, since that equilibrium is better for all of them
than is Expectation Regime 1.$^{33}$     The mechanics by which a judicial culture
arises  cannot easily be derived from economics or game theory, but it would seem
useful for  judges to  discuss jurisprudence informally and frequently, something
which various state and federal programs that now  exist primarily to discuss
specific substantive issues  would facilitate.   Or, if some outside party--- a
legislature, or the academic literature--- announces that
Expectation Regime 2 will be played, judges  may  use this
evidence when deciding how future   judges will respond.  
Announcements, even if they have no binding force, can matter if they change the
expectations of players in a game.

 The effect of   announcements is subtly different from the effect of changing
tastes, because  announcements operate on expectations, not on payoff functions.
    Tastes concern a player's personal
preferences, independent of the actions of other players, whereas
expectations are purely instrumental, and fundamentally concern what
other players do.  Alteration of tastes cannot be achieved simply by
an announcement; it requires conditioning, which is costly.
Expectations, on the other hand, are entirely about the behavior of
other players, and hence might be changed by a costless announcement,
if the announcement is plausible.  If the legislature tries to change
a judge's taste by announcing ``Judges enjoy following precedent for
its own sake,'' nothing will happen.  The judge knows it is false in
his own case, and that simply asserting the fact does not make it
true.  If, however, the legislature tries to change a judge's
expectations by announcing ``Future judges will not obey the
precedents of present judges who themselves have disregarded
precedent,'' the announcement might be self-confirming. 


 This suggests another way to   move from a Pareto-inferior equilibrium to one in
which judges follow precedent:   use   announcements to change the expectations of
the judges. Even if outside parties do not threaten the judges, they can influence
judicial behavior if they can change the judges' expectations. If  all   the
treatises, law professors, and law reviews say  that the regime has changed  and
predict that  future judges will obey precedent if present judges do, the
predictions  may become self-confirming. This is also true of predictions that
worsen the equilibrium: if everyone predicts that judges will flout precedent, it
may become in the interest of judges to break precedent.

  


 
\bigskip
 \noindent
 {\bf 5.  Judges Who Follow Precedent Even in the Absence of  External Incentives}


 What happens if there exist some conscientious judges who positively
enjoy following precedent, or some lazy ones who prefer it  to the effort of
creating new law?  Either of these can be
modelled by specifying that if judge $j$ breaks precedent then the
expected number of future judges who will follow $j$'s precedents is
not zero or $m$, but $\theta m$, where $\theta$  is the percentage of inflexibly
precedent-following judges. Let us consider the
decision of one of the judges who does {\it not} enjoy obeying
precedent, and see under what conditions he can be induced to obey
precedent in this modified model. His  payoff if he  obeys
precedent in an equilibrium in which all judges obey is
 \begin{equation} \label{e4}
 \pi(obey) = -  \sum_{i=1}^m \left( x  \right) + \sum_{i=1}^m
\left(\frac{1}{1+r}\right)^i \left(    y   \right)
 \end{equation}
 and his  payoff  if he deviates and follows no precedents
is, if his precedents are followed only with probability $\theta $:
 \begin{equation} \label{e5}
 \pi(deviate) = -  \sum_{i=1}^m \left(0\right) + 
\theta\sum_{i=1}^m \left(\frac{1}{1+r}\right)^i
\left( y \right).
 \end{equation}
 The feasibility condition is  $\pi(obey) - \pi(deviate) \geq 0$,
i.e.,
 \begin{equation} \label{e6}
  - m x + \left( 1-\theta \right) \sum_{i=1}^m
\left(\frac{1}{1+r}\right)^i \left(    y  \right)  \geq 0. 
  \end{equation}
 This feasibility condition is easiest to satisfy if  $\theta=0$.    The presence
of judges who enjoy following
precedent may therefore result in fewer judges following precedent, because
  the precedent-enjoying judges are unwilling to punish the
precedent-flouting judges.   It is a paradox of the same kind as the
paradox  that the number of wars  can increase   in the amount of disarmament  
because of the decline in deterrence.  The implication is that care
must be taken to avoid instilling overly crude preferences into
judges.$^{34}$   Training them
to blindly follow precedent by making their disutility of precedent
negative ($x <0$ in the model's notation)  can have consequences adverse to the
public
unless the system begins in judicial breakdown, since it reduces deterrence for
those judges for whom the training is ineffective.  If the public wishes
to condition future judges, it should condition them to enjoy
following a strategy such as that of Expectation Regime 3. Where conscientious
judges would be more useful is
when an irresponsible but clever judge can obscure his violations by
twisted reasoning.  I suggested above that this might make
Expectation Regime 4 more attractive; it also makes conscientious
judges more useful.$^{35}$ 


