Download Rational Expectations Coordinating Voting in American Presidential and House Elections

Rational Expectations Coordinating Voting in American
Presidential and House Elections
by
Walter R. Mebane, Jr.y
June 1, 1998
Prepared for delivery at the 1998 Summer Methods Conference, University of California San
Diego, July 23{26. A previous version was presented at the 1998 Annual Meeting of the Midwest
Political Science Association, April 23{25, Palmer House Hilton, Chicago, IL. A (defunct)
predecessor was presented at the 1997 Summer Methods Conference, Ohio State University,
Columbus, July 24{27. I made great progress working on the paper while visiting for the Fall
semester of 1997 at the Department of Social and Decision Sciences at Carnegie Mellon University.
Thanks to Jasjeet Sekhon, Jonathan Wand and Jonathan Cowden for helpful comments. Data
were made available in part by the Cornell Institute for Social and Economic Research and the
Inter-University Consortium for Political and Social Research. Thanks to Jonathan Cowden for
letting tron help macht with the computing. All errors are solely the responsibility of the author.
y Associate Professor, Department of Government, Cornell University. Email:
[email protected].
Abstract
Rational Expectations Coordinating Voting in American Presidential and House Elections
I dene a probabilistic model of individuals' presidential-year vote choices for President and for
the House of Representatives in which there is a coordinating (Bayesian Nash) equilibrium among
voters based on rational expectations each voter has about the election outcomes. I estimate the
model using data from the six American National Election Study Pre-/Post-Election Surveys of
years 1976{1996. The coordinating model passes a variety of tests, including a test against a
majoritarian model in which there is rational ticket splitting but no coordination. The results give
strong individual-level support to Alesina and Rosenthal's theory that voters balance institutions
in order to moderate policy. The estimates describe vote choices that strongly emphasize the
presidential candidates. I also nd that a voter who says economic conditions have improved puts
more weight on a discrepancy between the voter's ideal point and government policy with a
Democratic President than on a discrepancy of the same size with a Republican President.
Do Americans coordinate their votes? In general, there is coordination if every voter makes
its1 vote choices in a way that is in a strategic sense in equilibrium not only with every other
voter's choices but also with every voter's beliefs about every other voter's choices. Studies of
electoral coordination have often focused on the \wasted vote" logic of Duverger's Law, which is
said to keep the number of parties receiving votes small (e.g. Cox 1997; Fey 1997; Palfrey 1989). I
examine coordination that relates not to the number of parties|two are assumed|but rather to
possible \moderation" in voting for President and for the House of Representatives (Alesina and
Rosenthal 1995; Fiorina 1988). Coordination in this case means that each voter's presidential and
congressional vote choices are in equilibrium with the choices and beliefs of every other voter.
Building on earlier work (Alesina 1987; 1988; Alesina and Rosenthal 1989; Alesina and Sachs
1988), Alesina and Rosenthal (1995) use a unidimensional spatial voting model in which individuals coordinate their votes to explain important political and economic phenomena, including the
midterm loss phenomenon and election-related uctuations in economic growth. Assuming that
each individual's voting strategy is \conditionally sincere," Alesina and Rosenthal derive a version
of coordinating voting summarized in their pivotal voter theorem (1995). The theorem implies that
if the two political parties oer distinct policy positions and the presidential election outcome is,
in equilibrium, uncertain, then equilibrium behavior for some voters is to split their tickets at the
time of the presidential election. The intention to obtain a policy outcome between the positions
taken by the parties will lead some voters to vote for one party for President but for the other
party for the legislature. For the same reason, some voters will switch their votes between the
presidential and midterm elections. Alesina and Rosenthal argue that such switching can explain
why the President's party uniformly loses vote share at midterm. Alesina and Rosenthal consider
complications due to incumbent advantage, and they derive economic implications in the form of an
expected partisan business cycle (1995, 137{203). The latter have been tested using aggregate time
1
series data (Alesina, Londregan and Rosenthal 1993; Alesina and Rosenthal 1995, 204{242; Alesina
and Sachs 1988). Alesina, Roubini and Cohen (1997) study economic implications of similar models
using data from several industrial democracies.
What is missing is individual-level evidence to show that individuals do indeed make their voting
decisions in accordance with strategies of the kind that Alesina and Rosenthal posit. Several authors
(Alvarez and Schousen 1993; Born 1994a; Lacy and Paolino 1997) have reported individual-level
tests of a similar theory of moderation proposed by Fiorina (1988; 1992, 73{81), with controversially
(Born 1994b; Fiorina 1994) negative results. Fiorina's majoritarian theory diers from Alesina and
Rosenthal's in not allowing ticket splitting to depend on the expected election outcomes (Alesina
and Rosenthal 1995, 66{71). Fiorina's theory is therefore strictly speaking not a theory of coordination among voters. The individual-level tests of Fiorina's theory have not examined whether
voters' expectations about the election outcomes aect their choices.
In this paper I present a probabilistic voting model designed to test whether individuals' votes
for President and for the House of Representatives are coordinated, in a fashion similar to the
coordinating voter equilibria of Alesina and Rosenthal's theory. I use American National Election
Study (ANES) Pre-/Post-Election Survey data from 1976, 1980, 1984, 1988, 1992 and 1996 to
estimate the model and conduct the tests.2 In addition to facilitating the connection to data,
using a probabilistic model gives immediately the continuity property|that vote choice behavior
responds continuously to dierences in expected utility|that Alesina and Rosenthal (1995, 75)
obtain by imposing their conditional sincerity condition. Assuming, as do Alesina and Rosenthal,
that the parties have distinct policy positions, the model describes a Bayesian Nash equilibrium
among voters.3 The dierences between the current model and the models of Alesina and Rosenthal
(1995) do not change anything essential for their theoretical claims.4
The focus on voter equilibrium diers from other uses of probabilistic models that have sought
2
to explain candidates' and parties' policy choices (e.g. Calvert 1985; Coughlin 1992; Enelow and
Hinich 1989; Erikson and Romero 1990; Hinich 1977; Hinich and Munger 1994; Wittman 1990).
The current model also does not try to explain why people vote (Enelow and Hinich 1984; Hinich,
Ledyard and Ordeshook 1972; Ledyard 1984; Palfrey and Rosenthal 1985). Other probabilistic vote
choice models that have emphasized voters' expectations regarding others' votes have not featured
the kind of voter equilibrium I introduce here (Enelow and Hinich 1982; 1983a; 1983b). The voter
equilibria of McKelvey and Ordeshook (1985a; 1985b) come closest to covering the current concept,
though their models feature purely spatial utility and voting for only one oce.
The model is based on a stochastic loss function that I assume each voter acts to minimize
with its choices of Democratic or Republican party candidates for President and for the U.S. House
of Representatives in a presidential election year. The model ignores the Senate. In addition to
policy comparisons, the loss function allows for retrospective economic performance judgments,
partisanship and House incumbent advantage. The model does not explicitly address midterm
election phenomena, though the results have implications for Alesina and Rosenthal's (1989; 1995)
theory of midterm loss. I ignore third-party candidates: the theoretical model assumes a choice
between two candidates for each oce, and voters who chose a third-party alternative are excluded
from the data analysis. In the model, ideal points and beliefs about the policy positions of the
parties and of their presidential candidates vary over voters, though there are groups of voters
who have similar ideal points and beliefs. Voters use the similarities to form rational expectations
regarding the probability that the Republican presidential candidate will win and the proportion
of the two-party vote that Republican House candidates will win nationwide. Those two quantities
are central in voters' calculations of the losses they may expect from the election's policy outcomes,
and therefore central in determining their voting strategies. Coordination in the voter equilibrium
is based on voters' rational expectations about the presidential and House election outcomes.
3
It is important to keep in mind that the rational expectations of the current model are limited
to expectations about the electoral outcome, conditioning on distributions of ideal points, of beliefs
about policy positions and of a few other variables. The current model does not use any particular
model of the economy. Unlike, in particular, Alesina and Rosenthal (1989; 1995; Alesina, Londregan
and Rosenthal 1993), I am not trying to dene a model that includes rational expectations for
economic outcomes. I am not trying to explain economic outcomes along with the electoral ones.
In the next section I describe the probabilistic coordinating voting model. Readers not interested
in the details of the stochastic specication|I use a generalized extreme value (GEV) distribution
for each individual's vote choice and a beta distribution to evaluate the rational expectations|may
wish to skip from equation (4) to the discussion that follows equation (9). Following that I explain
and motivate a variable I use to allow for the possibility that voters treat policy-related losses from
the parties asymmetrically, in a way that depends on each voter's retrospective evaluation of the
economy. After that I describe the method used to measure each voter's ideal point and beliefs
about the policy positions of the parties and presidential candidates in what I call relative units.
To facilitate intuition about the resulting data, I show how the values are distributed over groups
dened by party identication and economic evaluation. I then complete the specication of the
vote choice model, for estimation. After dening tests for whether the model describes coordinating
behavior by voters, which entails a test of whether the coordinating model outperforms a simpler
spatial alternative, I dene a model to allow the coordinating voting theory to be tested against
Fiorina's majoritarian theory of ticket splitting. Then come estimates of the model parameters and
reports of test results. The coordinating model easily passes all the tests, including the test against
the majoritarian model. Finally I consider some substantive implications of the estimates, including
implications for midterm loss, and briey discuss the informational and institutional requirements
for coordinating voting to be, as a practical matter, possible.
4
A Rational-Expectations Coordinating Voting Model
In the model, each voter evaluates two parties (labeled D and R) in terms of a continuous set
of liberal-to-conservative policy alternatives, mapped onto the unit interval [0; 1]. There are M
groups of voters. Each voter i who is a member of group Sk (i 2 Sk ) has an ideal point (i ) and
beliefs about the positions of the two parties (#Di , #Ri ) and of the parties' presidential candidates
(#PDi , #PRi ) that are similar to those of the other members of Sk . Similarity means that the values
i = (i ; #Di; #Ri; #PDi ; #PRi) that each voter i 2 Sk has at election time are drawn (independently
across individuals) from a group-specic joint probability distribution, Fk . The Democratic party
and candidate values (#Di , #PDi ) need not be to the left of the Republican party and candidate
values (#Ri , #PRi ). Policy ideal points and positions all take values on [0; 1].
