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Measuring Competitiveness in Multi-Member Districts
Steven R. Reed
Faculty of Policy Studies
Chuo University
[email protected]
Kay Shimizu
Department of Political Science
Stanford University
[email protected]
Prepared for presentation at the Conference on Electoral and Legislative Politics in Japan,
Stanford University, June 11th-12th, 2007
Draft, please do not cite without authors’ consent
Comments welcome.
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For representative democracy to function properly, elections must be competitive. Voters
must have meaningful options and the result of the election must be in some doubt until the
votes are counted. When all candidates are all either safe (i.e., assured victory) or token (i.e.,
have no realistic chance of winning), voters may have some voice but they have no real choice.
The outcome is determined before the voting takes place. In these noncompetitive elections,
voter interest and turnout tends to drop leaving the legitimacy of the result in doubt. We thus
need a good measure of electoral competitiveness, both as a dependent variable in its own
right and as an independent variable explaining turnout.
For bipolar contests in single-member districts, we have an excellent measure of
competitivess, Closeness, the number of votes that separate the winner and the runner-up’
(Cox and Munger 1989). Closeness, however, fails to capture all of the competition in
multi-member districts because it ignores all but two candidates, the last winner and the first
runner-up. Competition in multi-member districts might be bipolar, involving only two
candidates, but it might also involve several more candidates. By definition, multi-member
districts elect more than one candidate. If all of the winners are safe and all the losers token,
the district is noncompetitive. However, more than one winner may be campaigning hard to
keep her seat and more than one loser might have a chance of winning. If either more than
one winner and/or more than one loser finds herself on the cusp between winning and losing,
Closeness underestimates the competitiveness of the district. Of course, single-member
districts may also have more than one competitive loser but the phenomenon is much more
common in multi-member districts.
In this paper, we propose a measure that distinguishes among three types of
candidates, safe candidates who are assured of victory, token candidates who have no chance
of winning, and cusp candidates who might win or might lose depending upon how voters
respond to their respective campaigns. Our measure of competitiveness will then be the
number of candidates on the cusp between winning and losing. We will then demonstrate
that this measure outperforms Closeness as an independent variable in explaining turnout in
Japanese elections between 1947 and 1993.
Cox and Munger (1989) test two hypotheses about the competitiveness of an election
and turnout. First, in the traditional rational choice model, each voter estimates the
probability that her vote might affect the outcome of the election and balances this
probability against the cost of voting. In developing their measure of competitiveness, Cox
and Munger doubt the capacity of voters to make these calculations and propose a second
model. In their “mobilization model” candidates, who have more information about the
election and are much more concerned with the outcome than the average voter, estimate the
closeness of the election and expend greater effort in mobilizing the vote when they expect
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the election to be close. Higher turnout thus results from greater party and candidate efforts
to turn out the vote, rather than calculations by individual voters about the probability of one
vote changing the election outcome. They use the total amount of campaign expenditures in
the district to estimate the intensity of the campaign and find that, when one includes
expenditures in the model, the impact of Closeness declines, though it does not fade into
insignificance.
We agree with Cox and Munger that competitiveness is primarily a matter of
campaign intensity and that campaign expenditures are a good measure of that intensity.
However, not all campaign expenditures are equal: who spends matters.
Thus we propose
an alternative to Closeness that includes information on more than two candidates. Our
measure is consistent with the limited interest and cognitive capacity of voters, but gives
voters a more active role than does Cox and Munger’s mobilization model. In their model,
voters merely respond to the mobilization efforts of parties and candidates. In our model,
voters respond differentially to the mobilization efforts of different types of candidates.
The Limits of Closeness
Closeness not only works perfectly well in single-member districts, but has also been
successfully applied to analyses of turnout in Japan’s multi-member districts (Cox,
Rosenbluth and Thies 1998). In both single- and multi-member districts, Closeness does a
good job of simply distinguishing between competitive and noncompetitive elections. When
the gap between the last winner and the first loser is so large that it is unlikely to be reversed,
the election is noncompetitive no matter how many winners or how many losers may be
running. All winning candidates are safe and all losing candidates are token. There are no
cusp candidates. In multi-member districts, however, Closeness does not accurately capture
the varying degree of competitiveness in those elections that are competitive. If Closeness is
small, we know that the last winner and the first runner-up are both on the cusp, but we
know nothing about any of the other candidates.