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

\bigskip
 \noindent
 {\bf 6.   Concluding Remarks}

 

 \begin{small} \begin{quotation} ``Hardly ten men of true integrity
and good faith can be found today, and yet the offices of the state
number in the hundreds. If they must be filled by men of integrity
and good faith, then there will never be enough men to go around; and
if the offices are left unfilled, then those whose business it is to
govern will dwindle in numbers while disorderly men increase.
Therefore the way of the enlighted ruler is to unify the laws instead
of seeking for wise men, to lay down firm policies instead of longing
for men of good faith'' (Han Fei Tzu: 109).  
  \end{quotation}
 \end{small}
 
 


  Writing in the third century B.C., Han Fei believed that a firmly
controlled bureaucracy was the only way for the state to ensure the
faithful administration of the law, because the Confucian ideal of
autonomous scholar-administrators required an unrealistically high
level of virtue. This article's model   has shown that the
  maintenance of a judicial system that is both independent and
responsible does not necessarily require men of integrity and good
faith. Judges need no professional conscience to impel them to obey
existing law even when they think it bad policy, but instead can be
made to obey it to maximize their own influence, in the hope that the
new law they create interstitially will be obeyed by future judges.
In theory, then, it is possible even for purely self-interested
judges to discipline each other. 


 The model also shows, however, that   though the judges in such a
system need not be virtuous, the climate of expectations and the
norms of judicial behavior must be carefully balanced to sustain
responsible behavior as a self enforcing equilibrium. Future judges
must impose sanctions on judges who break precedent and misinterpret
statutes by not following their precedents.  If all judges follow
precedent for its own sake, regardless of the behavior of the judge
who set the precedent, there is no problem, but if only some of them
do so, then the judges who are not internally motivated will be free
to warp the law without fear of losing their influence.

    The outcome does depend on expectations. If  judges care only about their own
policy
preferences and desires to affect the law, then one equilibrium
outcome is for precedent to be freely violated.  Responsible behavior
is another possible outcome, however, and can be achieved by a
variety of different norms. One equilibrium that can sustain it is for the
deviation of an irresponsible judge to trigger judicial breakdown
into a regime in which precedent is standardly violated.  A rational
but self-interested judge will follow precedent in order to avoid
undermining the legitimacy of the judicial system as a whole. Another
equilibrium is for the deviation of an irresponsible judge to result in
disregard of his own holdings by future judges. In this equilibrium he
will follow precedent to preserve the individual legitimacy of his
own precedents. In either case, legitimacy is preserved not by the
reverence of the individuals involved, but by their rational self
interest. 
    
     

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

(UNNUMBERED) I wish to thank Jack Hirshleifer, Thomas Krause, John Lott,
Karl Moehne, Richard Posner, J.  Mark Ramseyer, Ron Rogowski, Kathryn
Spier, Gary Schwartz,  and participants in the Indiana University Workshop in
Political Theory and the University of Chicago Law and Economics
Workshop for helpful comments.  Part of this article was written while
the author was Olin Faculty Fellow at Yale Law School and on the
faculty of UCLA's Anderson Graduate School of Management.  


1.  Judicial salaries are
under legislative control  but it is somewhat implausible that the
small changes in them has a strong effect on judicial decisions, though 
Anderson, Shughart and Tollison have found a positive correlation between the
salary of state chief justices and the willingness of the courts to
overturn legislation on the grounds of substantive due process.
Article III of the U.S. Constitution forbids Congress to reduce the
salary of federal judges. This  gives rise to a curious agency problem when it
must be interpreted.    In 1920 the Supreme Court
held that judges could not be required to pay income tax ({\it Evans
v. Gore}, 253 U.S. 45 (1920)); this was  extended to judges
whose terms started after the income tax was imposed  ({\it Miles v.
Graham},  268 U.S. 501 (1925)); and reversed after Congress expressly passed
a statute subjecting newly appointed judges to the income tax ({\it O'Malley v.
Woodrough},  307 U.S. 277 (1938)).


