platforms of the candidates and vote for the one whose platform is ... use their initiative in the face of new or unexpected events that arise ..... We can now state our major results. .... New. Key, V. (1966) The Responsible Electorate. New York: Vintage Books. ... (1971) Short Term Fluctuations in U.S. Voting Behavior, 1896-.
Public Choice 50:5-25 (1986). © 1986 Martinus N i j h o f f Publishers, Dordrecht. Printed in the Netherlands.
Incumbent performance and electoral control
JOHN FEREJOHN*
I.
INTRODUCTION
In the pure theory of
electoral
competition, citizens compare the
platforms of the candidates and vote for the one whose platform is preferred.
Candidate strategies
future performance in office.
are identified
with promises about
Models of this sort have been developed
in both static [McKelvey (1975)] and dynamic [Kramer (1977)I settings, and all appear to have the property that i f the set of alternatives is "large enough" in some sense, equilibrium platforms rarely exist.
But
these models have another feature that is quite as disturbing as their instability. In the static setting discussed by McKelvey, l i t t l e attention
is
paid to the possibility that, once in office, the politician's preferences may diverge from those of his constituents
and that he may
therefore choose policies at variance from his platform.
Instead i t is
simply assumed that promises will be kept whether or not such behavior is congruent with the interest of the officeholder.
I t is sometimes
argued that an "enforcement" mechanism may exist to discipline politicians for failing to keep promises, but without a specification of the mechanism i t is not obvious that i t would be in the interests of the
tSenior Research Fellow at the Hoover I n s t i t u t i o n and Professor of P o l i t i c a l Science at Stanford U n i v e r s i t y . Special thanks are due t o David Baron, Joseph Greenberg, Tom P a l f r e y , and Tom Romer f o r c a r e f u l reading and c r i t i c i s m of e a r l i e r v e r s i o n s of t h i s paper.
electorate to carry out threatened punishments. In Kramer's dynamic model, the incumbent's platform is identified with his current record in office so that, assuming that voters would believe any proposed platform,
a challenger will
able to propose a platform that will incumbent knows that he w i l l
v i r t u a l l y always be
defeat the incumbent. But i f the
lose his reelection bid, he might as well
simply pursue his own private interest while in office rather than doing what he promised during the campaign (or doing whatever he did during his previous term); he will Clearly,
in this
be turned out at the next election anyway.
case, the voters have no reason to take challenger
platforms as anything other than pure rhetoric; voters would soon learn that
rational
officeholders
would ignore
their
preferences
once in
office. In both of these cases, there is no reason for voters to pay attention to the candidates'
choice of platforms.
is no cause to believe that there w i l l
For this reason, there
be any predictable connection
between the profile of voter preferences and public policy.
I f there
actually is such a connection, neither of these theories can account for it. The pure theory of elections pays l i t t l e
attention to the sorts of
strategies or decision rules that might be followed by members of the electorate.
Instead, i t is usually hypothesized that citizens vote for
the candidate whose platform they like best, ignoring further strategic considerations.
Indeed, in two-candidate
contest,
if
candidates are
assumed to implement their platforms, voting for someone other than the preferred candidate
is
a dominated strategy.
The only interesting
question in this case is whether or not to vote. The purpose of this paper is to try to construct a coherent model in which voters have an incentive to base t h e i r choices on behavior of officeholders and in which officeholders choose their anticipation of this behavior.
strategies
in
Such a model is necessarily dynamic.
Voters are assumed to base t h e i r evaluations of officeholders on t h e i r actual performance in office rather than on hypothetical promises they might make during a campaign.
In this model, the key to the voting
decision is found not in the earnest pledges of the contenders but, rather, in the infamous remark of a Kansas farmer: done For me lately?"
"But what have you
I f voters vote on the basis of platforms or "issues," p o l i t i c i a n s have l i t t l e
incentive to do what they promise.
Thus, voters might be
well-advised to pay attention to the incumbent's performance rather than to the hypothetical
in office
promises of competing candidates.
By
basing t h e i r votes on evaluations of performance, voters may be able to motivate
officeholders
electors.