Consider a three-member district with six candidates. We can imagine two extreme
cases, each with the same value of Closeness but with very different levels of competition. In
one case, the first and second candidates are safe, the third and fourth candidates on the cusp,
and the fifth and sixth candidates are token. There are thus only two cusp candidates, the
third and fourth, whose elections are in doubt. Those two candidates are surely campaigning
hard but the other four candidates are less motivated, either because they have already won
or because they have already lost. At the other extreme, all six candidates might be grouped
together so tightly that none of the eventual winners are safe and all of the eventual losers
have some realistic chance of winning. In the first case, only two candidates are highly
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motivated because they are worried about their (re-)election chances while in the second all
six candidates are running scared. We expect a higher turnout when six candidates are
highly motivated to campaign hard than when only two are, even though Closeness might be
identical. Greater efforts to mobilize the vote should produce higher turnout. Thus for
multi-member districts, we need a measure that incorporates information on more than two
candidates.
An Alternative Measure
The logic behind Closeness is that the higher the probability of a single vote changing the
electoral outcome, the more competitive the election. This logic has proven problematic
theoretically (Grofman 1995) even while performing well empirically (Geys 2006:646-9).
Instead of trying to extend this logic to the case of multi-member districts, we decided to
experiment with a different logic. We hypothesize that voters utilize a simple heuristic to
evaluate candidates, dividing them into the three proposed categories: safe, cusp and token.
Candidates have more information and greater interest than the average voter and should
therefore be able to make more subtle distinctions, but we shall show that voters respond
differentially to the mobilization efforts of each type of candidate. Most notably, campaign
expenditures by cusp candidates produce a greater response from voters than do
expenditures by either safe or token candidates.
We propose a model in which voters use simple heuristics to estimate the
competitiveness of each of the candidates running in a particular election. First, voters decide
if the race is competitive or noncompetitive. Are there any candidates on the cusp between
winning and losing or is the outcome determined before the votes are counted? If there are at
least two candidates whose electoral prospects voters cannot predict with any confidence,
then the election is competitive. These two candidates straddle what we will call the “M-line”,
the line between the Mth candidate, the last winner and the M+1st candidate, the runner-up.
The voter next needs to decide if any other candidates are on the cusp between winning and
losing. One might well model voter heuristics by taking the distance between each
candidate’s vote and the M-line but we take a different tack. We assume that in all
competitive elections, voters see a clump of indistinguishable candidates straddling the
M-line. If we can identify the candidates in this clump, we have divided the candidates into
our three categories. Those included in the clump are on the cusp. The candidates who are
expected to get more votes than those on the cusp are safe, and those who are expected to get
fewer votes are token.
We identify cusp candidates based on the average percentage difference in votes
between all unique pairs of candidates included in the calculation. We begin with the two
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candidates straddling the M-line and subsequently add those candidates closest in votes.
For each pair of candidates we take the difference between their votes and divide by the sum
of their votes. We then divide the sum of those percentages by the total number of unique
candidate pairs used in the calculation. The denominator is the total number of unique pairs
that can be made among the n candidates included, calculated as (n!/(2!(n-2)!). This procedure
yields an index, which we call K, which has characteristics that mirror those of Closeness.
When K is “small”, all candidates are clumped so closely together than they cannot
be easily distinguished from one another. When K is “large”, however, at least one candidate
can easily be distinguished from the others and is therefore outside the clump. When K is
averaged across all candidate pairs, a single candidate who is either far ahead or far behind
the others rapidly inflates the value of K. One “outlier” adds a large percentage difference for
each of the other candidates to whom she is compared. Since we are interested in the clump
on the cusp straddling the M-line, we designed an iterative procedure, adding one candidate
at each step until K becomes “large”. We have no prior or theoretical expectations about the
value of K that should be taken as large enough to indicate that at least one candidate is
outside the clump. Therefore, we experimented with several values of K and found that a
cutoff value of 0.10 produced the best results. Whenever the value of K exceeds 0.10 we
declare it to be “large”. We further declare the candidate whose addition pushes K above 0.10
to be outside the clump and all the candidates included before that point to be on the cusp.