The preferences that each voter has regarding the candidates for each oce are based on comparisons between the voter's ideal point and the policies the voter believes will result from various
election outcomes. Let the party positions the voter acts on, Di and Ri , be
Di = D#PDi + (1 , D)#Di ;
0 D 1
(1a)
Ri = R#PRi + (1 , R)#Ri ;
0 R 1 :
(1b)
The idea is that each party's post-election policy position is a composition of its pre-election position and the position articulated by its presidential candidate. Using H to denote the rational
expectation for the proportion of the two-party vote that will be cast nationally for Republican
candidates, over all House races, anticipated post-election policies under a Democratic and a Republican President are, respectively,
Ri + (1 , H )Di ] ;
~Di = D Di + (1 , D )[H
0 D 1
(2a)
Ri + (1 , H )Di ] ;
~Ri = R Ri + (1 , R)[H
0 R 1 :
(2b)
5
The forms of ~Di and ~Ri dier from the simplest policymaking technology that Alesina and Rosenthal consider, by allowing the parameter to vary with the party of the President and by allowing
the policy positions voters act on to vary over voters. As in Alesina and Rosenthal's (1995, 47)
specication, the value = 1 means that the President dictates policy and the legislature plays no
role, while = 0 means that the legislature determines policy and the President is irrelevant. I
assume that a voter's losses with, respectively, a Democratic and a Republican President are
Di = iji , ~Di jq + Di
Ri = (1 , i )ji , ~Rijq + Ri
where i satises 0 < i < 1, Di and Ri are continuous random variables, and q > 0 is a
constant. The variable i allows for the possibility that voters do not treat equally the policyrelated discrepancies ji , ~Di jq and ji , ~Ri jq associated with each party's presidential candidate.
Using P to denote the rational expectation for the probability that the Republican presidential
candidate wins, the voter's expected loss is
i = (1 , P)iji , ~Di jq + P(1 , i )ji , ~Ri jq + i
Ri . I assume that i is independent of P and H .
with i = (1 , P )Di + P
To minimize its expected loss i, a voter should make the vote choice that reduces rather
than increases i . Let PRi denote the probability that the Republican presidential candidate wins
if the voter chooses the Republican, and let PDi denote the probability if the voter chooses the
Democrat. Because the eect of a single voter's choice on P is small, a reasonable measure of the
eect on i of the voter's choosing the Republican presidential candidate is (PRi , PDi )@i=@ P .
If (PRi , PDi )@i=@ P is positive, voting for the Republican increases the voter's expected loss.
Likewise, with H Ri denoting the proportion of the national two-party vote received by Republican
House candidates if the voter chooses the Republican running in the voter's district and H Di
6
denoting the proportion if the voter chooses the Democrat, (H Ri , H Di )@i=@ H measures the
eect on i of the voter's choosing a Republican House candidate. Because American electoral
institutions are positively responsive, PRi , PDi > 0 and H Ri , H Di > 0. The coecients (PRi , PDi )
and (H Ri , H Di ) therefore do not aect the signs of the measures and may be ignored. Using
@i=@ P = @i=@ H = 0,
P + @i=@ P
@i=@ P = wPi + wHi@ H=@
H + @i=@ H
@i=@ H = wHi + wPi @ P=@
where
wPi = (1 , i )ji , ~Ri jq , i ji , ~Di jq
wHi = q(Di , Ri )[(1 , R )P (1 , i)ji , ~Rijq,1 sgn(i , ~Ri)
+ (1 , D )(1 , P )iji , ~Di jq,1 sgn(i , ~Di )]
with sgn(x) = ,1 if x < 0, sgn(x) = 0 if x = 0, and sgn(x) = 1 if x > 0. Let yPi = 1 denote a vote
for the Republican presidential candidate, yPi = 0 a vote for the Democratic presidential candidate,
yHi = 1 a vote for the Republican House candidate and yHi = 0 a vote for the Democratic House
P and bPH = @ P =@ H , the voter's rule for the presidential vote
candidate. Writing bHP = @ H=@
choice should be
8
>>
<1
yPi = >
>:0
if wPi + bHP wHi + @i=@ P < 0
(3)
if wPi + bHP wHi + @i=@ P > 0
and for the House vote choice
8>
><1
yHi = >
>:0
if wHi + bPH wPi + @i =@ H < 0
if wHi + bPH wPi + @i =@ H > 0 :
7
(4)
Equations (3) and (4) together dene the voter's strategy, which, in general, depends on P and
H , the rational expectations for the aggregate outcome of everyone's vote choices.5 The terms
wPi + bHP wHi and wHi + bPH wPi implement the voter's intention to minimize its expected loss
from the post-election policy, subject to the best possible prediction the voter can make about
everyone else's vote choices. If wPi + bHP wHi and wHi + bPH wPi are similar, the voter will tend to
make similar choices for President and for House member.
The voter's choices for President and for House member are likely to be similar also because
both choices depend on the same pair of random variables, Ri and Di . In the Appendix I argue
that the combined choice can be well modeled by one of two GEV distributions. To dene them,
start by dening
vRPi = expf,aP wPi , aHP wHi + zPig
vDPi = expfaP wPi + aHP wHi , zPi g
vRHi = expf,aH wHi , aPH wPi + zHi g
vDHi = expfaH wHi + aPH wPi , zHig
where aP > 0, aH > 0, aHP and aPH are constants, zPi denotes additional observed attributes
pertinent to the presidential vote choice and zHi denotes such attributes pertinent to the House vote
choice. Note that, from (3) and (4), bHP = aHP =aP and bPH = aPH =aH . Let vRRi = vRPi vRHi,
vRDi = vRPi vDHi, vDRi = vDPi vRHi, vDDi = vDPi vDHi and, for 0 ; D; R < 1,
1=1, + v 1=1,
Ji = vRDi
DRi
1,D ;
GDi = vRRi + IDi
1=1,D + J (1, )=1,D
IDi = vDDi
i
1,R ;
GRi = vDDi + IRi
1=1,R + J (1, )=1,R :
IRi = vRRi
i
Parameter measures similarity induced between the split-ticket alternatives by the common random variables. There is no such similarity if = 0. In the distribution FDi = e,GDi , if there is
8
greater similarity due to the random variables between the Democratic candidates than between
the Republican candidates then D > 0. In the distribution FRi = e,GRi , R > 0 if there is greater
similarity between the Republican candidates than between the Democratic candidates.
For preferences with unobserved random components that are GEV-distributed e,G , the probability Pr(y = j ) of choosing alternative j describes stochastic utility maximizing behavior if
Pr(y = j ) = (vj =G)@G=@vj , where vj > 0 measures the observed attributes of alternative j (McFadden 1978; Borsch-Supan 1990b). Using that formula with FDi , the probabilities for the four
possible combinations of presidential and House choices are
Pr(yPi = 1; yHi = 1) RRi = vRRi=GDi
(5a)
1=1, J , +(1, )D =1,D I ,D =G
Pr(yPi = 1; yHi = 0) RDi = vRDi
Di
i
Di
(5b)
1=1, J , +(1, )D =1,D I ,D =G
Pr(yPi = 0; yHi = 1) DRi = vDRi
Di
i
Di
(5c)
1=1,D I ,D =G :
Pr(yPi = 0; yHi = 0) DDi = vDDi
Di
Di
(5d)
For FRi the choice probabilities are
1=1,R I ,R =G
RRi = vRRi
Ri
Ri
(6a)
1=1, J , +(1, )R =1,R I ,R =G
RDi = vRDi
Ri
i
Ri
(6b)
1=1, J , +(1, )R =1,R I ,R =G
DRi = vDRi
Ri
i
Ri
(6c)
DDi = vDDi =GRi :
(6d)
For either distribution, let i = RRi + RDi denote the probability that i votes for the Republican
rather than the Democratic presidential candidate, and let i = RRi + DRi denote the probability
that i votes for the Republican rather than the Democratic candidate for the House.
For either distribution, FDi or FRi , P and H are rational expectations that depend on the
distribution of voters' ideal points, beliefs about party and candidate policy positions, attributes
zPi and zHi , and variable i. I assume that P takes into account the Electoral College.
9
Let Sjk be the set and Njk the number of voters in State j who are members of group Sk . The
P N , and N = PS N is the number of voters
total number of voters in the State is Nj = M
k=1 jk
j =1 j
in all S States. Let = fNjk ; 1 j S; 1 k M g be the set of counts of all the group sizes
in all the States. Recall that each i 2 Sk has the same distribution, Fk , for its ideal point and
believed policy positions i . Let zi denote the set of all the variables in (zPi ; zHi; i). Without loss
of generality we can assume that zi also has a distribution that is a function of k. For each i 2 Sk ,
let fk denote the joint probability measure of (i ; zi).6 Let denote the set of all the parameters
of (5a{d) (or (6a{d)). Given and , the expected proportion of the votes going to the Republican
presidential candidate in State j is
yPj = Nj,1
M XZ
X
k=1 i2Sjk
M
X Njk
=
k ;
k=1 Nj
with k =
PS C
j =1 j
i dfk (i; zi)
R df ( ; z ).
i k
i i
(7)
Let Cj denote the number of Electoral College votes for State j ,
= 538, and let R denote the proportion of Electoral College votes for the Republi-
can. The probability that the Republican wins, given and , is Pr(R > 21 j ; ). Because
P
State populations are large, the expectation of R , given and , is R = Sj=1 yPj Cj =538 and the
P
P
variance is 2R = ( Sj=1 Cj2 ),1 Sj=1 yPj (1 , yPj )Cj2. To evaluate Pr(R > 21 j ; ) I use the beta
distribution on [0; 1] obtained by matching moments. Setting P equal to that estimate gives
P =
Z 1 p ,1(1 , R)p ,1
R
dR ;
1
1=2
2
(8)
B(p1; p2)
where p1 = R2 (1 , R)=2R , R and p2 = R (1 , R )2=2R , (1 , R ) match the mean R and
variance 2R (Johnson, Kotz and Balakrishnan 1995, 222), and B (p1 ; p2) denotes the beta function.
If p1 0 or p2 0, the beta distribution is inappropriate.
Given , the rational expectation for the Republican's share of the national two-party vote for
10
House candidates is
H = N ,1
=
M
X
M XZ
X
k=1 i2Sk
idfk (i; zi)
Mk ;
k
k=1 N
(9)
R
where Mk is the number of voters in group Sk and k = idfk (i ; zi).
Given assumptions about common knowledge (Fudenberg and Tirole 1991, 541{546), there is a
Bayesian Nash equilibrium among voters if every voter chooses among candidates according to the
probabilities (5a{d), with each voter having P of (8) as its expectation regarding the likely outcome
of the presidential election and H of (9) as its expectation regarding the outcome of voting for House
seats. In that case, each voter is choosing among candidates so as to minimize its loss from the
election outcome, and each voter, in choosing, has the beliefs about the outcome that are implied
by every other voter's acting, with the same beliefs, to minimize its own loss. A voter equilibrium
can likewise exist if the choice probabilities are (6a{d) rather than (5a{d). If D = R = 0 then
FDi = FRi so that (5a{d) and (6a{d) are the same and so are the voter equilibria.