2.  A
judge's equals can also overrule him, which is one reason why
appellate courts have more than one judge---e.g., 3-judge appellate panels, and
the  9-judge Supreme Court of the U.S.
Federal system. The problem remains that if a majority of the judges
in a court agree and wish to substitute their personal opinions for
the law, it is hard to discipline them---impeachment, in fact,
becomes even more difficult.  And if a panel of judges substitutes
personal belief for precedent and statute, the law can become even
more unstable than with a single irresponsible judge, due to voting
cycles, as Easterbrook (1982) has noted.   

3.  Such amendments have worked
on occasion, however.  The Eleventh and Sixteenth Amendments were
passed to overrule the U.S. Supreme Court decisions {\it Chisholm v.
Georgia},  2 U.S.  419 (1793) and {\it Pollock v. Farmers' Loan and Trust Co.},
158
U.S. 601 (1895).  See also {\it Cory v. Shierloh}, 629 P2d. 8 (1981), in
which the California Supreme Court acknowledges the constitutionality
of a statute that states ``The Legislature hereby declares that this
section shall be interpreted so that the holdings in cases such as
{\it Vesely v. Sager},  5 Cal.3d 153, {\it Bernhard v. Harrah's Club}, 16 Cal.3d
313,   and {\it Coulter v. Superior Court},  21 Cal.3d 144  be abrogated in
favor of prior judicial interpretation finding the consumption of
alcoholic beverages rather than the serving of alcoholic beverages as
the proximate cause of injuries inflicted upon another by an
intoxicated person.'' West's Annotated California Codes, Business and
Professions Code (1985: 454), $\S$25602(c).  For a formal model of
the interaction between legislature and court, see Gely and Spiller.



4.  Even in modern Europe, an independent judiciary
does not mean the same thing as in the United States.  ``Oversight
and disciplinary measures may be directed toward judicial activity
outside the core ({\it Kernbereich}) decisional process protected by
judicial independence.  Thus, sanctions can be applied against a
judge who fails to apply a well-known general statute, who applies a
formally repealed statute, or who ignores a binding decision from the
Federal Constitutional Court'' (Clark: 1840). 

5. See, for example, Solum's article on the virtues to be sought in
judges, which 
  spends 2 pages on ``judicial wisdom'' and 10 1/2 pages on ``judicial
intellect,'' but only 1 page on ``judicial integrity'' (``a special
fidelity to the law and its coherence''). Is this because integrity
is so common, because it is so rare, or because it is so easily
faked? 

6. Judge Cardozo, for example, wrote of   judges who did not
try to make policy that ``Their notion of their duty is to match the
colors of the case at hand against the colors of many sample cases
spread out upon their desk.  The sample nearest in shade supplies the
applicable rule. But, of course, no system of living law can be
evolved by such a process, and no judge of a high court, worthy of
his office, views the function of his place so narrowly. If that were
all there was to our calling, there would be little of intellectual
interest about it''  (Cardozo: 20).  

7.  Posner (1993)   discusses this
motivation for judges. 

8. These other judges might, in fact, include
contemporaries. Some courts, such as the U.S. Courts of Appeal,
divide into smaller panels to hear cases. Each judge would like all
other panels in his circuit to follow his precedents, which they
customarily do. 

9.  Traditionally,
judges said that they ``discovered'' the common law rather than
``created'' it, but the model still applies. The difference is
unimportant so long as the discovering judge, like the discovering
scientist, cares very much about having the truth established, and
with his name attached. 

10. ``The civil law judge is not a culture hero
or a father figure, as he often is with us. His image is that of a
civil servant who performs important but essentially uncreative
functions. It is a logical, if not a necessary, consequence of the
quite different status of the civil law judge that he is not widely
known, even among lawyers'' (Merryman: 38). 