That
to
pay
attention
such a strategy
f o r c e f u l l y argued by V.O. Key (1966). or punish officeholders officeholders
will
of
the
has been most
but w i l l
in o f f i c e ,
also be motivated to
in the face of new or unexpected events that arise empirical
elections
only a partial
nomena.
interests
on the basis of t h e i r performance
between elections. There is abundant is,
the
Key argued that i f voters reward
not only be d i l i g e n t
use t h e i r i n i t i a t i v e
to
may be a t t r a c t i v e
at best,
evidence
that
the
description
Much of recent data suggest that
pure theory
of electoral
of phe-
voters do respond to the
performance of incumbent candidates in office as well as to the platform promises of competing
candidates
[Kramer (1971), Fiorina
both the aggregate and individual that
have been studied,
effect there
on the electoral is
evidence that
level
(1981)I.
and in v i r t u a l l y
the performance
all
try
nations
of the economy has a major
fate of the incumbent executive. officeholders
At
to
anticipate
Moreover, performance-
oriented voting in t h e i r choice of policies while in o f f i c e . I Thus, i t appears that voters employ decision rules that are based, in part, on the past performance of the government in o f f i c e .
Moreover,
the actual evidence for extensive issue voting is f a i r l y weak. incumbent
administration has
been successful
growth and avoiding major wars,
it
will
in
promoting
I f the economic
tend to be rewarded at the
polls, no matter how a t t r a c t i v e the policy positions of the opposition. 2 This paper begins an investigation of the structure of electoral
ISee the poiltical business-cycle literature, especially Tufte (1978), Recent work on Congress [Mayhew (1974)] suggests that similar incentives structure the behavior of Congressmen. 21n splte'of the great quantity of statistical investigations of issue voting, the evidence for effects of candidate platforms on the vote is mixed. See Page and Jones (1979).
behavior that takes account of the motivations
of o f f i c e h o l d e r s .
We
wish to know how voters ought to behave i f they wish to get t h e i r representatives to pursue the interests of the e l e c t o r s . this
question,
ticians
we need to develop a formal
In order to address
model within which p o l i -
can be induced to act in the i n t e r e s t s
of the electors.
The
natural mechanism to transmit such incentives is the fact that elections take place repeatedly and that officeholders
desire to r e t a i n o f f i c e .
Under these circumstances, voters can adopt strategies that can a f f e c t the incentives
of o f f i c e h o l d e r s
in various
ways.
separating the actions of the candidates in o f f i c e the performance of date.
With t h i s
"principal-agent" electors, facing
a government which separation,
is
insist
on
from the notion of
led by an incumbent candi-
the s i t u a t i o n
becomes a variant
problem in which the o f f i c e h o l d e r
and voters
We also
of the
is an agent of the
have the opportunity to structure the incentives
the o f f i c e h o l d e r
agent to
induce him to act to enhance t h e i r
well-being. The paper introduces an a l t e r n a t i v e theory of e l e c t i o n s , as pure in i t s own way as the classical
one exposited by McKelvey and Kramer.
In
t h i s model voters respond only to the performance of the candidate in office
and do not pay any a t t e n t i o n whatsoever to the promises of the
challenger or, f o r that matter, to the promises of the incumbent.
All
that counts f o r a voter here is how well he fares under a given administration. In the model, voters assume that a newly elected o f f i c e h o l d e r w i l l pursue his own i n t e r e s t s once in o f f i c e , the context of the campaign. because there them. that
is
On t h i s view, promises play no role at a l l
no way f o r
As long as p o l i t i c i a n s they
have the
correctly anticipate
no matter what he claimed in
candidates to commit themselves to keep are a l l
same preferences
of the same "type," in the sense and a b i l i t i e s ,
how the o f f i c e h o l d e r w i l l
stance that may confront
him.
the
voter
can
behave in every circum-
No promise to do otherwise would be
credible and so none would be heeded. Given t h i s hypothesis about the behavior of p o l i t i c i a n s
in o f f i c e ,
the voters w i l l
choose a decision rule that maximizes t h e i r well-being
subject
constraint
interest.
to the
Nevertheless,
that voters
politicians
are pursuing t h e i r
are constrained
in
their
self-
choice of
decision rules to recognize that at any future time, prescribed voting
behavior must be in the i n t e r e s t of the electors at that time.
They are
unable to bind or precommit themselves or t h e i r o f f s p r i n g to choices in the future that w i l l rules
seem u n a t t r a c t i v e at that time.
based on " i n c r e d i b l e "
threats
Thus, those voting
are not available
because o f f i c e -
holders would recognize that such threats would not be carried out.