We begin by calculating K at the M-line, the difference in votes between the last
winner and the first runner-up divided by the sum of their votes:
K (2) =
(Vm − Vm + 1)
(Vm + Vm + 1)
The “2” in K(2) indicates the number of candidates included in the calculation. The subscripts
to V, the number of candidate votes, are set at m (the district magnitude) for the last winner
and m+1 for the first runner-up. If K(2) is greater than 0.10, we declare the district
non-competitive and code all winners as safe and all losers as token. If K(2) is less than 0.10,
however, the district is competitive and at least two candidates are on the cusp. We then add
one more candidate, the one closest in votes to the two already in the clump.
K(3) can take one of two forms depending upon which candidate is added to the
original two. The candidate who finishes just ahead of the last winner is subscripted as m-1
and the second runner-up is subscripted as m+2. Thus, if (Vm+1-Vm+2) < (Vm-1-Vm) the second
runner-up is closer to the first runner-up than the last winner is to the next-to-last winner
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and we add Vm+2 and calculate K across Vm, Vm+1 and Vm+2. K(3)m+21 is then calculated as:
K (3) m + 2
(Vm − Vm + 1) (Vm − Vm + 2) Vm + 1 − Vm + 2)
+
+
(Vm + Vm + 1) (Vm + Vm + 2) (Vm + 1 + Vm + 2)
=
3
If (Vm+1-Vm+2) > (Vm-1-Vm), however, the next-to-last winner is closer to the last winner than
the second runner-up is to the runner-up and we add Vm-1 and calculate K across Vm-1, Vm and
Vm+1 and K(3)m+1 is calculated as:
K (3) m +1
(Vm − 1 − Vm) (Vm − 1 − Vm + 1) Vm − Vm + 1)
+
+
(Vm − 1 + Vm ) (Vm − 1 + Vm + 1) (Vm + Vm + 1)
=
3
From K(3)m+2, which includes candidates m, m+1 and m+2, we calculate K(4) by
adding either candidate m-1 or candidate m+3, depending on whether (Vm-1-Vm) is greater or
less than (Vm+2-Vm+3). From K(3)m+1, which includes candidates m-1, m and m+1, we
calculate K(4) by adding either candidate m-2 or m+3, depending on whether (Vm-2-Vm-1) is
greater or less than (Vm+1-Vm+2). We continue adding candidates until the value of K(n)
exceeds 0.10.
Note that cusp candidates may be either winners or losers. In our three-member
district example given above, two districts might both have four cusp candidates but in one,
the cusp candidates are the first through the fourth while, in the other, the cusp candidates
are the third through the sixth candidates. Since both districts have four competitive
candidates we expect turnout to be the same, other things being equal, even though the first
district has no safe candidates but two token candidates while the latter district has no token
candidates but two safe candidates. We will have cause to distinguish between safe and token
candidates later in the analysis, but for present purposes we treat safe and token candidates
as equivalent and having no effect on competitiveness. The number of cusp candidates thus
ranges from zero to the total number of candidates.
In Table 1 we present some examples of how these calculations work out in practice.
Turnout is highest in the 1976 election, which is both the closest and the election with the
highest number of cusp candidates. Our calculations indicate that voters would have had a
hard time distinguishing among the electoral prospects of all six candidates. Turnout is
1
The subscript on K identifies the last candidate included in the calculation.
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lowest in the 1983 election, which has the highest value of Closeness and the fewest cusp
candidates. Only the two candidates straddling the M-line are in doubt, the two candidates
above them being safe and the two candidates below them being token. The 1972 election
falls between the two other examples on turnout, Closeness and Cusp Candidates. This is a
classic case of the M+1 equilibrium with the top four candidates fighting for the three
available seats. In practice, it works out that K exceeds 0.10 when the last candidate added is
separated from her neighbor by around 10,000 votes.