11. Each judge is
representing an entire court. Collegial bodies have internal dynamics
which will be ignored here, but which are central to  Easterbrook (1982),
Kornhauser (1992a, 1992b), and Schwartz.

12.  It
is perhaps even more important for a judge to faithfully interpret
statutes as for him to follow precedent.  This could be incorporated
into the model by specifying a number $z$ of statutes that each judge
has the choice between following and violating, and the model's
results would be essentially the same. When I talk of the problem of
inducing judges to follow precedent, this is for expositional
convenience, and the reader can feel safe in adding ``and inducing
judges to follow statutes.'' The only caveat is that this model could
not operate entirely without judge-made law: a judge needs some
carrot in the form of law he can create if a precedent-following
equilibrium is to be possible. 

13.  Landes and Posner (1976: 255) found
that the median age of citations from the U.S. Courts of Appeals to
the Supreme Court was 9.8 years and to appeals courts was 4.3 years
(from a sample of 658 decisions, 1974-75).    Some precedents gain strength with
age, but others lose strength.  Easterbrook (1988: 424) notes that the 1871
Original Package Rule was overturned with   very little comment in 1976 ({\it Low
v. Austin}, 80 U.S.  29 (1871), overturned in {\it Michelin Tire Corp. v. Wages},
423 U.S. 276 (1976)).
    
14. This model is a
descendant of the overlapping generations model of Paul Samuelson.
In Samuelson's model, individuals live for two periods, but they
receive income only in their youth, and wealth is not storable. Thus,
if there are no transfers, old people starve. If, however, a
convention is established that young people give part of their income
to old people, this can take the place of storable wealth.   

15. The situation in which judges follow the $m^*$ precedents that immediately
precede them is preferred by judges to the more complicated strategies in which
they ``skip over'' some precedents. This is because of concavity of $\pi(m)  $.
The function is not differentiable, so we cannot say that $\pi''<0$,  but its rate
of increase increases at a negative rate:     $[\pi(m)   - \pi  (m-1)] -  [\pi (m-
1) - \pi (m-2)] =  \left[\left(
\frac{1}{1+r}\right)^m -\left(
\frac{1}{1+r}\right)^{m-1} \right](y)  <0$.    

16. It may be that this habit wears off over time.
Members of the Supreme Court, from  Nixon   Republican Justice Blackmun back to
the Jeffersonian
Republicans who served with Justice Marshall, have surprised their
backers by deciding that expansive judicial power was not so bad
after all, once they became the ones to exercise it.  

17.  The reduction in judicial effort is one reason why the system of precedent is
efficient. Macey (p.95) has suggested that even judges who wish to make an impact
on the law  may follow precedent  in most areas so they can concentrate on one
area of expertise. This concentration is most useful,   however, for judges whose
concentration   allows them  to write opinions which must have persuasive   as
well as precedential force.

18.   Restricting the number of clerks and amicus briefs  will help to
stabilize the law if the judge has any preference   for
spending less rather than more time writing opinions, even if  leisure is
not his primary motivation, because following precedent becomes
relatively cheaper. Abolishing briefs altogether would have the
opposite effect, since without the litigants' briefs the judge would
have to discover the precedents himself, and using his own reasoning
might be easier.   


19.  In fact, while on the U.S.
Supreme Court, Cardozo's citations by the lower federal courts were
fewer than those of his less distinguished but more senior
colleagues  (Posner, 1990: 88).   

20.  An implication of the model will be that a
brilliant judge, who knows that his ideas will be influential
regardless of their value as precedents, may very well be an
irresponsible judge.  

21. For further exploration of the motives of judges,
see Posner (1993). He emphasizes the desire to vote, to register an
opinion rather than to exert influence, as a motive for judges,  and
  balances this  against the  desire for leisure. 


 22. The literature on reputation and
product quality is descended from Klein and Leffler.
  For a formalization as an infinitely repeated game see Rasmusen
(1989: 96). For applications to law, see Palay or Ramseyer. The
Klein-Leffler model is about trust when information is asymmetric;
the influence model here is a game of perfect information with
symmetric players.  