2.
PREVIOUS RESEARCH
There has been some investigation of the incentives that certain types of
performance-oriented
(1975)}. myopic,
rules
confer
on incumbents
[Nordhaus
However, most of this work focuses on a r e l a t i v e l y specialized
implication years
voting
of performance-oriented voting:
i f voters are s u f f i c i e n t l y
incumbents have an incentive to behave d i f f e r e n t l y than at
other
business cycles.
times
and therefore
to t r y
in e l e c t i o n
to create p o l i t i c a l
Whether or not incumbents are able to create p o l i t i c a l
business cycles, however, depends on a v a r i e t y of other factors i r r e l e vant to our present concern with the control choice of voter-decision rules.
of incumbents through the
Indeed, recent work suggests that
voters are able to take account of economic constraints, induced business
cycles
Moreover, the formulation
may not
occur
of p o l i t i c a l
[Chappell
if
politically-
and Keech (1985)].
business-cycle models does not
pay much a t t e n t i o n to the choice of optimal voter-decision rules, given the opportunities of incumbents. More relevant to the present paper is Robert Barro's (1973) seminal investigation
of
the control
of p o l i t i c i a n s .
Barro investigates
the
question of how much the f a c t of repeated elections may induce o f f i c e holders to act on the preferences of the electorate rather than t h e i r own objectives. spects.
Barro's
approach d i f f e r s
from ours
in
F i r s t , he assumes that o f f i c e h o l d e r s have a f i n i t e
known horizon.
Thus, in
their
last
several
re-
and commonly
term of o f f i c e t h e i r behavior is
10
uncontrollable. 3
In light
of this
uncontrollability,
the electorate
would not return an officeholder seeking his last term; the p o l i t i c i a n would then see this and be uncontrollable in the penultimate term, and the process would unravel.
The present model is formulated with an
i n f i n i t e horizon, so that such last-period effects are avoided.
The
reader may think of the competitors for office as p o l i t i c a l parties that last
indefinitely and must solve the "last-period" problem for their
officeholders through the use of internal incentives. 4 Second, Barro's model is formulated
in a world of perfect infor-
mation, whereas the present model contains an informational asymmetry: the electorate is not able to observe the actions of politicians directly.
With perfect information the voter is able to extract most of
the rents
in the transaction.
In equilibrium,
at each period,
the
electorate demands that the officeholder provide a quantity of e f f o r t that leaves him indifferent between leaving and staying in office.
Here
we allow a natural informational asymmetry in favor of o f f i c i a l s , which allows
them opportunities
sitions. officials
Intuitively,
to take advantage of their privileged po-
the greater the informational
advantage that
hold, the greater t h e i r a b i l i t y to earn rents from o f f i c e -
holding. Finally,
Barro's model contains only one "representative" voter.
In effect, this formulation assumes not only that voter preferences are identical,
an assumption that may in some circumstances be j u s t i f i e d ,
but also that there are no distributional competition,
issues at stake in p o l i t i c a l
surely a more controversial
hypothesis.
W h i l e we are
unable to provide a complete analysis of the general case, we do show that the introduction of distributional
issues profoundly changes the
nature of the relationship between the electorate and its o f f i c i a l s , vastly reducing the level of electoral control.
3The mechanism suggested t o overcome the l a s t - p e r i o d problem is the one introduced by Becker and S t i g l e r (1974)o Becker and S t i g l e r argue t h a t misbehavior can be c o n t r o l l e d i f o f f i c e h o l d e r s face the loss of a pension ( o r , e q u i v a l e n t l y , a posted bond) in the event of malfeasance in their last term, Barro suggests that political parties might offer future appointment t o o f f i c e as an inducement f o r good l a s t - p e r i o d performance. 4See previous note.
ii
In the next section we o u t l i n e a simple dynamic model of e l e c t o r a l competition that allows us to analyze the incentives of o f f i c e h o l d e r s and to see how they would respond to v a r i a t i o n s in e l e c t o r a l behavior. This model, electorate)
like
Barro's,
contains only one voter
and two or more candidates.
(or a homogeneous
The "space" over which the
performance of the o f f i c e h o l d e r is defined is i d e n t i f i e d with an i n t e r val
on the
real
line.