I assume that the following are common knowledge: the structure of the voting game, which
includes the facts that each voter simultaneously chooses one of two candidates for each oce and
that everyone's loss has the form i based on the policymaking technology of (1a,b) and (2a,b)
and with random elements GEV-distributed according to FDi (or FRi ); the fact that each voter
maximizes stochastic utility; the values of the parameters ; the measures fk and the fact that the
variables (i ; zi ) are independent of the GEV-distributed random variables in i ; the set ; and
the functional forms (7), (8) and (9), including the counts Cj . In the Appendix I show that an
equilibrium exists for almost every set of parameter values (given q 1), for any set of measures
fk or of group sizes . The particular set of parameter values that occurs depends on political
processes that I do not specify|for instance, on the electoral campaign.
11
Economic Evaluations and Asymmetric Weighting of Losses
I specify i to be a function of each voter's retrospective evaluation of the national economy,
i = (1 + expf,bE0 , bE1ECi g),1 ;
where bE 0 and bE 1 are constants and higher (lower) values of the variable ECi indicate judgments
that the national economy has gotten better (worse). One reason economic evaluations may aect
i is that voters may have dierent kinds of concerns depending on whether they think things
are getting worse or getting better. Voters may believe that worsening economic conditions call
for increased government intervention to protect or create jobs, or in other ways to protect those
likely to become vulnerable due to economic diculties. A voter with such beliefs who thinks
economic conditions are worsening may give more of the benet of the doubt to the political party
that has the stronger reputation for choosing such policies, while more closely scrutinizing the
other party. During the 1976{96 time period, the Democratic party had a stronger reputation
for choosing interventionist policies than the Republicans did (e.g., Palmer and Sawhill 1984). A
voter with the indicated beliefs who thinks economic conditions are worsening may therefore weigh
the policy discrepancy associated with a Republican President more heavily than the discrepancy
from a Democrat (i < 21 ). If a voter with such beliefs thinks economic conditions are improving,
presumably it is the Democratic party, with the interventionist reputation, that receives the closer
scrutiny (i > 21 ).
Another possibility is that voters believe that declining economic conditions call for reduced
government intervention, or at least for a reduced rate of expansion, because that is when the
country can least aord it. In this case we should have i < 12 for voters who think economic
conditions are improving, and i > 21 for voters who think economic conditions are getting worse.
12
Ideal Points and Policy Positions
In assuming that the distribution of voters' ideal points is uniform on an interval of unit length,
Alesina and Rosenthal (1989; 1995, 86) are using a scale that measures the cumulative proportion
of support for each policy position, not the substantive content of each position in whatever the
natural units of the policy may be. With their measure, for instance, the ideal point of the median
voter on [0; 1] is always = 12 (Alesina and Rosenthal 1995, 22). The measured values represent
relative positions|people's positions relative to one another|rather than absolute positions that
are dened in terms of the substance of the policy alternatives.7
To estimate the models expressed by equations (5a{d) and (6a{d), I also use relative rather than
absolute measurement scales for each voter's ideal point and beliefs about the policy positions of
the parties and candidates. Each voter's observed ideal point, i , is to be interpreted as measuring
the proportion of all voters that support a position as liberal as or more liberal than the position for
which voter i expresses support. Likewise, each voter's observed belief about the position of a party
or candidate measures the proportion of all voters that support a position at least as liberal as the
position at which voter i places the party or candidate. I use substantive political considerations
to order the response categories of particular survey items from \liberal" to \conservative." For
each survey I use all sets of items that ask each respondent to place each of the ve referents|self,
Democratic party, Republican party, Democratic presidential candidate and Republican presidential
candidate|on a scale that either refers to liberal-conservative ideological labels or pertains to a
policy issue. Each of the values i , #Di , #Ri , #PDi and #PRi is the average of the values for the
named referent from all the sets of items for which voter i placed all ve referents on the scale.
The Appendix lists the scales used from each of the ANES Pre-/Post Election Surveys of years
1976{1996 and describes in detail the scoring method used for each scale.
In measuring each survey item only in relative terms and not requiring all voters to take positions
13
on or have beliefs about all policy issues, I avoid having to assume that the single policy dimension of
Alesina and Rosenthal's model represents an underlying ideological dimension from which positions
on assorted policy issues are all somehow derived. It is possible, instead, to have in mind a world
in which dierent people may care about dierent things, with no common philosophical basis to
make them comparable.8 The idea would be that rather than an ideological dimension, there is
at any particular time a main line of two-party competition that reects coalitions formed among
the otherwise disparate interests. The conception of a predictive dimension developed by Hinich
and Pollard (1981) and Enelow and Hinich (1982; 1994) encompasses this idea. As Cox (1997,
186{202) discusses, the institutional features that tend to favor the existence of such coalitions
occur in the United States, and especially so if there is coordination in voting for President and for
seats in the national legislature as specied in Alesina and Rosenthal's theory. Multidimensional
scaling analysis by Poole and Rosenthal (1984) supports the view that the political parties usually
represent the principal opposing bundles of policy positions in American national elections.
I estimate the models of (5a{d) and (6a{d) without using any particular assumptions about
the set of groups to which voters belong. But to get some sense of what dierences between ideal
points and policy positions mean given the relative scale of measurement, it is useful to see how
the ideal points and attributed policy positions are distributed over groups dened by categories
of partisanship and economic evaluation.
Table 1 shows that in each presidential election year from 1976 through 1996, voters' mean
ideal points vary considerably as a function of individual party identication and the individual's
retrospective evaluation of the national economy.9 As one would expect, the means at each level
of economic evaluation in each year are smaller for Strong Democrats, Democrats or Independent
Democrats than they are for Strong Republicans, Republicans or Independent Republicans. The
one exception occurs for those few (20 voters) who rated the economy as \better" in 1980.
14
*** Table 1 about here ***
Table 2 shows that the policy positions voters attribute to the parties exhibit a marked asymmetry: Republicans see the Democratic party as being more liberal than Democrats see it, and
Democrats see the Republican party as being more conservative than Republicans see it. Brady
and Sniderman (1985) explain such perceptual asymmetries in terms of what they call a \likability
heuristic." Table 2 shows the asymmetries to be larger for the policy positions of the Democratic
party than for the positions of the Republican party. The asymmetries in the attributed Democratic party positions are greater for those who rate the economy as \better" than for those who
rate the economy as \worse." Similar patterns (not shown) occur with the presidential candidates.
*** Table 2 about here ***
Complete Choice Model Specications
To completely specify the probabilities (5a{d) and (6a{d), we must dene the additional observed
attributes that pertain to the presidential and House vote choices, namely zPi in vRPi and vDPi
and zHi in vRHi and vDHi . I dene both sets of attributes to include measures of retrospective
economic evaluations and individual partisanship. The zHi attributes also include measures to take
into account incumbent advantage.
According to Alesina and Rosenthal's analysis, a voter's retrospective evaluation of the economy
may be relevant to the voter's choice as an expression of two considerations: the voter's taste for
macroeconomic outcomes (1995, 167{171); and the voter's judgment of the competence of the
incumbent administration (1995, 191{195).10 Alesina and Rosenthal treat these considerations in
the context of particular, rational (economic) expectations models that they assume describe the
relationship between output and ination in the actual economy. For the current analysis I do not
rely on any such model. Rather I assume that each voter reports its evaluation when responding
15
to a question asking whether the national economy has gotten worse or better over the past year.
The variable ECi , which ranges from ,1 to 1, measures those responses. ECi = ,1 corresponds to
a judgment that the economy is \much worse" and ECi = 1 corresponds to a judgment that the
economy is \much better."11
Alesina and Rosenthal's theory has no place for party identication by voters, except possibly
as another index of tastes for policy outcomes and of judgments accumulated over time about
the competence of the parties' successive administrations. That people who support dierent
parties also tend to have dierent policy preferences is a well known fact that Table 1 once again
illustrates. The question for the current analysis is whether, as in most individual-level models for
vote choices in American national elections, a voter's party identication has an eect on the vote
that is not completely mediated through dierences between the measured ideal points i and the
expected policy outcomes ~Di and ~Ri . Several authors have reported individual-level empirical
results suggesting that individual party identication both reects party policy positions and is in
signicant part a kind of running tally of judgments regarding the parties' performances when in
oce (Fiorina 1981; Franklin and Jackson 1983; Franklin 1984; Jackson 1975; Markus and Converse
1979; Page and Jones 1979).
To take incumbent advantage into account, I include in zHi a pair of dummy variables that
indicate whether a Democratic or Republican incumbent is running for reelection or whether there
is an open seat: DEMi = 1 if a Democratic incumbent is running for reelection in individual i's
congressional district, otherwise DEMi = 0; REPi = 1 if a Republican incumbent is running for
reelection, otherwise REPi = 0.12 If both DEMi = REPi = 0, the district has an open seat.
16
In sum,
zPi = cP 0 + cP 1 PPi ECi + cD PIDD i + cID PIDID i + cI PIDIi + cIRPIDIRi
+ cR PIDR i + cSR PIDSRi
(10a)
zHi = cH 0 + cH 1PPiECi + cDPIDD i + cID PIDID i + cI PIDI i + cIRPIDIRi
+ cR PIDR i + cSR PIDSRi , cDEM DEMi + cREP REPi
(10b)
where cP 0, cP 1, cH 0 and cH 1 are coecients constant in each year, and cD , cID , cI , cIR, cR, cSR,
cDEM and cREP are coecients constant over all years. The variable PPi changes sign depending
on the incumbent President's party: PPi = 1 if Republican; = ,1 if Democrat. The variables
PIDD i , PIDIDi , PIDI i , PIDIRi , PIDR i and PIDSR i are dummy variables corresponding to the levels
of the ANES seven-point scale measure of partisanship, with \Strong Democrat" being the reference
category.13 Coecient signs should be cP 0 , cH 0 < 0 and cP 1, cH 1, cDEM , cREP , cD , cID , cI , cIR,
cR, cSR > 0.
The log-likelihood for each voter is
LYP i ;YHi = !i [yPi yHi log RRi + yPi(1 , yHi) log RDi + (1 , yPi )yHi log DRi
+ (1 , yPi )(1 , yHi ) log DDi ] ;
where !i is a sampling weight derived from the probability that the voter is included in the ANES
sample.14 To measure vote choices yPi and yHi I use the post-election choices reported by individuals who said they voted.15
To estimate P and H in each year, I do not use information about group memberships but
rather use the sampling weights to compute yPj and H by what amounts to a nonparametric Monte
Carlo integration method. Conditioning on the ideal point, policy position, economic evaluation,
party identication and incumbent status values observed for each voter, I use Horvitz-Thompson
17
estimators for sample means to approximate the integrals, at each step of the iterative procedure
described in the Appendix.