[Table 1 about here]
Analysis
Using the procedure described above, we classified all candidates as safe, cusp, or token and
counted the number of cusp candidates per district for all Japanese elections to the House of
Representatives between 1947 and 1993 (n=2,219). We found that 26 percent of the districts
had no cusp candidates and could thus be considered noncompetitive. More importantly, we
find only 123 districts (5.5 percent of the total, 7.5 percent of all competitive districts) in
which two and only two candidates were on the cusp. In 1,518 (68.4%) districts there were
more than two cusp candidates.2 In these districts, we expect the number of cusp candidates
to incorporate more information on the competitiveness of the district than does Closeness. It
is also worth noting that the distribution of Cusp Candidates is bimodal, with one mode at
zero and the other at M+1. Districts tend to be either non-competitive or “fully” competitive
with every candidate from the top to the runner-up on the cusp between winning and losing.
Both Closeness and the number of competitive candidates are measures of
competition so it comes as no surprise that they are correlated (correlation = -0.635). However,
the correlation is much smaller (-0.196) when calculated for competitive districts only.
Closeness and Cusp Candidates tend to make similar distinctions between competitive and
non-competitive districts, but come to very different estimates of the intensity of competition
in competitive districts. The question is which variable does the better job of measuring
competitiveness. We therefore decided to analyze the effect of the two variables on turnout.
We measured turnout as the number of valid votes divided by the total number of eligible
voters. Neither measure of competitiveness is particularly highly correlated with turnout in a
bivariate analysis so we include a series of control variables that are known to affect turnout.
2
The most common competitive district involves four to six cusp candidates and there are a few
cases with nine or ten candidates who are unsure of their (re-)election chances and should thus be
campaigning hard.
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First, we include measures of urbanization. Turnout in Japan is significantly higher
in rural than in urban areas (Cox, Rosenbluth and Thies 1998; Horiuchi 2005). We begin by
using the only urban-rural measure available for the whole postwar period, a four-point scale
developed by Masumi Ishikawa (Ishikawa and Hirose 1989). For the period since 1958,
however, we have the ideal measure of urbanization, the percentage of the population living
in “densely inhabited districts” as defined by the census (Horiuchi and Kohno 2004). The
second most important variable is campaign expenditures (Cox, Rosenbluth and Thies 1998).
Fortunately, these scholars have generously shared their data with us and we have updated
it to include the 1993 elections. Unfortunately, however, these data are available only since
1967. We use the total expenditures of all candidates in the district divided by the limit for
any single candidate. The legal limits are set by law and are based on estimates of the cost of
campaigning in the district.
We run each model three times, first for the whole postwar period, 1947-1993, second
for the period in which the ideal measure urban-rural becomes available, 1958-1993, and
third for the period since expenditure data has become available, 1967-1993. The earlier
models have the advantage of larger n’s while the latter models have the advantage of better
control variables.
Second, we also control for change in the number of eligible voters. Japan
experienced a great deal of population movement during these years and one consistent
finding of research on turnout is that the longer a person has lived in the district the more
likely she is to vote (see, for example, Geys 2006:644). Since we expect population growth to
lower turnout but have no expectations about a drop in population, all values less than zero
were reset to zero. Third, since 1967 Japan has had a religious party, Koumei, with an
enthusiastic campaign organization and loyal support base (Hrebenar1986). When Koumei
runs a candidate in a district their campaign reliably increases turnout and when they stop
running in a district turnout drops. We therefore coded a Koumei variable equal to 1 when
the Koumei enters the district, -1 when Koumei exits the district and zero otherwise. Finally,
turnout has been falling in Japan as in many other industrial democracies so we included a
trend variable that is simply a counter running from 1 for 1947 to 19 for 1993.
The results presented in Table 2 indicate that Cusp Candidates does indeed
outperform Closeness in explaining turnout levels. First, each of the control variables works
as expected. In all models, turnout is lower in urban areas and lower in those districts which
have experienced population growth since the last election. Turnout goes up when the
Koumei enters a district and declines when Koumei exits. Campaign expenditures reliably
raise turnout. Only the trend variable fails to reach significance in some models. In all other
cases, the control variables are strong and reliable.