In t h i s
dimensional outcome space is
context,
the r e s t r i c t i o n
to a one-
inconsequential, though in other settings
i t may not be. When we turn our a t t e n t i o n to a model in which there are several voters, the s i t u a t i o n changes s u b s t a n t i a l l y .
In Section 4 we show that
the introduction of preference d i v e r s i t y permits the incumbent to escape electoral
control
aggregate voting.
unless the voters
performance
index
I f voters u t i l i z e
incumbent w i l l advantage.
as
"agree" to u t i l i z e
their
criterion
for
some sort
of
retrospective
i n d i v i d u a l i s t i c or group-based c r i t e r i a ,
the
have the opportunity to e x p l o i t voter d i v i s i o n s to his
The nature of such an agreement does not e n t a i l any precom-
mitments by the voters, in the sense of requiring anyone to vote against his
or
her
interests
at
some future
agreement would be c r e d i b l e . that
electoral
control
point
in time,
and so such an
We may i n t e r p r e t t h i s r e s u l t as saying
with
a
nonhomogeneous electorate
requires
" s o c i o t r o p i c " voting - - that i s , voting based on an aggregate c r i t e r i o n - - rather than i n d i v i d u a l i s t i c voting [Kiewiet (1983)I.
3.
A SIMPLE MODELOF REPEATED ELECTIONS WITH A HOMOGENEOUS ELECTORATE
Many of the a c t i v i t i e s of o f f i c e h o l d e r s are not d i r e c t l y observable by members of the e l e c t o r a t e . the
effects
Further,
of
governmental
governmental
activities
Instead, electors are only able to assess performance
performance
is
of officeholders as well
essentially probabilistic factors. an agent of
on
known to
their
own well-being.
depend j o i n t l y
on the
as on a v a r i e t y of exogenous and In other words, the o f f i c e h o l d e r is
the electorate whose behavior is
imperfectly monitored.
Officeholders are assumed to desire r e e l e c t i o n
in order to take ad-
vantage of
the perquisites of o f f i c e
ideas about p o l i c y .
as well
as to pursue t h e i r
own
I t is the desire to r e t a i n o f f i c e together with the
12
p o s s i b i l i t y of an indirect monitoring by the electorate which drive the incentive effects that we observe in the model. Before setting out the model, we should emphasize that we have assumed that candidates for office are a l l essentially the same in the sense that they have the same preferences and a b i l i t i e s , and that this is common knowledge among a l l the actors.
In other words, the voter's
problem is to police moral hazard rather than to find and elect the more capable of ~benevolent officeholders.
Rules of the sort we are ad-
dressing here may have the property of separating different types of officeholders in an appropriate
setting, but we do not address those
aspects here. In
this
functional
paper we take
the
liberty
of
working with
Forms that are r e l a t i v e l y easy to analyze.
explicit
Some of the
arguments developed here might be generalized in other settings, but for now we have chosen to t r y to obtain clear results in the context of a very simple model in order to aid our i n t u i t i o n about the ways in which the behavior of electors might induce officeholders to pay attention to their preferences. The officeholder observes a random variable, e ~ ~ = [0, m], a subset of the nonnegative real numbers, and then takes an action, a [0,~), conditioned on that observation.
We l e t F denote the d i s t r i -
bution
it
Function
entiable.
of
e and assume that
is
continuously
differ-
The single-period preferences of the officeholder are written
as v(a,e)
= w -
~(a),
where W is the value of holding office for a single term and ¢ is a positive monotone convex function and ¢(0) = O.
W may be thought of as
the e x p l i c i t compensation of the officeholder plus any rents he may earn as a result of his tenure and ¢(a) is the cost of action a. The voter is unable to distinguish the actions of the officeholder from exogenous occurrences. Rather than d i r e c t l y observing "policy," he is restricted to monitoring product
of
"performance," which is defined to be a
policy and exogenous occurrences.