Tests of Coordinating Voting
According to Alesina and Rosenthal's (1989; 1995) theory, each voter coordinates its presidential
and legislative choices only because the policy to be enacted after the election depends on both the
presidential and legislative election outcomes. The same is true in the current choice models, with
the House representing the legislature. If the President solely determines policy (D = R = 1),
then there is no coordination because ~Di = Di , ~Ri = Ri and wHi = 0, so that voters' strategies
do not depend on P or H . A necessary condition for coordination is therefore that at least one
of D < 1 or R < 1 is true. If the legislature solely determines policy (D = R = 0), then
Ri + (1 , H )Di and a voter's strategy depends on P and H only if i 6= 21 . A
~Di = ~Ri = H
second necessary condition for coordination is therefore that at least one of 0 < D or 0 < R is
true, or if D = R = 0 then i 6= 21 .
The test against the specication with D = R = 1 is important also because the restricted
specication is the familiar kind of model that includes a unidimensional spatial comparison along
with nonspatial characteristics: in (3) and (4), wHi = 0. Such a model is obviously much simpler
than the coordinating voting model, so there is both theoretical and practical interest in determining
whether the coordinating model ts the data substantially better.
Other conditions necessary for the choice models to describe coordination are that q > 0 and
that at least one of aP , aHP , aH and aPH is not zero. If q = 0 then we have the degenerate value
wHi = 0, and wPi = 1 , 2i. If aP = aHP = aH = aPH = 0, then whatever the discrepancies
ji , ~Dijq and ji , ~Rijq may be, they have no eect on voters' choices.
18
Coordinating Voting versus a Majoritarian Model
I compare the coordinating voting model to another model that also claims to explain ticket-splitting
behavior, but does so without asserting that there is coordination among voters. That alternative
explanation is Fiorina's (1988; 1992, 73{81) majoritarian theory of ticket splitting. According to
that theory, each voter chooses the mix of party control of the presidency and the legislature|
the form of government|that will produce a policy outcome nearest the voter's ideal point, but
those choices are not aected by the anticipated election results. At stake in the contest with
the majoritarian theory is the specic form of rational behavior and equilibrium that characterizes
the American national electoral institution. Do voters pay attention to one another's beliefs and
intended actions, or does each respond solely to what each believes about the parties and their
candidates for oce? Coordinating voting theory says the former describes American elections
while the majoritarian theory says the latter is what happens.
To test the coordinating theory against the majoritarian theory in the most powerful way, it
is best to formulate the majoritarian vote choice model to resemble the coordinating model as
closely as possible. To do that I replace wPi and wHi in the coordinating voting model with terms
that are suitable for the majoritarian theory, but otherwise leave the attributes zPi and zHi and
the probability forms (5a{d) and (6a{d) unchanged. The model is dened in the Appendix. The
key feature of the model is that the choice attributes vRRi , vRDi , vDRi and vDDi are functions of
neither the expected proportion measure H nor the probability P that the Republican presidential
candidate wins. Nothing in the majoritarian model makes the choice of voter i depend on the
choice or likely choice of any other voter. In the majoritarian model, voters do not coordinate.
19
Estimation and Test Results
I estimate the choice models using data pooled from the ANES Pre-/Post-Election surveys of
1976{1996. Overall sample size is 4859. In the Appendix I show that only a small proportion
(386/5245 cases) of the data are missing due to failure to measure the ideal point, policy position,
economic evaluation or party identication variables. The low proportion of missing data enhances
the credibility of inferences from the current sample to the full population of voters. Maximum
likelihood estimates (MLEs) and standard errors (SEs) for the parameters of (5a{d) appear in Table
3.16
*** Table 3 about here ***
The coordinating voting model easily passes the tests of the conditions necessary for it to
describe coordinating behavior. This includes greatly outperforming the simpler spatial model
produced by imposing the restrictions D = R = 1. Seven of the twelve 95% condence intervals
for D or R have upper bound less than 1.17 The likelihood ratio test statistic for the hypothesis
that D = R = 1 for all six years is X^ 2 = 52:26. There is a complication in evaluating the
distribution of the statistic because with wHi = 0 the parameters aH and aHP become undened.
Using formula (3.4) of Davies (1987, 36) with 12 degrees of freedom gives an upper bound of :000002
on the signicance probability, which is well below the usual test levels.18 Note that the test result
does not change if the party identication variables are omitted from the model.19 Regarding the
hypothesis D = R = 0, only one of the condence intervals for D or R |that for R;96|includes
zero. Plainly the D and R values are not all zero. Regarding the other necessary conditions,
condence intervals show q to be bounded well away from zero, as are aP , aHP and aH .20
The coordinating and majoritarian models produce similar results, but the coordinating model is
superior. Most of the parameters that have the same interpretation in both models have statistically
indistinguishable estimates.21 The function i in the coordinating model and the corresponding
20
functions in the majoritarian model imply similar patterns of sensitivity to retrospective economic
evaluations.22 In view of the similarities, it is a major point in favor of the coordinating model
that its log-likelihood (,3185) is so much greater than that of the majoritarian model (,3225).
Formal tests (Dastoor 1985) clearly reject the majoritarian model.23 The coordinating model is
better even though the majoritarian model has one more free parameter.
The estimates of P and H for each year in the coordinating model are reasonable. Table 4 shows
that P < :5 whenever the Democratic candidate won the presidential race and P > :5 whenever the
Republican candidate won.24 The estimated P values indicate that the 1976 election was expected
to be very close while the other elections were expected to be either not very close (1988) or not
close at all (the rest). The estimates for H show that in four of the six years Democratic House
candidates were expected to win substantial majorities of the national two-party vote, in one year
(1996) Republicans were expected to win a substantial majority, and in the remaining year (1980)
the parties were expected to nish nearly even, albeit with a slight Republican advantage.
*** Table 4 about here ***
The random elements that aect both presidential and House vote choices tend to reduce slightly
a voter's propensity to split its ticket.25 The 95% condence interval for is (.33,.48), indicating a
non-trivial degree of unobserved similarity between the two split-ticket alternatives. The similarity
measured by has a small eect on the choice probabilities.26 Because the attributes zPi and
zHi include party identication, the similarity probably does not reect unmeasured eects of
each voter's partisanship. If party identication is omitted from the model, the similarity increases
(^ = :62, SE .02). With party identication in the model, there is no extra similarity between the
Democratic party candidates; ^D is small and statistically insignicant.27 The MLEs for (6a{d)
have, likewise, ^R = :025 (SE .046). Apparently, D = R = 0, so that the MLEs for (5a{d) and
for (6a{d) are describing the same voter equilibrium.
21
Discussion
The coordinating voting model parameter estimates describe vote choices that emphasize the presidential candidates. The high estimates for D and R indicate that the policy positions attributed
to the presidential candidates are weighted more heavily than the positions attributed to the parties. Most of the D and R point estimates are greater than :5, suggesting that voters usually
believe the President to have more weight in policy outcomes than the House. Jimmy Carter running for reelection in 1980 is an exception (^D;80 = :406), but the most striking case of a weak
President-in-anticipation is Bob Dole in 1996 (^R;96 = :088). A reasonable interpretation is that
Dole was expected to be subservient to the highly centralized and confrontational House of Newt
Gingrich. The estimates for aP , aHP , aH and aPH suggest that in equilibrium it is the presidential
candidate who, at the margin, is believed to bring along support in the legislature, and not the
P ) is a^HP =a^P = 1:8, while the estimated eect of
reverse. The estimated eect of P on H (@ H=@
H on P is a^PH =a^H = :03. In fact the estimate for aPH is statistically insignicant, so the simplest
H = 0.
thing is just to say that @ P=@
A voter who says economic conditions have improved gives the potential Democratic President
closer scrutiny than the potential Republican President, in the sense that the voter puts more
weight on the policy-related discrepancy it would experience should the Democratic candidate win
the presidency than on the discrepancy should the Republican win. Using the MLEs for bE 0 and bE 1,
^i = :68 for a voter who says economic conditions are \much better" and ^i = :63 for one who says
\better." There is no corresponding advantage for Democratic candidates among voters who say
economic conditions have deteriorated, however. A voter who rates economic conditions as \much
worse" (^i = :46) or \worse" (^i = :52) treats the discrepancies from each party about equally.
It appears that when many voters believe economic conditions have improved, Democratic party
candidates suer electorally from their party's interventionist reputation. But Democratic party
22
candidates do not benet from the reputation when many believe that economic conditions have
declined. These eects are independent of the usual kind of retrospective voting eects (Fiorina
1981) in which candidates of the President's party lose votes among those who think economic
conditions have gotten worse. The MLEs for the coecients cP 1 and cH 1 all have the correct,
positive signs to represent such eects, though not all of the estimates are statistically signicant.
The estimated values for P oer plenty of scope for a pattern of midterm losses for the President's party due to collapsing uncertainty, as in the theory of Alesina and Rosenthal (1989; 1995).
Immediately after the election, voters experience a policy surprise, as the pre-election expected loss
(1 , P )iji , ~Di jq + P (1 , i )ji , ~Ri jq becomes the actual loss i ji , ~Di jq if the Democrat wins the
presidency or (1 , i)ji , ~Ri jq if the Republican wins. Table 5 shows dierences between actual and
expected losses for groups dened by retrospective economic evaluation and party identication.
The typical result is that when the Republican wins the presidency, Democratic identiers experience a bigger-than-expected loss and Republican identiers a smaller-than-expected loss, with the
reverse pattern of surprises occurring when the Democrat wins. The striking exception to the pattern is year 1976, when the mean-valued Democrats also experienced bigger-than-expected losses.28
Because q^ does not dier substantially from 1, the surprise values are measured in the same units as
the ideal points and policy positions. It is therefore easy to see that the policy surprises are often
substantial. For instance, the value of :09 for a Strong Republican who evaluated the economy
as \better" in 1976 is 29% of the dierence of #Ri , #Di = :31 that such a voter saw between
the Democratic and Republican party policy positions (see Table 2), and 41% of the dierence of
~Ri , ~Di = :54 , :32 = :22 that such a voter saw between the policies that would occur given a
Republican rather than a Democratic President.
*** Table 5 about here ***
It is not a trivial step to go from the post-election policy surprises to a complete vote choice
23
model that would explain midterm loss, not least because of the dierences in turnout between
presidential year and midterm. Another, relatively minor complication is that typically each individual's ideal point and beliefs about the policy positions of the President and the parties vary over
the time between the two elections. For any denition of groups, the distributions Fk probably
vary over time also. But the surprise results are nonetheless strongly in line with the requirements
of Alesina and Rosenthal's (1989; 1995) theory of midterm loss. An alternative route to explaining
midterm loss would open if an individual's probability of turning out at midterm were shown to
be an increasing function of the post-election surprise the person experienced. Studies of negative
voting since Kernell (1977) have not found such eects (Born 1990; Cover 1986). But such a relationship could explain both the negative correlation \between the prior Democratic presidential
vote and the Democratic presence in the midterm electorate" and the positive correlation \between
the prior Democratic presidential vote and the presence of Republicans in the midterm electorate"
that Campbell (1987, 975) found puzzling. If there were both vote switching as in Alesina and
Rosenthal's theory and the indicated surprise-related bias in turnout, Erikson's (1988) \presidential penalty" explanation for midterm loss would nd support from two dierent directions.