23. See the articles on
the public attitude towards the judiciary cited in Posner (1990:
136).   

24. Cooter  has written on the incentives of private judges, who  in competing
for business from litigants would tend to make efficient decisions, and suggests
that public judges would  do the same to acquire prestige. Prestige is very
different from income, however, and it may only be among economists that an
admirable decision is one which maximizes wealth.

25.  See
Fudenberg and Maskin: 92 or Rasmusen (1992).  The present model is
not a repeated game, strictly speaking, since the player is different
at each stage, but it has the same properties as a repeated game
because the payoff functions link the payoffs of one player to the
actions of later players.   

26.  These are also ``subgame perfect equilibria'' in
that no judge can benefit from deviating even if the game has
departed from its equilibrium path when he makes his decision   
(Rasmusen, 1989: 85).  

27.  This argument is
an implication of the equilibrium concept of subgame perfectness. For
an equilibrium to be subgame perfect, it must be Nash for every
subgame as well as for the entire game, including for subgames that
start off the equilibrium path. 

28.  One way that $x$ is reduced is if the judge can have some influence even when
he follows precedent, by   making the  precedent significantly stronger. He may be
able to do this by adding to his opinion new arguments for why the precedent is
good policy or good law. This is one reason why  we should think twice before
criticizing judges who write opinions in easy cases  rather than ruling without
written opinion.


29.  ``Thou shalt not muzzle the ox
that treadeth out the corn.''  1 Timothy 5:18, King James Version.
This may also help to recruit talented judges, as a legitimate perk
of the office.  See also Cardozo, {\it supra} note 6.  

30. A curious feature of the model is that 
Expectation Regimes 1 through 4 remain equilibria even if the public wishes for
judges
never to follow precedent. This is because the tastes of the public
do not affect the behavior of judges.  
   Other
models of social control have the same feature; see   Hirshleifer
and    Rasmusen: 101.   

31. The problem is akin to that of an
oligopoly deciding when a member has cheated based on noisy
information. See Stigler or the more recent
 Abreu, Pearce and Stacchetti and the references therein. It is also
related to the issue of how much to punish recidivists, where it has
been found that light initial punishments followed by heavy
punishments for repeat offenders are optimal when the probability of
false conviction is substantial. See Rubinstein: 406. 

32. This too might require more formal modelling, because
it raises a free-rider problem: Judge $j$ might push the burden of
overruling the obviously wrong decision $j-1$ onto Judge $j+1$, so that
$j$ himself can choose as his one precedent to violate some decision
that only $j$ dislikes.   

33. Formalizing the
effect of communication---of what game theorists call ``cheap
talk''--- is surprisingly difficult.  See Farrell for a relatively
nontechnical discussion.

34. Contrary to the opinion of  Sir John Salmond (p.
384), who says, ``If, therefore, a precedent belongs to the class
which is absolutely authoritative, it does not lose its authority
simply because it is contrary to law and ought not to have been
made.'' (He refers to precedents made by the Court of Appeals and the
House of Lords for themselves and for the lower courts.) It is
unclear whether Salmond considered the possibility of blatantly
illegal decisions, as opposed to ones that are simply mistaken, but
his statement at least illustrates his first reaction. 

35.  An important caveat is that since in reality judges sit on panels rather than
individually, if most judges follow precedent for its own sake, they will outvote
the judges who value their own influence more than precedent. This is one reason,
no doubt, why higher courts tend to have more members than lower courts. In the
federal system of the United States, trial courts have one judge, appellate courts
ordinarily sit on three-judge panels, and the Supreme Court has nine members.
   


 \newpage
\bigskip
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\newpage
 TABLES

 \begin{tabular}{|l|l|l|l|  l|l|l|l|l| l|l|l|l|l|}
\hline 
 $m$  &  1 &2  & ... & 11 & 12 & 13 & {\bf 14} &   15 &    16  & 17 & 18 & 19 &
20\\
 $\pi(m)  $ & 90& 172&... &  561 & 573 & 579&  {\bf  580} & 576 & 568 & 555& 538 &
517 & 492 \\
\hline
 \end{tabular}

{\bf Table 1: Payoffs     When $m$ Precents are Followed }
 
 

  

  \end{document}