single-period preferences are represented as
T h u s , the elector's
13
u(a,e) = ae. Lacking an a b i l i t y
to observe the a c t i v i t i e s
e l e c t o r adopts a simple performance-oriented rule:
if
the u t i l i t y
office
is
high enough,
of the incumbent, the
(or retrospective)
voting
received at the end of the incumbent's term in he votes to
return
the
incumbent to o f f i c e ;
otherwise he removes the incumbent and gives the job to someone else. I t is clear that,
under certain conditions,
such a rule w i l l
induce the
incumbent to pay a t t e n t i o n to the requirements of retaining o f f i c e . is
also clear
utility will
that
the elector
level appropriately,
not find
it
must be careful
since i f
it
to
It
set the required
is set too high the incumbent
worthwhile to t r y to r e t a i n o f f i c e
and w i l l
instead
choose to take advantage of the opportunities c u r r e n t l y available to him as an o f f i c e h o l d e r . incumbent w i l l
On the other hand, i f the level is set too low, the
find
it
o f f i c e that he w i l l It will
sufficiently
easy to sustain his hold on the
choose too low a level of a.
turn out that the incumbent's behavior depends c r i t i c a l l y
on his l i k e l i h o o d of being able to return to o f f i c e in the future in the event that he is defeated. polar cases:
(i)
In the following analysis we consider two
in the event of a loss of o f f i c e , the incumbent has no
chance of returning;
(2)
in the event of a loss of o f f i c e ,
the in-
cumbent is replaced by another agent and returns to o f f i c e i f and when that
other agent loses.
We think of the f i r s t
assumption as corre-
sponding more or less to multiparty competition with small p a r t i e s , which a party out of o f f i c e gaining i t quite
final
system.
has a r e l a t i v e l y
at the next e l e c t i o n . from
This
the
also
small p r o b a b i l i t y of re-
The loss o f - o f f i c e would appear to be
standpoint
case could
in
of
the
incumbent
party
model the candidate's
in
such
perspective
a as
opposed to the party perspective in two-party system in which the comp e t i t o r s are party "teams" that a l t e r n a t e in o f f i c e . Several remarks about t h i s formulation seem important. model contains an extreme informational ficial
is
while
the
somewhat,
able to voter
resolve a l l
cannot.
we could
uncertainty
At the
introduce
asymmetry.
cost
of
an additional
First,
the
The incumbent o f -
before taking complicating disturbance
his the
action, notation
representing
uncertainty that the candidate is unable to resolve p r i o r to his choice of
policy.
In
this
case,
the
candidate
would
view
his
election
14
prospects as uncertain.
While t h i s case is perhaps more r e a l i s t i c ,
does not permit us to gain any additional
it
insights into e i t h e r incumbent
or voter strategies. Both o f f i c i a l s
and voters are assumed to be r i s k
neutral.
This
assumption s i m p l i f i e s the analysis somewhat and also a f f e c t s the nature of optimal strategies.
I f the candidate and voter d i f f e r
aversion, issues related to risk sharing would arise. cases may be more r e a l i s t i c ,
they
would
in t h e i r r i s k
Again, while such
needlessly
complicate
the
present analysis and so we leave them aside. F i n a l l y , for reasons alluded to in the introduction,
the challenger
plays no active role in the model.
The importance of challengers l i e s
entirely
availability.
It
gives
whatever leverage
in
their
officeseekers incumbent.
that
the voter
is
the
existence
of
willing
he has on the
For this reason, i t is important that the e l e c t i v e o f f i c e is
valuable enough r e l a t i v e to a l t e r n a t i v e sources of employment to a t t r a c t challengers. Given the one-period preferences outlined above, and assuming that the elector employs a retrospective voting r u l e , we can u t i l i z e techniques of dynamic programming havior.
to determine optimal
standard
candidate
Once the incumbent has observed a value of et, he w i l l
an action
which
maximizes
his
(discounted)
utility
from
be-
choose
that
time
onward, assuming that the voter employs a retrospective voting rule with cutoff
levels,
Kt ,
Kt+l,
Kt+ 2 . . . . .
from time t
forward.
Under the
conditions assumed above, t h i s amounts to choosing a(et) to maximize t h e present value of u t i l i t y
stream.
Obviously,
if
is not possible to be reelected, then he w i l l
et is so small that i t
choose a(et) = O.
If it
is possible to be reelected, then the candidate may choose a(et) so the reelection constraint
is
just
satisfied:
would he be w i l l i n g to choose any a(et)
a(e) = Kt/e t .