Americans coordinate their votes. In choosing between candidates for President or the House,
each voter pays attention to what other voters believe and to the choices other voters intend to
make. The evidence for such a conclusion from the estimates and tests is strong, but an important
question remains. How do they do it? How, practically, is such coordination possible?
The information requirements introduced to dene the rational expectations P and H via (7),
(8) and (9) are clearly excessive if the idea is that each voter somehow independently keeps track
of all the component facts (e.g., the set of group sizes ). Fortunately it is not necessary to assume
that each voter acts alone. In models and experiments with non-stochastic spatial utility and
voting for a single oce, McKelvey and Ordeshook show that polls (1984; 1985a; Fey 1997) or
24
interest groups and history (1985b) may support rational expectations voter equilibria even when
many voters are poorly informed. Their results do not apply directly to the current model, but
they suggest that it is reasonable to assume that there exists an institution we might call Polls
and Pundits that allows each voter to monitor the current values of P and H without exerting
much personal eort. To learn, to a pretty good approximation, what are the candidates' chances
in the presidential race and what is the expected outcome in House races across the country, a
voter need only invest a little time|perhaps less than a minute|listening to pundits and pollsters
say what they think will happen. Similarly, a small amount of attention to media commentators
may let a voter know how strong each presidential candidate may be expected to be relative to his
party and to the legislature. Having learned from Polls and Pundits the widely accepted values for
the expectations here modeled as P , H , D , R, D and R , all a voter would need in order to
coordinate successfully would be an idea of its ideal point, beliefs about the policy positions of the
parties and candidates, and values for its attributes zPi and zHi .
The question then becomes how accurate may we expect Polls and Pundits to be about the
information voters rely on them to provide. It is beyond the scope of the current discussion to pursue
this question very far. Competitive pressures may be expected to discipline nationally prominent
pollsters, reporters and commentators. This does not mean that each is unbiased, but only that each
performs reliably. But what they report can accurately inform voters only if poll respondents and
other sources act appropriately. From an equilibrium point of view, voters' reliance on information
from such sources, and the suitably informing actions of the sources themselves, can be sustained
only if there are suitable congurations of beliefs and strategies on everyone's part. The necessary
beliefs go beyond beliefs about preferences (in the current model, these would be beliefs about the
Fk distributions), to include beliefs about others' strategies and about others' beliefs. One way
to summarize the requirements is to say that everyone must be participating in a suitable political
25
culture. Greif's (1994) analysis of cultural beliefs in medieval social and economic organizations
illustrates the range of issues that would need to be addressed to develop an equilibrium model.
To say the least, it would be an immense undertaking. Meanwhile, we can refer to the vast body
of work that has demonstrated the strongly participatory character of American politics, reaching
far beyond elections (e.g. Verba, Schlozman and Brady 1995), to support a belief that something
like the necessary political culture does exist.
Appendix
Motivation for the GEV Vote Choice Models: I assume Di = Di + DiDi and Ri =
Ri + Ri Ri , where Di > 0, Ri > 0, Di and Ri are nonrandom, dierentiable functions of P and
H , and Di and Ri are random variables, independent of P and H , with a joint GEV distribution
Pr(Di < VD ; Ri < VR ) = expf,G(e,VD ; e,VR )g where G(e,VD ; e,VR ) = (e,VD =1, + e,VR =1, )1,
for constant , 0 < 1. If = 0 then Di and Ri are independent (Maddala 1983, 70{72). The
assumed forms give
@i=@ P = cPi + cPRiRi + cPDi Di
@i=@ H = cHi + cHRiRi + cHDiDi
Ri + (1 , P )Di ]=@ P ,
where the nonrandom coecients, functions of P and H , are cPi = @ [P
Ri =@ P , cPDi = @ (1 , P )Di=@ P , cHi = @ [P
Ri + (1 , P )Di ]=@ H , cHRi = @ P
Ri=@ H
cPRi = @ P
and cHDi = @ (1 , P )Di =@ H .
The form of the dependence between presidential and House member votes that is induced by
the common random variables, which are now Ri and Di , depends on the values of the coecient
functions cPRi , cPDi , cHRi and cHDi. It seems reasonable to assume that a voter i becomes more
sensitive to variations in Ri if there is an increase in either the Republican presidential candidate's
26
probability of winning or the Republican party's proportion of the two-party vote in House races.
In other words, cPRi > 0 and cHRi > 0. Likewise, it seems reasonable to assume that a voter
becomes less sensitive to variations in Di if there is an increase in either the Republican presidential
candidate's probability of winning or the Republican party's proportion of the two-party vote in
House races, i.e., cPDi < 0 and cHDi < 0. For instance, for 0 < P ; H < 1, the coecients have the
indicated signs if Ri = P + H and Di = (1 , P )+(1 , H ), or if Ri = P H and Di = (1 , P )(1 , H ).
The assumptions about the coecients imply that straight-ticket voting will be more frequent
than would occur if the random elements for the presidential vote choices were independent of the
random elements for the House vote choices. Substituting for the partial derivatives in equations
(3) and (4) and using cPRi > 0 and cHRi > 0 gives the voting rules
8
>>
<1
yPi = >
>:0
8
>>
<1
yHi = >
>:0
if Ri < bP 0i + bP 1i Di
if Ri > bP 0i + bP 1i Di
if Ri < bH 0i + bH 1iDi
if Ri > bH 0i + bH 1iDi ;
where bP 0i = ,(wPi + bHP wHi + cPi )=cPRi, bP 1i = ,cPDi =cPRi, bH 0i = ,(wHi + bPH wPi + cHi )=cHRi
and bH 1i = ,cHDi =cHRi. For any given value of Di , a large negative value of Ri will make both
Ri < bP 0i + bP 1i Di and Ri < bH 0i + bH 1iDi true, producing votes for both the Republican
presidential and the Republican House candidates. A large positive value of Ri will make both
inequalities false, resulting in votes for both Democratic candidates. Split-ticket votes occur only
for a relatively narrow range of intermediate Ri values. Another aspect of the dependence between
the two vote choices relates to the coecients bP 1i > 0 and bH 1i > 0. If both bP 1i > 1 and bH 1i > 1,
there is a pro-Republican bias in the sense that large, equal values of Di and Ri favor votes for
Republican rather than Democratic candidates. Similarly, there is a pro-Democratic bias if both
27
bP 1i < 1 and bH 1i < 1.
The form of the dependence between the two vote choices suggests that the combined choice
can be well modeled by either FDi or FRi . In both distributions the two split-ticket alternatives are
treated as more similar to one another than they are to either of the straight-ticket alternatives.
Such a treatment is justied because split-ticket votes occur only for a band of Ri and Di values.
In contrast, for any value of Ri , a Republican straight-ticket vote occurs for all values of Di more
positive than some threshold value, and a Democratic straight-ticket vote occurs for all values of
Di more negative than some threshold value. The dierence between FDi and FRi is that FDi
allows the vote combinations that include at least one Democratic candidate to be more similar
to one another than they are to the Republican straight-ticket combination, while FRi allows the
combinations that include at least one Republican candidate to be more similar to one another
than they are to the Democratic straight-ticket alternative. FDi corresponds to the case where
bP 1i < 1 and bH 1i < 1, FRi to the case where bP 1i > 1 and bH 1i > 1.29
Existence of Bayesian Nash Equilibria I consider only sets of parameter values in which
q 1 (for q < 1, technical problems arise due to innite discontinuities in wHi). Let i`| and i`|
denote the values of i and i when evaluated using P = ` and H = | for some ` 2 [0; 1] and
| 2 [0; 1]. Let P`| denote the value of P as dened by (7) and (8) when i = i`| and let H `| denote
the value of H as dened by (9) when i = i`| . Because i`| varies continuously as a function of
` for each i and P`| is a continuous function of the i`| values, there is at least one xed point of
P`| as a function of ` for each xed value of |, i.e., there is at least one value ` such that P`| = `.
Because P0| > 0 and P1| < 1, the number of xed points is odd. For q > 1 there is similarly an odd
number of xed points H `| = | for each `. If q = 1, the step functions in wHi imply that H `| does
not vary continuously as a function of |, so if q = 1 there is not necessarily a xed point H `| = |.
28
But for a nite number N of voters, the number of points of discontinuity is nite. So the values of
` for which there is no xed point H `| = | are isolated: for any > 0 there is a value `0, j` , `0j < such that there is a xed point H ` | = | for some | 2 [0; 1]. Now consider the graph of the set of
0
xed points P`| = ` as | varies over [0; 1] and the graph of the set of xed points H `| = | as ` varies
over [0; 1]. When q > 1 both graphs are continuous and so necessarily intersect. That is, there is
necessarily at least one pair of values (`; |) such that simultaneously P`| = ` and H `| = |. If q = 1,
each graph is in general not continuous, because of the step functions in wHi, but each graph does
have a nite number of continuous components. In this case, the graphs need not intersect. But
because the number of points of discontinuity is nite, each set of parameter values for which there
is no intersection is isolated. Let 0 be a set of values for the parameters for which there is
no intersection. In every neighborhood of 0 there is a set of values 00 for which an intersection
exists; an intersection exists for almost every set of parameter values. Intersections in the graphs
correspond to equilibria among voters. So we conclude that there is an equilibrium corresponding
to almost every set of parameter values. For nite N > 0, the argument holds for arbitrary nite
sets of probability measures fk or of group sizes .
To specify which particular set of parameter values is chosen requires further assumptions.
One approach is to assume that there is a probability distribution over the parameter space, that
the parameter values used in (5a{d) are the posterior mean of that distribution given information
conveyed through some kind of public political process (e.g., an election campaign), and that before
the political process all voters begin with the same prior distribution. Then from Aumann (1976;
see also Fudenberg and Tirole 1991, 548{550) we know that that the assumption that the parameter
values are common knowledge implies that all voters have the same posterior distribution, obtained
by Bayesian updating. To specify the result in further detail would require a detailed specication
of the referent distribution and of the public process.
29
Measuring Ideal Points: To measure an individual's ideal point and beliefs about the policy
positions of the Republican and Democratic parties and candidates, i , I use a scoring method
based on the empirical cumulative distributions of the observed responses to several seven-point
(and one four-point) ANES survey items. The general motivation for the method is the observation
that any continuous random variable X can be mapped onto a scale such that the values of the
scale have probability mass spread uniformly over [0; 1]. Simply map each value x of the variable
to the value of the variable's distribution function, FX (x) = Pr(X < x). If X is multivariate with
components X1; : : :; Xk , the mapping from vectors (x1 ; : : :; xk ) to a uniform distribution on [0; 1]
goes through the same way, using the distribution function FX (x) = Pr(X1 < x1 ; : : :; Xk < xk ).