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[Table 2 about here]
Looking first at Model 1, we see that Closeness performs as expected in each subset
of the data. In Model 2 we add the number of cusp candidates and find that Closeness loses a
great deal of its explanatory power because the two variables are correlated. Finally, in Model
3 we replace Closeness with Cusp Candidates. In every case, Cusp Candidates alone explains
slightly less variance than Closeness did alone but the overall fit of Model 3, as measured by
the F statistic, is substantially higher for Model 3 than for Model 1. We conclude that the
number of candidates on the cusp explains most of the variance explained by Closeness and
that the model based on Cusp Candidates is better specified than the model based on
Closeness. That said, however, the explanatory power of both models is derived primarily
from the distinction between non-competitive and competitive elections. We therefore decided
to look at non-competitive and competitive elections separately.
Turnout in Non-Competitive Districts
One puzzling finding from above is that Closeness continues to have some effect even after
entering the number of cusp candidates in each of the models. If our theory is correct, voters
in non-competitive districts should not care whether a token candidate has a 0.01 probability
of being elected or a 0.001 probability. Neither should a token candidate spend much effort
trying to raise his probability of getting elected from 0.001 to 0.01. For all practical purposes,
token candidates are going to lose and everyone knows that they are going to lose. Any
further distinctions should have no effect on turnout but in fact they do. We address this
problem by analyzing non-competitive districts, those with no cusp candidates. The results
are presented in Table 3. We find that Closeness continues to have a powerful effect on
turnout even though, by our measure, all candidates are either safe or token and voting is
extremely unlikely to have any effect on the outcome. Only when expenditures are added to
the equation does the effect of Closeness decline.
[Table 3 about here]
In an analysis of turnout in the 1996 general election, Reed (2003:157-159) found
that districts in which the only challenger came from the Japan Communist Party (JCP) had
significantly lower turnout than expected on the basis of Closeness. In addition, he found that
in those races where the LDP’s only challenger was the JCP, the number of votes for both
parties rose (Reed 2003:154). It appears that given the choice between a safe LDP incumbent
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and a lone JCP challenger, some voters who would have voted for another opposition party if
that choice had been available are unwilling to vote at all. Some people who wish to vote
against the LDP are willing to vote for any challenger including a Communist candidate, but
some are unwilling to go that far and thus turnout drops. We decided to test the hypothesis
that voters distinguish between token Communist candidates and other token candidates by
including a dummy variable, JCP Only, that takes the value of 1 when the only token
candidate in the district is a Communist. When JCP Only is added to the model that includes
expenditures, it proves highly significant and Closeness loses much of its explanatory power.
When both expenditures and JCP Only are included in the model, Closeness is driven into
insignificance.
We conclude that voters do not distinguish among token candidates on the basis of
differences in the minute probabilities of them being elected. All token candidates are, quite
appropriately, treated as sure losers. On the other hand, voters do distinguish among token
candidates on the basis of their party affiliation. Token Communist candidates turn more
voters away from the polls than token candidates from other parties.
Turnout in Competitive Districts
After analyzing turnout in non-competitive districts, we took the obvious next step and
analyzed turnout in competitive districts. Within competitive districts, Closeness never had a
significant impact on turnout. Once a district has at least two candidates on the cusp between
winning and losing, Closeness no longer counts. The Cusp Candidates variable performed
better but was still not very impressive (results not shown but available from the authors on
request). The key to understanding turnout in competitive districts turns out to be
differential voter reactions to the mobilization efforts by type of candidates.
Before moving on, we should note that the JCP Only variable had no effect in
competitive districts. JCP candidates who are either safe or on the cusp are treated like any
other safe or cusp candidate. Only token JCP candidates are treated differently from other
token candidates.
Two literatures lead us to expect that expenditures by challengers might have
greater effect on turnout than expenditures by incumbents. First, a great deal of research has
confirmed that challenger expenditures have a greater effect on the challengers’ votes than
incumbent expenditures have on the incumbents’ votes (Jacobson 1978; Kenny and
McBurnett 1994; Jacobson 2006; Moon 2006). Greater challenger spending in U.S.