In no event
larger than the smallest amount
that w i l l ensure his r e e l e c t i o n . In the remainder of t h i s section, we present a characterization of equilibrium voter and incumbent strategies Then,
we examine
electoral
control
alternative
party
(Proposition
present a comparative s t a t i c
4).
result
(Propositions
systems Finally, that
from in
implies
the
i through 3). standpoint
Proposition that
control
5,
of we
of
in-
observes the value et
and
cumbents is greater f o r more valuable o f f i c e s . After
each e l e c t i o n ,
the o f f i c e h o l d e r
15
chooses a(et) = Kt/e t i f and only i f w
(KtJ0 t) +
w+
(i)
I
and,n i f (i) is not s a t i s f i e d , he chooses a(et) = O.
In ( i ) ,
VIt+l
and
V~+I stand for the expected values of staying in office or leaving o f f i c e , respectively, given optimal play by voters and candidates from the next election forward, and a represents the (common) discount factor employed by all agents.
I t is important to note that
are independent of et and Kt .
V~+ I-_
and V~+ I_
Re-arranging terms permits us to es-
tablish the following characterization of optimal incumbent strategies: PROPOSITION 1: Given the retrospective voting rule optimal incumbent strategy is a(et) = Kt/e t i f f
I
8t ~ Kt/~-l(~(Vt+ I
_
V0 t +l ) ).
{Kt}#=O, the
(2)
PROOF: (1) implies that a(et) = Kt/8 t i f and only i f et ~ e~, I 1 - Vt+l) 0 The Inequality then where 0~ satisfies a(Vt+ = ¢(Kt/e~) . " follows from the fact that ~ is positive monotone, convex, and ¢(0) = O. In other words, the incumbent w i l l
expend effort only i f he ob-
serves a s u f f i c i e n t l y favorable value of et .
Notice that this ex-
pression implies that i f the value of office is r e l a t i v e l y small, the incumbent may choose to accept defeat though he could have been reelected. G i v e n the retrospective voting rule,
the incumbent's
optimal strategies are optimal at each time t forward.
Thus an optimal
REMARK:
strategy is credible because the incumbent would actually carry i t out for each value of et that he could realize. Or, to put i t another way, they are equilibrium strategies in each subgame (e.g.,. subgame perfect). In order to characterize an equilibrium, we must determine the optimal retrospective rule. expressed as follows:
The expected u t i l i t y
of the voter may be
oo
U = Z atKtPr{e t _ I > Kt/¢-l(a ( Vt+l - V~+l))} t=O
(3)
We can give a characterization of optimal retrospective rules by maxi-
16
mizing (3) over all retrospective rules. PROPOSITION 2:
If the et are independent, identically distributed
random variables with cumulative distribution function F(-) and density f(.),
an optimal retrospective
voting
rule
satisfies
the following
equality: Kt PROOF:
[1 - F(e~ )] f(e~) #-i(~ ( VIt + l - V0 t+l)) This follows
directly
(4)
from the first-order
conditions
derived from equation (3). The important thing to notice about equation (4) is that Kt depends I 0 Vt+l-Vt+ 1. The larger is the value of remaining in
positively on
office to the incumbent, the more the voter can ask of him.
In the
special case in which F is uniform and ¢ is the identity function, we obtain a clearer characterization. COROLLARY: If the et are independent, uniform, random variables on [ 0 , i ] , and i f ¢(a) = a and a ~ [ 0 , I ] , an optimal retrospective rule must satisfy the Following equation:
(4')
Kt = min{1/2,6(V~+I - V0+1)/2} for all t.
Equations (4) and (4') period,
the elector
can be interpreted as follows.
In each
sets Kt to equate the expected value to the i n -
cumbent of staying in o f f i c e
to the value of choosing a(et)
= 0 and
accepting defeat. PROPOSITION 3: then
e~
If
[l-F(x)]/f(x)
is monotone decreasing f u n c t i o n ,
is independent of 6, t , and W.
PROOF:
Substitute
for
Kt
using equation (4)
in the following
expression e~ : Kt/¢-l(a(VI-vO)) yields the equation
e~ : [1 - F(e~)]If(e~),
(5) which has a unique so-
lution under the assumption of monotonicity. REMARK: An optimal retrospective voting rule is subgame perfect in the sense that its restriction to any subgame is an equilibrium strategy in that subgame. Assuming he is restricted to employing some retro-
17
spective voting rule, the elector can do no better than employing a rule that satisfies
(4).
For this reason, incumbents will
regard optimal
retrospective rules as credible. COROLLARY: to l i e in [ 0 , i ] , REMARK:
I f F is uniform on [ 0 , 1 ] , then
e~ = 1/2
and
~(a) = a and a is r e s t r i c t e d
Pr({e t ~ e~}) = i / 2 .