To measure i , I use a collection of sets of ve seven-point placement scales. Each set includes
one scale for self, one for each party and one for each presidential candidate. Tables 6 and 7
list descriptions and variable numbers for the survey items used for each year. A \set" of scales
corresponds to the set of ve items|referring to self, parties and candidates|for each substantive
description. All items are oriented so that the \liberal" position during the given time period has
the lower number. The label \reversed" in the tables indicates items that had their categories
reordered to reverse the original 1-to-7 (or for Abortion in 1996, 1-to-4) ordering.
*** Tables 6 and 7 about here ***
I do not try to estimate the joint, ve-dimensional distribution function for the ve scales of
each substantive description. Rather I approximate the joint distribution by computing the simple
average of the observed one-dimensional marginal distributions.
To assign codes in the [0; 1] interval to each scale, rst compute the cumulative response proportions for the ve scales for each substantive description. Let 0 = rsj 0 rsj 1 rsj 6 rsj 7 = 1 denote the successive cumulative proportions for substantive description s (e.g., s = \Liberal/Conservative") and scale j 2 fS; D; R; PD; PRg, S = self, D = Democratic party, R = Repub30
lican party, PD = Democratic candidate and PR = Republican candidate. For each m 2 f0; : : :; 7g,
compute rsm = (rsSm + rsDm + rsRm + rsPDm + rsPRm )=5. For all ve scales of type s, the numerical
code used for original response category m 2 f1; : : :; 7g is rsm = (rs;m,1 + rsm )=2. Tables 8 and 9
show the codes computed by this procedure for each substantive description. To determine values
for i for each voter, average the score for each scale over all the substantive descriptions for which
the person responded to all ve scales for that substantive description.
*** Tables 8 and 9 about here ***
Iterative Computation of Rational Expectations and MLEs: Given estimates for the
parameters and estimates P` and H ` from iteration step `, use (5a{d) (or (6a{d)) to compute
probability values i;` = RRi;` + RDi;` and i;` = RRi;` + DRi;` for each voter. For each State j
with at least one voter included in the survey data, compute the Horvitz-Thompson estimate
0 1,1
X
X
yPj;` = @ !i A
!i i;` ;
i2sj
i2sj
where sj is the set of voters in the sample from State j in the referent year. Use the yPj;` values to
compute mean R;` and variance 2R ;` , and use a version of (8) to get an updated estimate P`+1 .30
The corresponding estimate H `+1 is
H `+1 =
n !,1 X
n
X
i=1
!i
i=1
!i i;` ;
where n is the total sample size of voters for the referent year. Use P`+1 and H `+1 and the parameter
values of step ` to apply one step of Gauss-Newton maximization to the log-likelihood function,
to get new parameter values for use in iteration ` + 1. Iterations continue until, for successive
iterations ` and ` + 1, (P` ; H ` ) = (P`+1 ; H `+1) and the parameter estimates satisfy the rst- and
second-order conditions for a local maximum of the log-likelihood.
31
A Majoritarian Vote Choice Model: Let policy outcomes under unied government be Di
or Ri of (1a,b), while policy outcomes under divided government are
~DRi = D Di + (1 , D )Ri ;
0 D 1
~RDi = RRi + (1 , R)Di ;
0 R 1 :
~DRi is the policy that voter i believes will occur with a Democratic President and Republican
controlled House and ~RDi is the policy with a Republican President and the House controlled by
the Democrats. For the observed attributes of each choice, dene
vRRi = expf,aM RRiji , Ri jq + cP 0 + cH 0 + cREP REPi
+ (cP 1 + cH 1)PPi ECi + cD PIDD i + cID PIDIDi + cI PIDIi + cIRPIDIRi
+ cRPIDR i + cSR PIDSRi g
vRDi = expf,aM RDiji , ~RDi jq + cP 0 , cH 0 + cDEM DEMi
+ (cP 1 , cH 1)PPi ECi g
vDRi = expf,aM DRiji , ~DRi jq , cP 0 + cH 0 + cREP REPi
+ (,cP 1 + cH 1)PPi ECi g
vDDi = expf,aM DDiji , Di jq , cP 0 , cH 0 + cDEM DEMi
+ (,cP 1 , cH 1)PPi ECi , cD PIDD i , cID PIDID i , cI PIDI i , cIR PIDIR i
, cRPIDRi , cSRPIDSRi g ;
where aM > 0 is constant over all years, cP 0 , cP 1 , cH 0, cH 1, cDEM , cREP have the same interpretations as in (10a,b), and cD , cID , cI , cIR , cR, cSR are the same except multiplied by a factor of two.
The factors that make the weight of the loss associated with each form of government depend on
32
retrospective economic evaluations now have the form
expf,bjE 0 , bjE 1ECi g
;
j 2fRR;RD;DRg expf,bj E 0 , bj E 1ECi g
ji = 1 + P
0
0
0
j 2 fRR; RD; DRg
DDi = 1 , RRi , RDi , DRi
for coecients bjE 0, bjE 1, j 2 fRR; RD; DRg. There is no asymmetry in the treatment of the loss
from each form of government if RRi = RDi = DRi = DDi = 14 .
Missing Data: Table 10 shows how the sample size is reduced by the requirement that the voter
chose a Democrat or Republican in both the presidential and House races. The losses from ignoring
third-party votes substantially aect only presidential votes. Among the 7198 cases where any vote
cast was cast for a Democrat or a Republican, 1426 (about 20%) cast a vote for only one oce.
Among the 5772 who said they voted for Democratic or Republican candidates for both oces, 527
were excluded because the incumbent in their district was running unopposed. Of the remaining
cases, 379 were missing data for the ideal points and believed policy positions or the retrospective
economic evaluations (295 missing only i , 58 missing only ECi , 26 missing both), and seven more
cases were missing data for party identication.
*** Table 10 about here ***
33
Notes
1. I use the gender-neutral singular pronoun to refer to an individual voter.
2. Data are from Miller and Miller 1977; Miller and the National Election Studies 1982; 1986;
1989; Miller, Kinder, Rosenstone and the National Election Studies 1992; Rosenstone, Kinder,
Miller and the National Election Studies 1997.
3. Fudenberg and Tirole (1991, 209) dene and give examples of Bayesian Nash equilibria.
4. Alesina and Rosenthal's (1995, 86{120) assumptions of a quadratic form for voter utility
and of a particular device for producing random distributions of voters are plainly choices made
for analytical convenience, not denitive or essential assertions. Having voters assess their policy
losses in terms of another metric (absolute, according to the estimate for parameter q in Table 3)
and with preferences that vary according to a dierent random device (mostly unspecied in the
current model) does not change the important qualitative features of their theory. Alesina and
Rosenthal (1995) already consider extensions to their basic theory of the same type that appear in
the current model, namely, heterogeneous parties, incumbent advantage and retrospective voting.
So those features of the current model do not diminish its relevance for their theory. The most
signicant dierence between the current model and Alesina and Rosenthal's theory is then that the
current model allows voters to have dierent beliefs about the policy positions of the parties, while
Alesina and Rosenthal (1995) assume that the positions are universally known constants. This
dierence is probably also inessential. The distinction that Hinich and Pollard (1981) introduced
between issues and predictive dimensions supports the interpretation that the parties have xed
and distinct positions on a single predictive dimension but voters make idiosyncratic translations
from those positions to the outcomes that they care about.
5. Because the partial derivatives of i are continuous, @i=@ P = 0 and @i=@ H = 0 are measure
zero events that can be ignored. But for deniteness and to maintain continuity of behavior, we
34
can assume that the voter in those cases chooses 1 or 0 with probability 21 .
6. In practise, i has continuous and bounded support while zPi , zHi and i take any of a nite
number of discrete values. The integrals in (7) and (9) are Riemann-Stieltjes integrals (Billingsley
1986, 230).
7. McKelvey and Ordeshook (1985a) also use relative measurement of positions.
8. The idea in the text may be compatible with Converse's (1964) conception of issue publics,
but Converse argues that discourse among political elites has an ideological foundation. Such a
foundation could certainly facilitate bipolar coalition formation, but is not necessary for it to occur.
9. The table entries are smoothed means of the observed i values. The smoothing model's log-
h
i
likelihood for voter i is based on a beta density: Li = !i log iu1i ,1 (1 , i )u2 ,1 =B (u1i ; u2) , with
!i being a sampling weight, u2 > 0 being a constant and u1i = expfd0i + d1iECig, where d0i and
d1i are constants that depend on the party identication of voter i. Using the MLEs d^0jk , d^1jk and
u^2 , the mean for party identication category j and economic evaluation ECk is u^1jk =(^u1jk + u^2)
where u^1jk = expfd^0j + d^1j ECk g.
10. Alesina, Roubini and Cohen (1997) further review \rational retrospective voting" models.
11. For 1976 the question refers to \business conditions," with wording, \Would you say that at
the present time business conditions are better or worse than they were a year ago?" For 1980, 1984
and 1988 the question wording is \What about the economy? Would you say that over the past
year the nation's economy has gotten better, stayed about the same, or gotten worse?" For 1992
the initial part of the question changed to read, \How about the economy." For 1996 the initial part
was \Now thinking about the economy in the country as a whole." For all years except 1976, the
responses are coded \much worse" (,1), \somewhat worse" (,:5), \same" (0), \somewhat better"
(.5) and \better" (1). For 1976 only three levels of response were recorded, coded here \worse now"
(,:5), \about the same" (0) and \better now" (.5). The ANES variable numbers for each year are
35
3139 (1976), 150 (1980), 228 (1984), 244 (1988), 3532 (1992) and 960386 (1996).
12. For 1976, incumbency status variables were built from NOTE 17 in the codebook le
nes1976.cbk. The ANES variable numbers for the other years are 740 (1980), 59 (1984), 50 (1988),
3021 (1992, with errors corrected as indicated in the codebook le nes92int.cbk) and 960097 (1996).
13. The levels of the party identication scale are Strong Democrat, Democrat, Independent
Democratic, Independent, Independent Republican, Republican and Strong Republican. The variable numbers are 3174 (1976), 266 (1980), 866 (1984), 274 (1988), 3634 (1992) and 960420 (1996).
14. The weight !i is dened to adjust for variations in the probabilities of inclusion due to
varying household sizes, and to allow panel cohorts to be pooled with newly selected respondents.
The weight is the number of adults in each household, multiplied by a time-series weight in years
(1976, 1992, 1996) when part of the Pre-/Post-Election Study sample was part of a multiyear panel
cohort. I rescaled the number of adults and time-series weight variables to give each a mean of 1.0
over the whole of each survey. The ANES variable numbers for each year are 3003 and 3021 (1976),
43 (1980), 70 (1984), 91 (1988), 29, 3076 and 7000 (1992), 960046A and 960005 (1996).
15. The ANES variable numbers for each year are 3665 and 3673 (1976), 994 and 998 (1980),
788 and 793 (1984), 763 and 768 (1988), 5609 and 5623 (1992), and 961082 and 961089 (1996).