Congressional elections tends to produce more competitive races and we know that more
competitive races tend to increase turnout. Second, challenger expenditures also have a
greater effect on voter interest and knowledge than do incumbent expenditures (Coleman and
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Manna 2000). Both interest and knowledge are associated with higher turnout. Both sets of
findings lead us to expect challenger expenditures to have a greater effect on turnout than
incumbent expenditures.
We hypothesize that the primary causal mechanism linking challengers’
expenditures and turnout is information (Horiuchi, Imai and Taniguichi 2005). Incumbents
are well known and their advertising expenditures face diminishing returns in increasing
voter information on incumbents. Challengers, on the other hand, are usually not well known
and any expenditure on advertising can significantly increase voter information. Challenger
spending should thus have a greater effect on turnout than incumbent spending.
Although the differential effect of incumbent and challenger spending on the
candidate’s votes and on voter interest and knowledge is suggestive, our main interest lies
with the differential effect of expenditures by safe, cusp and token candidates on turnout. We
expect spending by candidates on the cusp to have a greater effect on turnout than spending
by either safe or token candidates. The intuition is simply that elections in which more
money is spent by candidates on the cusp between winning and losing are more competitive
than elections in which more money is spent either by safe or by token candidates. Several
mechanisms probably come into play, but the simplest is that when a cusp candidate tells her
supporters that “we can win if we try hard”, she is telling the truth and her supporters know
it.
We summed expenditures by each category: by incumbents and challengers, and
then by safe, cusp and token candidates dividing by the legal limit for expenditures in the
district as above.. The results are presented in Table 4.
[Table 4 about here]
We find first, in Model 1, that challenger expenditures do indeed have a greater
effect on turnout than do incumbent expenditures. Increasing the total expenditure of
incumbent candidates by one per cent of the legal limit raises turnout by 0.7 percent while a
similar increase by in challenger expenditures raises it by almost 0.9 per cent. Turning to
Model 2, however, we find bigger differences. Most notably, expenditures by safe candidates
has no significant effect on turnout, a finding that mirrors Moon’s finding that expenditures
by incumbent candidates have no effect on their vote. Expenditures by both cusp and token
candidates, however, raise turnout by about one percentage point. This is true whether the
cusp candidate is an incumbent or a challenger. Spending by token candidates raises turnout
by about the same amount as spending by cusp candidates but has less overall impact on
turnout for three reasons. First, as one might expect, token candidates spend less than either
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incumbents or cusp candidates. Whereas incumbents spend a bit over 60 per cent of the limit
and cusp candidates spend a bit less than that, token candidates average only 44 per cent of
the limit. Second, there are many fewer token (less than 2,000) than cusp candidates (over
4,000). Finally, spending by cusp candidates has a more reliable effect on turnout than does
spending by token candidates, reflected in the much higher standard error for the latter.
Conclusions
Our most important finding is that a measure of the number of candidates on the cusp
between winning and losing explains turnout better than the traditional measure, Closeness.
Closeness distinguishes between competitive and non-competitive districts quite well but
fails to explain much variance in turnout within either category.
Based on this finding, we make the following two claims. First, we argue that a
categorical logic of clumping candidates into groups captures the limits of voter perceptions
better than does a continuous logic of calculating probabilities. We argue this point even
while recognizing the obvious fact that some candidates will always be on the borderline
between the safe and cusp categories or between the cusp and token categories. A few errors
of categorization, either because some voters are more informed and perceptive than others
or because of imperfect statistical techniques do not obviate the advantage of a categorical
approach. We are aware that this is likely to be controversial but believe that our results
justify making the claim. Second, we argue that the K calculation introduced in this paper is
a very good way of categorizing candidates. We would not be too surprised if someone came
up with improvements on our measures but expect K to hold its ground in the competition
and prove the basis for whatever measure emerges in the end as standard practice.
Our second finding is that Japanese voters do not distinguish among token
candidates on the basis of their electoral viability but rather on whether their party
affiliation is Communist or not. They further distinguish among token candidates on the
basis of the amount of money they spend on their campaigns.
Our third finding is that the effect of campaign expenditures on turnout varies by
the type of candidate doing the spending. Mobilization efforts by safe candidates have no
significant effect on turnout, while spending by either cusp or token candidates has a great
effect.