I t f o l l o w s from the f o r m u l a t i o n t h a t any s o l u t i o n to (3)
must be s t a t i o n a r y in the sense t h a t
Kt = K f o r a l l
t.
To see t h i s ,
note t h a t i f equation (3) i s r e w r i t t e n as f o l l o w s ,
(3')
U0 = KoPr(e0 z e~) + ~U1
U1 = U0 since s t r a t e g i e s and payoffs are the same at time i as at time O.
Moreover, UI does not depend on KO.
Thus, i f K0 maximizes ( 3 ' ) ,
K0
must maximize UI, too, and so on f o r each t . In
the
stationarity pected u t i l i t y
special implies
case
of
uniformly
the f o l l o w i n g
distributed
convenient
disturbances,
expression f o r
the
ex-
of the v o t e r , using an optimal r e t r o s p e c t i v e v o t i n g r u l e ,
K:
(3")
U : K/2(1-a) = min{I/2,6(V I - V0)/2}/2(i-6).
Thus, up to the point where the expected marginal value to the incumbent of continuing
in office
exceeds 1/2,
u t i l i t y depends on this marginal value.
the voter's expected
The more attractive the present
value of office is to the incumbent, the more satisfaction the voter can anticipate. offices. receive
However, this effect holds only~or r e l a t i v e l y unattractive
Indeed, for very unattractive offices, the voter can expect to almost nothing
from the
officeholder.
For more valuable
offices, the effects of increasing value do not accrue to the elector in increased control
of the
incumbent but flow,
instead,
to the p o l i -
ticians. Having described
optimal
strategies,
we may now calculate
the
equilibrium payoffs to the game. Turning f i r s t to the incumbent we see that i f the voter is playing a stationary retrospective voting strategy with criterion K, we may write the expected value of being an incumbent, before observing e, as follows:
18
vl
m = : [W - ~( K / e ) e*
e* + : [W + avO]dF(e) 0
+ ~VI]dF(e)
The discounted expected u t i l i t y
(6)
of a candidate out of office may be
s i m i l a r l y written.
o* V0 = : [x~V I + ( I - x ) s v O ] d F ( o ) 0
m
+ : ~vOdF(o) o*
(7)
where x is the probability of obtaining office i f the current incumbent is
defeated at the next election, which is taken to be exogenously
determined.
In this interpretation a pure two-party system corresponds
to x = i ,
so that V0 = a(VI+vO)/2.
At the other extreme, a "pure"
multicandidate system would have x = O, and therefore, V0 = O. Solving (6) and (7) we obtain the following expressions for VI and V0, m [W - : e . ~ ( K x / e ) d F ( e ) ] [ 1
I Vx =
[1-a(1-xp)][1-a(1-p)]
- ~(1-xp)]
(8)
- xa2p 2
m
x~p[W -
0 =
Vx
fe,¢(Kxlo)dF(o)]
[l-~(l-xp)I[l-a(l-p)l
(9)
- xa2p 2 '
where p = F(e*) and where the subscripts indicate the dependence on x. We can now state our major results. An increase in x lowers the u t i l i t y of the voter. I - Vx 0 with respect By i m p l i c i t l y differentiating Vx = Vx
PROPOSITION 4:
PROOF:
to x and rearranging terms, we see that
aVx/Bx is negative and, from
equation (4), this implies that the derivatives of Kx and Ux with respect to x must be negative as well. REMARK:
As the number of parties is restricted, the welfare of the
elector declines. parties f a l l s
As the proof suggests, this occurs as the number of
(i.e.,
as x gets larger) and the incumbent's r e l a t i v e
valuation of office declines.
He becomes less concerned with losing
office and is, therefore, less controllable by the voter. An alternative interpretation of this result may be given i f we l e t : 0 depict the incentives of candidates rather than parties.
In this
case we see that the voters can attain higher levels of control
by
19
holding candidates rather than parties responsible for poor outcomes. This is accomplished by refusing ever to reelect an officeholder who governed in a period of poor performance. Finally,
essentially
the
same argument as
above yields
the
following result: PROPOSITION 5: PROOF: solving f o r
The u t i l i t y of the voter is increasing in W.