16. Estimates were computed using SAS PROC NLIN (SAS Institute Inc. 1989{95) with numerical derivatives. Source code and data are available from the author. Over all years, the percent
correctly classied by \predicting" for each observation the pair of vote choices that has the highest probability using the parameter MLEs is 73.6% (by year, 68.8%, 67.0%, 74.3%, 75.9%, 74.7%,
78.4%). Over all years the average probability of the pair of choices actually made is .64 (by year,
.58, .58, .65, .66, .65, .69). Unreported estimates using (6a{d) are virtually identical, albeit slightly
inferior. The log-likelihood value for the coordinating model using (6a{d) is ,3186:1.
17. The existence of parameter estimates on the boundary of the conceptually admissible range
36
[0; 1] makes it doubtful that the distribution of the estimates is asymptotically normal. The results
do not change if the parameters shown as boundary constrained are instead xed at the boundary
values. Doing that does not improve the distributional situation much, if at all, however, since the
hard constraints are being imposed only after having inspected the MLEs. I rely on the fact that
the test results are so strong that it would take a tremendous departure from normality to reverse
them. It would not help to use robust standard errors because the theory that motivates them also
assumes interior solutions (White 1994, 88{92).
18. To produce the unidimensional nuisance parameter to which the Davies (1987) formula
applies, I used the MLEs a^HP and ^aH to redene aHP as aHP = (^aHP =a^H )aH and then proled
the coordinating model likelihood for values of aH on the interval [.01,15]. The log-likelihood
diminished monotonically on either side of ^aH , with below-MLE minimum value of ,3210:7 at
aH = :01 and above-MLE minimum value of ,3215:7 at aH = 15. I used those two values and the
MLE log-likelihood to compute the approximate variance used in formula (3.4).
19. With party identication omitted, X^ 2 = 54:34.
20. Under either of the two adverse null hypotheses, q = 0 or aP = aHP = aH = aPH = 0,
nonregularities arise from parameters becoming undened. I do nothing special to address the
nonregularities that arise in these cases, but rather base inferences about the referent parameters
on the naive asymptotic condence intervals for their MLEs.
21. The estimates for cD , cID , cI , cIR , cR and cSR in the majoritarian model are somewhat
more than twice as large as in the coordinating model|they should be twice as large|but the
values are nonetheless quite similar.
22. Indeed, using the MLEs for each model, ^i = ^DRi + ^DDi.
23. For instance, let ^Mi denote the probability computed using the majoritarian model MLEs
for the choice that voter i actually made. Dene a log-likelihood by Li = (1 , )LYP i ;YHi +
37
!i log ^Mi , 0 1, where LYP i ;YHi is the coordinating model log-likelihood and !i is the
sampling weight. Fixing ^Mi , the maximum likelihood point estimate for
is ^ = 0 with 95%
condence interval (0,.23).
24. It is dicult to compare the P estimates to the options pricing method estimates of Alesina,
Roubini and Cohen (1997), because the latter are not constrained to be rational (political) expectations under an explicit voting model.
25. The model does not do especially well classifying split-ticket voters separately from straightticket voters. Of the 587 voters \predicted" to have split their tickets, 48% did so, but of the 1101
voters who split their tickets, only 26% were \predicted" to have done so.
26. Consider the case vRPi = vRHi = vDPi = vDHi . With (; D ) = (0; 0), the choice probabilities all equal :25. But with (; D) = (:4; 0), RRi = DDi = :284 and RDi = DRi = :216.
If vRPi = vRHi = 2vDPi = 2vDHi , then (; D) = (0; 0) implies (RRi; RDi ; DRi; DDi ) =
(:44; :22; :22; :11), but (; D ) = (:4; 0) implies (RRi ; RDi; DRi ; DDi) = (:50; :19; :19; :12).
27. If party identication is omitted, extra similarity appears (^D = :19, SE .04). To connect to
the motivating argument in the Appendix, the estimates for and D suggest that bP 1i and bH 1i
both have values near 1.
28. As Tables 1 and 2 suggest, the exceptional result reects the fact that the mean Democrat
ideal point was higher than the mean policy positions attributed to the Democratic party and
Carter that year.
29. Each distribution groups together the vote-choice pairs that have the largest variances. In
a Monte Carlo experiment, Borsch-Supan (1990a, 215) nds such grouping to be important for
the success of nested logit models (equivalent to GEV models) for four alternatives when the true
distribution is multinomial probit.
30. I assign all the electoral votes of States for which there were no voters in the ANES data to
38
the candidate who won the State. Let CNR denote the number of such electoral votes assigned to
the Republican candidate, and let CND denote the number assigned to the Democrat. Conditioning
on those numbers, the proportion of the remaining electoral votes that the Republican candidate
needs to win is = (269 , CNR)=(538 , CNR , CND ). Instead of (8), I use the functional form
R
P = 1 Rp1 ,1 (1 , R )p2,1=B (p1 ; p2)dR.
39
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47
Table 1: Mean Ideal Points by Economic Evaluation and Party Identication, 1976{96
Party Identication
Strong
Indep
Indep
year evaluation Dem Dem Dem Indep Rep
1976
worse
.50
.50 .50
.49
.66
1976 better
.49
.54 .49
.56
.64
1980
worse
.40
.48 .46
.56
.57
1980 better
.34
.43 .51
.51
.44
1984
worse
.38
.43 .36
.43
.56
1984 better
.40
.49 .41
.55
.58
1988
worse
.39
.46 .44
.42
.54
1988 better
.39
.44 .39
.48
.60
1992
worse
.37
.43 .43
.48
.58
1992 better
.39
.49 .46
.57
.70
1996
worse
.38
.45 .43
.51
.56
1996 better
.38
.42 .44
.46
.53
Rep
.66
.61
.59
.49
.54
.59
.51
.55
.59
.64
.58
.54
Strong
Rep
.66
.69
.67
.67
.53
.64
.60
.64
.64
.69
.70
.62
Note: Means are smoothed as described in the text, separately for each year.
Table 2: Mean Party Positions by Economic Evaluation and Party Identication, 1976{96
(a) Democratic Party
Party Identication
Strong
Indep
Indep
year evaluation
Dem Dem Dem Indep Rep
1976
worse
.42
.43 .41
.37
.30
1976
better
.43
.39 .39
.40
.29
1980
worse
.41
.41 .37
.38
.34
1980
better
.39
.41 .39
.42
.47
1984
worse
.36
.39 .41
.44
.35
1984
better
.36
.38 .34
.30
.29
1988
worse
.38
.43 .41
.41
.34
1988
better
.42
.35 .43
.44
.27
1992
worse
.36
.37 .38
.36
.26
1992
better
.36
.33 .38
.24
.26
1996
worse
.44
.39 .42
.35
.35
1996
better
.39
.38 .40
.41
.31
(b) Republican Party
Party Identication
Strong
Indep
Indep
year evaluation
Dem Dem Dem Indep Rep
1976
worse
.62
.56 .59
.56
.59
1976
better
.55
.57 .59
.57
.62
1980
worse
.61
.57 .60
.54
.57
1980
better
.62
.54 .59
.53
.49
1984
worse
.67
.65 .65
.65
.58
1984
better
.71
.64 .68
.64
.65
1988
worse
.69
.67 .70
.62
.64
1988
better
.63
.66 .70
.54
.62
1992
worse
.70
.67 .69
.64
.61
1992
better
.66
.65 .69
.60
.68
1996
worse
.59
.60 .65
.58
.63
1996
better
.66
.66 .66
.64
.68
Rep
.35
.34
.34
.36
.42
.30
.40
.31
.31
.29
.34
.33
Strong
Rep
.33
.28
.35
.42
.40
.28
.32
.25
.25
.21
.22
.25
Rep
.61
.57
.56
.52
.54
.64
.58
.65
.65
.64
.61
.65
Strong
Rep
.61
.59
.60
.61
.59
.64
.61
.65
.67
.70
.72
.70
Note: Means are smoothed as described in the text, separately for each year.
Table 3: Parameter Estimates for the Coordinating and Majoritarian Vote Choice Models
Coordinating Majoritarian
parameter MLE
SE MLE
SE
q
1:026 :064 1:089 :093
aP
3:869 :398
|
|
aHP
7:107 1:249
|
|
aH
5:033 1:124
|
|
aPH
:138 :347
|
|
aM
|
| 21:326 1:966
D;76
1 :141 :809 :076
D;80
:406 :187 :695 :071
D;84
:779 :125 :883 :054
D;88
:687 :138 :743 :064
D;92
1 :089 :854 :042
D;96
:830 :085
1 :046
R;76
:765 :183 :977 :086
R;80
1 :090
1 :063
R;84
:549 :091 :760 :056
R;88
:740 :115 :902 :068
R;92
:552 :110 :860 :053
R;96
:088 :139
0 :116
D;76
1
:184
1 :163
D;80
:862 :186 :900 :182
D;84
1 :226
1 :217
D;88
:795 :195 :904 :209
D;92
1 :195
1 :133
D;96
:746 :154 :678 :184
R;76
:645 :284 :742 :230
R;80
1 :181
1 :162
R;84
:770 :204
1 :284
R;88
:633 :244 :645 :253
R;92
:534 :165 :846 :139
R;96
1 :195 :797 :282
cD
:428 :054 :926 :109
cID
:369 :060 :794 :119
cI
:926 :074 1:976 :149
cIR
1:370 :072 2:933 :144
cR
1:401 :070 2:989 :140
cSR
1:733 :077 3:713 :153
Coordinating
parameter MLE SE
:402 :038
D
:057 :044
bE 0
:305 :104
bE 1
:469 :164
bRRE0
| |
bRRE1
| |
bRDE0
| |
bRDE1
| |
bDRE0
| |
bDRE1
| |
cP 0;76
,1:028 :080
cP 0;80
,:835 :090
cP 0;84
,:630 :073
cP 0;88
,:867 :086
cP 0;92
,:862 :097
cP 0;96
,1:112 :088
cH 0;76
,:919 :084
cH 0;80
,:891 :096
cH 0;84
,:841 :079
cH 0;88
,1:030 :089
cH 0;92
,:728 :090
cH 0;96
,:828 :085
cP 1;76
:215 :123
cP 1;80
:414 :111
cP 1;84
:469 :119
cP 1;88
:290 :146
cP 1;92
:344 :115
cP 1;96
:660 :141
cH 1;76
:213 :103
cH 1;80
:039 :097
cH 1;84
:008 :087
cH 1;88
:270 :115
cH 1;92
:217 :086
cH 1;96
:308 :117
cDEM
1:003 :103
cREP
1:293 :113
Majoritarian
MLE SE
:389 :043
:052 :047
| |
| |
,:293 :134
,:725 :213
,:114 :092
,:366 :159
:223 :079
,:173 :129
,1:094 :081
,:858 :089
,:746 :073
,:886 :087
,:953 :095
,1:229 :088
,:959 :085
,:900 :098
,:918 :078
,1:053 :086
,:811 :085
,:947 :089
:200 :124
:465 :110
:497 :116
:309 :150
:343 :115
:658 :139
:117 :109
:159 :099
:066 :085
:282 :117
:186 :087
:373 :119
1:007 :103
1:289 :117
Note: Maximum likelihood estimates using (5a{d). indicates a boundary-constrained parameter.