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References
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Quality of Democracy” The Journal of Politics 62:757-789.
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U.S. House Elections” American Political Science Review 83:217-232.
Cox, Gary W. Frances M. Rosenbluth, and Michael F. Thies (April 1998) “Mobilization, Social
Networks, and Turnout: Evidence from Japan” World Politics 50:447－74.
Geys, Benny (2006) “Explaining Voter Turnout: A Review of Aggregate-Level Research”
Electoral Studies 25:637-663.
Grofman, Bernard (1995) “Is Turnout the Paradox that Ate Rational Choice Theory?” in
Bernard Grofman (ed.) Information, Participation and Choice (Ann Arbor: The University of
Michigan Press).
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(London: RoutledgeCurzon).
Horiuchi, Yusaku, Kosuke Imai and Naoko Taniguichi (2005) “Estimating the Causal Effects
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The Structure of Long-Term Dominance) (Tokyo: Iwanami Shoten).
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Jacobsen, Gary (1978) “The Effects of Campaign Spending in Congressional Elections”
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Studies 25:195-226.
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Table 1: Some Examples
The 1972 Election
Candidate Party Vote
Tanabe
JSP
70,285 W
Kubota
LDP 66,095 W
Hanyuda
LDP 62,956 W
Kumagaya LDP 53,870 L
Inagaki
JCP 42,145 L
Fukushima LDI
13,274 L
Turnout
Closeness
Cusp Candidates
78.8%
9,086
4
from Gunma 1st District
The 1976 Election
Candidate Party Vote
Tanabe
JSP
64,692 W
Kubota
LDP
64,243 W
Hanyuda LDP
61,354 W
Kaneko
LDI
53,397 L
Kumagaya LDP
53,103 L
Inagaki
JCP
45,504 L
Turnout
Closeness
Cusp Candidates
81.7%
7,957
6
The 1983 Election
Candidate Party Vote
Omi
LDI
77,381
Tanabe
JSP
76,205
Kumagaya LDP
61,658
Kubota
LDP
50,758
Inagaki
JCP
40,862
Sugano
LDP
24,047
Turnout
Closeness
Cusp Candidates
Shaded candidates are on those on the cusp between winning and losing.
72.7%
10,900
2
W
W
W
L
L
L
16
Table 2: Competitiveness and Turnout
Model 1
A.1947-1993
Urban-Rural
-4.58 (0.138)**
Electorate Growth
-0.04 (0.003)**
Koumei Entry Exit
1.91 (0.47)**
Trend
-0.18 (0.02)**
Closeness
-0.12(0.00)**
Closeness Squared
0.00(0.00)
Cusp Candidates
-Constant
F
R-square
n
88.6 (0.44)**
334.1
0.492
2076
Model 1
B. 1958-1993
Percent DID
-22.6 (0.53)**
Electorate Growth
-0.03 (.003)**
Koumei Entry Exit
1.64 (0.40)**
Trend
1.033 (0.141)**
Closeness
-0.14 (0.003)**
Closeness Squared
0.00(0.00)
Cusp Candidates
--
Model 2
-4.61 (0.13)**
-0.04 (0.003)**
1.88 (0.47)**
-0.19 (0.02)**
-0.05 (0.037)
0.00(0.00)
0.23 (0.08)*
Model3
-4.641 (0.138)**
-0.0437 (0.003)**
1.747 (0.472)**
-0.203 (0.026)**
--0.334 (0.05)**
87.6 (0.58)**
288.5
0.494
2076
87.058 (0.475)**
399.1
0.490
2076
Model 2
-22.7 (0.53)**
-0.03 (0.003)**
1.63 (0.40)**
0.042 (0.036)
-0.09 (0.003)*
0.00(0.00)
0.20 (0.08)*
Model3
-22.7 (0.534)**
-0.03 (0.003)**
1.72 (0.40)**
0.023 (0.036)
-0.486 (0.05)**
Constant
F
R-square
n
85.1 (0.47)**
458.0
0.632
1607
84.1 (0.62)**
394.84
0.633
1607
82.638 (0.493)**
539.42
0.627
1607
C. 1967-1993
Percent DID
Electorate Growth
Koumei Entry Exit
Expenditures
Trend
Closeness
Closeness Squared
Cusp Candidates
Model 1
-23.1 (0.57)**
-0.03 (.003)**
1.54 (0.40)**
0.99 (0.13)**
0.13 (0.05)
-0.13 (0.27)**
0.00(0.00)
--
Model 2
-23.1(0.57)**
-0.03 (.004)**
1.55 (0.40)**
0.94(0.14)**
0.13 (0.05)
-0.10 (0.03)*
0.00(0.00)
0.12 (0.09)
Model3
-23.2 (.57)**
-0.03 (.004)**
1.61 (0.41)**
0.95 (0.14)
0.12 (0.05)
0.39(0.06)**
Constant
80.2 (0.94)**
79.8(0.99)**
78.2(0.90)**
F
323.2
283.1
371.7
R-square
0.645
0.645
0.641
n
1253
1253
1253
Note: the parameters for Closeness have been multiplied by 1000.