By implicitly differentiating ~V~/~W,
V~ with respect to W and
we see that Vx is increasing in W.
This implies
that U increases in W, too. Most of the conclusions that are drawn from t h i s simple model of repeated elections are in accord with i n t u i t i o n . that
voters
office
is
discounted. office,
have more control relatively
high
over officeholders
and
when the
Like Barro, we find when the
future
is
less
value of heavily
To the extent that voters can d i r e c t l y a f f e c t the value of
they should choose i t
optimally.
How t h i s should be done is
discussed in Barro's paper, and we r e f e r the reader to his discussion. Roughly speaking, an increase in the value of o f f i c e can be expected not only to cost something but also to increase the level of competition f o r o f f i c e among nonincumbents ( t h i s is not e x p l i c i t l y modelled e i t h e r here or in Barro's paper). termined by the
To the extent that the value of o f f i c e is de-
(legal or i l l e g a l )
behavior of incumbent p o l i t i c i a n s ,
that value may tend to be set at a higher level than the voters would wish.
In e i t h e r case, however, we might expect systems to evolve in
such a way that p o l i t i c i a n s desire to hold onto t h e i r o f f i c e s and in which, therefore, the electorate is accorded a modicum of c o n t r o l . Perhaps more surprising merits of
party systems.
is our conclusion about the comparative
While our depiction of the two systems is
s i m p l i s t i c , we believe that the basic conclusion w i l l
hold up in more
sophisticated models of repeated elections as long as there is no motive f o r the development of party reputations.
As long as the p a r t i e s do not
d i f f e r in t h e i r c a p a b i l i t i e s or preferences in some unobserved way, they have no way of d i s t i n g u i s h i n g themselves in the minds of the voters.
In
such a s e t t i n g , the r e s t r i c t i o n of e l e c t o r a l competition to two p a r t i e s has the e f f e c t of decreasing the level of voter control holders.
over o f f i c e -
Voters are better o f f in t h i s model to the extent that they
can prevent the system from evolving into two-party competition.
In a
two-party system the loss of o f f i c e is not as consequential as i t would
20
be in a pure candidate (or, indeed, a multiparty) system and so officeholders are not given a strong incentive to pay attention to the interests of the electors.
4.
ELECTORALCONTROLWITH A NONHOMOGENEOUSELECTORATE
The development of assumption formance.
of
the model of electoral
homogeneous voter
control
preferences
While there is some empirical
was based on the
over
government
evidence in favor of the hy-
pothesis that voter evaluations of incumbents are correlated, still
reason to suspect that
government performance.
there is
voters may disagree in t h e i r ratings
Indeed, many of the real
parties and candidates may be due to d i s t r i b u t i o n a l p o l i c i e s they pursue.
per-
differences
of
among
differences in the
How far may the results of our model be extended
in a world in which the voters maintain separate evaluative standards f o r officeholders? We begin by considering Section 2 and extending i t only about the quantity,
a simple s p e c i a l i z a t i o n
of the model in
to the case of N voters, each of whom cares xi
that
he receives.
We l e t
the value of
o f f i c e be W, and the incumbent's objective is to maximize W - a; but, in this
case,
the incumbent must also decide how to divide the output,
Ba(6), among the voters.
Thus, his strategies are represented by an
(N+l)-vector (a,x), where x=(xl,x2,x 3 . . . . . XN) and where Zxi = ea(e). The game proceeds just as before: Ki ,
the voters announce t h e i r retro-
spective voting
levels,
and then the incumbent observes Bt
and
chooses (a,x).
Then each voter observes the output he receives and
votes to re-elect the incumbent i f and only i f i t is satisfactory in the sense that x i ~ Ki .
For the present, we r e s t r i c t our attention to
stationary equilibria in order to economize on notation.
This will not
entail any essential loss of generality. The following
proposition
characterizes the equilibria
of
this
model: PROPOSITION 6:
I f is an equilibrium, i t is
equal to zero in all i t s components. PROOF: Given the voters' choice of Ki , i = 1,...,N, the incumbent w i l l choose the majority coalition, ~, to minimize Zxi c
subject to the
21
constraint that x i ~ Ki for all i ~ ~.
Obviously, this implies that x i
= Ki for i ~ ~ and that ~ is a minimal majority.
I f this minimum is
positive, any j i c would have been better off to offer Kj