Pooled ANES Pre-/Post-Election Survey data, 1976{96, n = 4859 cases. Log-likelihood values:
coordinating model, ,3184:6; majoritarian model, ,3224:8.
Table 4: Rational Expectations Probability that Republican President Wins and Proportion Republican in National Two-party Vote, by Year
year
1976
1980
1984
1988
1992
1996
P
H
.496
.618
.620
.540
.416
.431
.465
.506
.473
.453
.430
.536
Note: Computed using the parameter MLEs in Table 3 and 1976{96 ANES data.
Table 5: Post-election Policy Surprise by Economic Evaluation and Party Identication, 1976{96
winner for
Strong
year President evaluation Dem Dem
1976
D
worse
:00
:00
1976
D
better
:01
:04
1980
R
worse
:03
:02
1980
R
better
:03
:02
1984
R
worse
:04
:03
1984
R
better
:03 ,:00
1988
R
worse
:05
:03
1988
R
better
:02
:01
1992
D
worse
,:05 ,:02
1992
D
better
,:03 :02
1996
D
worse
,:02 ,:00
1996
D
better
,:02 ,:02
Party Identication
Indep
Indep
Dem Indep Rep
:01
:01
:05
:01
:05
:09
:03 ,:02 ,:02
:01 ,:00
:00
:03
:02 ,:03
:02 ,:05 ,:06
:05
:02 ,:03
:03 ,:01 ,:08
,:03 :01 :06
,:00 :07 :09
,:02 :02 :03
,:01 :01 :05
Rep
:05
:06
,:03
,:01
,:02
,:06
,:02
,:05
:05
:08
:03
:04
Strong
Rep
:06
:09
,:05
,:04
,:02
,:07
,:05
,:09
:07
:11
:06
:07
Note: Quantities are P [ik jik , ~Dik jq , (1 , ik )jik , ~Rik jq ] if the Democrat won the
presidency in the referent year and (1 , P )[(1 , ik )jik , ~Rik jq , ik jik , ~Dik jq ] if the
Republican won, using coordinating voting model MLEs from Table 3 for all parameters and
smoothed group means for all ideal points and policy positions.
Table 6: Variables Used to Measure Ideal Points and Policy Positions, 1976{84
year description
1976 Government Guaranteed Job and Living Standard
Rights of the Accused
School Busing to Achieve Integration
Government Aid to Minorities
Government Medical Insurance Plan
Liberal/Conservative Views
Government Guaranteed Job and Living Standard
Urban Unrest
Legalization of Marijuana
Change in Tax Rate
Equal Rights for Women
1980 Liberal/Conservative
Defense Spending
Government Services/Spending (reversed)
Reduce Ination/Reduce Unemployment (reversed)
Liberal/Conservative Views
Government Aid to Minorities
Getting Along with Russia
Equal Rights for Women Scale
Government Guaranteed Job and Living Standard
1984 Liberal/Conservative Placement
Liberal/Conservative
Government Services/Spending (reversed)
Minority Aid/No Aid
Involvement in Central America (reversed)
Defense Spending
Social/Economic Status of Women
Cooperation with Russia
Guaranteed Standard of Living/Job
variable numbers
3241{3245
3248{3252
3257{3261
3264{3268
3273{3277
3286{3290
3758{3762
3767{3771
3772{3776
3779{3783
3787{3791
267{269, 278, 279
281{283, 286, 287
291{293, 296, 297
301{303, 306, 307
1037{1039, 1053, 1054
1062{1064, 1073, 1074
1078{1080, 1089, 1090
1094{1096, 1105, 1106
1110{1112, 1121, 1122
119{121, 123{125, 127{129
131{133, 135{137
369, 371{374
375{379
382{386
388{392
395{399
401{405
408{412
414{418
Note: Variable numbers for 1976{84 refer to data on the \ANES 1948-1994 CD-ROM" release of
May, 1995.
Table 7: Variables Used to Measure Ideal Points and Policy Positions, 1988{96
year description
1988 Liberal/Conservative
Government Services/Spending (reversed)
Defense Spending
Government-Funded Insurance
Guaranteed Standard of Living/Job
Social/Economic Status of Blacks
Social/Economic Status of Minorities
Cooperation with Russia
Women's Rights
1992 Ideological Placement
Government Services/Spending (reversed)
Defense Spending
Job Assurance
1996 Liberal/Conservative
Government Services/Spending (reversed)
Defense Spending
Abortion (reversed)
Jobs/Environment
Environmental Regulation
variable numbers
228, 231, 232, 234, 235
302{304, 307, 308
310{312, 315, 316
318{322
323{325, 328, 329
332{334, 337, 338
340{342, 345, 346
368{370, 373, 374
387{391
3509, 3514, 3515, 3517, 3518
3701{3705
3707{3711
3718{3722
365, 369, 371, 379, 380
450, 453, 455, 461, 462
463, 466, 469, 477, 478
503, 506, 509, 517, 518
523, 526, 529, 535, 536
537, 538, 539, 541, 542
Note: Variable numbers for 1988{92 refer to data on the \ANES 1948-1994 CD-ROM" release of
May, 1995. 1996 variable numbers omit the prex `960'.
Table 8: Item Response Scores Used for Each Set of Ideal Point and Policy Position Scales, 1976{84
year description
original
1976 GGJaLS
RotA
SBtAI
GAtM
GMIP
L/CV
GGJaLS
UU
LoM
CiTR
ERfW
1980 L/C
DS
GS/S(r)
RI/RU(r)
L/CV
GAtM
GAwR
ERfWS
GGJaLS
1984 L/CP
L/C
GS/S(r)
MA/NA
IiCA(r)
DS
S/ESoW
CwR
GSoL/J
item response scores
1
2
3
.0643 .1938 .3430
.0706 .2035 .3453
.0572 .1668 .2822
.0571 .1892 .3697
.0827 .2276 .3648
.0174 .1140 .2823
.0408 .1339 .2771
.0711 .2154 .3889
.0232 .0730 .1606
.0552 .1640 .2989
.0920 .2580 .4301
.0180 .0993 .2386
.0168 .0678 .1663
.0504 .1863 .3714
.0277 .1126 .2786
.0108 .0823 .2278
.0294 .1161 .2635
.0567 .1945 .3713
.0823 .2539 .4421
.0371 .1359 .2892
.0948 .2459 .3668
.0229 .1264 .2812
.0433 .1564 .3165
.0429 .1520 .3122
.0426 .1489 .2945
.0307 .1151 .2416
.0442 .1507 .3042
.0416 .1364 .2706
.0356 .1300 .2726
4
.5391
.5512
.4476
.5910
.5401
.4777
.4877
.6255
.3765
.5087
.6694
.4117
.3247
.5753
.5289
.4102
.4715
.5678
.6452
.4880
.4451
.4560
.5122
.5267
.4784
.4175
.5316
.4685
.4745
5
.7220
.7521
.6160
.7733
.7066
.6819
.6967
.8271
.6284
.7096
.8642
.6003
.5314
.7610
.7628
.6021
.6941
.7558
.8164
.6863
.5355
.6336
.6935
.7292
.6697
.6128
.7494
.6769
.6846
Note: See Table 6 for full identication of the variables.
6
.8446
.8690
.7317
.8789
.8239
.8753
.8483
.9253
.7815
.8288
.9373
.8155
.7544
.8949
.9044
.8255
.8640
.8969
.9210
.8470
.6819
.8249
.8410
.8679
.8350
.7906
.8832
.8391
.8459
7
.9482
.9557
.8907
.9590
.9375
.9854
.9553
.9791
.9188
.9378
.9784
.9696
.9324
.9737
.9768
.9773
.9646
.9754
.9793
.9583
.8758
.9696
.9563
.9623
.9555
.9381
.9677
.9549
.9576
Table 9: Item Response Scores Used for Each Set of Ideal Point and Policy Position Scales, 1988{96
year description
original
1988 L/C
GS/S(r)
DS
G-FI
GSoL/J
S/ESoB
S/ESoM
CwR
WR
1992 IP
GS/S(r)
DS
JA
1996 L/C
GS/S(r)
DS
A(r)
J/E
ER
item response scores
1
2
3
.0258 .1285 .2744
.0430 .1663 .3443
.0275 .1022 .2225
.0564 .1671 .2934
.0318 .1128 .2402
.0291 .1009 .2285
.0410 .1337 .2713
.0440 .1499 .3181
.1011 .2845 .4590
.0271 .1309 .2887
.0408 .1559 .3278
.0260 .1101 .2687
.0310 .1150 .2455
.0263 .1293 .2807
.0329 .1332 .3011
.0171 .0782 .2080
.1661 .4370 .7087
.0290 .1177 .2774
.0359 .1363 .3110
4
.4394
.5635
.4182
.4704
.4312
.4552
.4792
.5626
.6723
.4715
.5400
.5069
.4348
.4544
.5092
.4209
.9378
.5178
.5506
5
.6197
.7674
.6465
.6599
.6393
.6853
.6944
.7801
.8497
.6510
.7409
.7388
.6383
.6346
.7105
.6777
6
.8197
.8990
.8333
.8160
.8148
.8345
.8471
.9014
.9342
.8293
.8842
.8883
.8031
.8284
.8714
.8815
7
.9677
.9741
.9572
.9438
.9475
.9477
.9533
.9717
.9812
.9649
.9706
.9718
.9381
.9705
.9693
.9778
.7542 .9055 .9804
.7663 .9050 .9787
Note: See Table 7 for full identication of the variables.
Table 10: Sample Size and Sizes of Sets of Voters by Year
Voted for Democrats or Republicans
Voted for Any Candidate
a
b
c
sample P & H pres. House
P & H pres. House
year size
voters voters voters voters voters voters voters voters
1976
683
784
826
804
846
804
846
804
846
1980
627
762
877
859
974
842
972
859
989
1190 1398 1223 1431
1984
976
1144 1376 1187
1419
1988
719
1030 1195 1054
1219
1047 1209 1062 1224
1382 1665 1392 1675
1992
980
1126 1357 1370
1601
1996
874
926 1034 1031
1139
1024 1134 1049 1159
6289 7224 6389 7324
total 4859
5772 6665 6305
7198
Notes: a voted for both a presidential and a House candidate; b voted for a presidential candidate;
c
voted for a House candidate.
Source: Computed from ANES Pre-/Post-Election surveys of 1976{1996.