* = significant at the .01 level. ** = significant at the .001 level.
17
Table 3: Turnout in Noncompetitive Districts
A.1947-1993
Urban-Rural
Electorate Growth
Koumei Entry Exit
Trend
Closeness
Closeness Squared
JCP Only
Model 1
-4.23 (0.27)**
-0.04 (0.008)**
2.61 (0.90)*
-0.20(0.06)**
-0.24 (0.06)**
0.00(0.00)
--
Model 2
-4.34 (0.27)**
-0.05(0.008)**
2.35 (0.904)*
-0.219 (0.059)**
-0.19 (0.06)*
0.00(0.00)
-2.60(0.89)*
89.6(1.09)**
80.37
0.478
532
87.46 (1.08)**
71.07
0.487
532
B. 1958-1993
Percent DID
Electorate Growth
Koumei Entry Exit
Trend
Closeness
Closeness Squared
JCP Only
Model 1
-20.7 (1.14)**
-0.02 (.009)*
2.56 (0.81)*
-0.01 (0.07)
-0.28 (0.06)**
0.00(0.00)*
--
Model 2
-21.6 (1.14)**
-0.03 (0.009)**
2.26 (0.80)*
0.015 (0.07)
-0.20 (0.06) *
0.00(0.00)
-3.41 (0.08)**
Constant
F
R-square
n
86.3 (1.17)**
92.39
0.562
438
85.7 (1.16)**
84.64
0.580
438
C. 1967-1993
Percent DID
Electorate Growth
Koumei Entry Exit
Expenditures
Trend
Closeness
Closeness Squared
JCP Only
Model 1
-22.3 (1.21)**
-0.03 (.009)**
2.85 (0.78)**
1.47 (0.30)**
0.24 (0.10)
-.19 (0.06)*
0.00(0.00)*
--
Model 2
-22.9 (1.22)**
-0.03 (.009)**
2.70 (0.78)**
1.29 (0.31)**
0.19 (0.104)
-0.13 (0.06)
0.00(0.00)
-2.39 (0.90)*
Constant
F
R-square
n
Constant
77.2 (2.07)**
77.96 (2.07)**
F
68.12
61.55
R-square
0.593
0.601
n
335
335
Note: the parameters for Closeness have been multiplied by 1000.
* = significant at the .01 level. ** = significant at the .001 level.
18
Table 4: The Differential Effectof Campaign
Expenditures on Turnout in Competitive Districts
C. 1967-1993
Percent DID
Electorate Growth
Koumei Entry Exit
Trend
Incumbent Exp
Challenger Exp
Safe Exp
Cusp Exp
Token Exp
Model 1
-23.8 (0.65)**
-0.03 (.004)**
0.96 (0.482)
0.04 (0.061)
0.69 (0.21)**
0.88 (0.19)**
----
Model 2
-23.7 (0.65)**
-0.031 (.004)**
1.043 (0.48)*
0.05 (0.48)
--0.62 (0.26)
1.00 (0.18)**
1.02 (0.33)*
Constant
82.16 (1.11)**
81.28 (1.12)**
F
305.82
267.43
R-square
0.668
0.672
n
918
918
* = significant at the .01 level. ** = significant at the .001 level.