Incumbency Effects and the Strength of Party Preferences:
Evidence from Multiparty Elections in the United Kingdom

June 1, 2016

Abstract
Previous researchers have speculated that incumbency effects are larger when voters have weaker
partisan preferences, but evidence for this relationship is surprisingly weak. We offer a fresh
look at the question by examining the U.K.’s multiparty system. In general, the electoral valueof incumbency should depend on the proportion of voters who are nearly indifferent between theparties competing for incumbency; in a multiparty system, that proportion may differ acrossconstituencies depending on which parties are locally competitive. After first showing that
U.K. voters in recent decades have stronger preferences between Conservatives and Labour thanbetween Conservatives and Liberals, we show that incumbency effects are larger in close contests
between Conservatives and Liberals than in close contests between Conservatives and Labour.
By documenting how partisanship influences incumbency effects, our analysis shows that thecomparative study of incumbency effects offers broader insights into electoral accountability
across political systems.

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1

Introduction

The study of incumbency effects started with questions about the re-election rate of members of the
U.S. Congress1 and developed into a huge literature in American politics examining the trajectoryand source of incumbents’ electoral advantages.2 In recent years, researchers have begun to examine
incumbency effects outside the U.S. (see e.g. Hainmueller and Kern 2008; Uppal 2009; Kendall andRekkas 2012; Ariga 2015). While this comparative literature builds on questions about incumbent
insulation that motivated the early U.S. studies, it also has the potential to yield insights into a
broader set of questions about how the behavior of politicians and voters varies with the nature ofpolitical campaigns, legislative institutions, and party systems.
One explanation for variation in incumbency effects is partisanship, by which we mean thestrength of voters’ preferences between competing parties. Scholars studying American elections
have suggested that the rise of incumbency effects in the post-World War II U.S. might be explainedby the weakening of ties between voters and parties (Mayhew 1974; Krehbiel and Wright 1983;
Ansolabehere et al. 2006); Jacobson (2015) attributed a recent drop in incumbency advantage torising partisanship. Similarly, a number of researchers argue that incumbency effects are weaker in
the U.K. than in the U.S. because British voters have stronger partisan preferences (Cain, Ferejohn
and Fiorina 1984; Gaines 1998; Katz and King 1999).
Although variation in the strength of party preferences seems to make sense of important variation in incumbency effects in the U.S. and between the U.S. and U.K., the evidence for a relationshipbetween partisanship and incumbency effects (whether in these cases or elsewhere) remains surprisingly weak. There are of course many differences between elections in the U.S. and the U.K. otherthan the strength of party preferences that could explain why incumbency effects are larger in the
U.S. For example, campaign spending in British parliamentary elections is tightly restricted at theconstituency level (and has been since the late 19th century), whereas spending in U.S. federal
campaigns has never been restricted; to the extent that the incumbency advantage in the U.S. results from campaign spending (Fouirnaies and Hall 2014), this difference in regulation alone could
1 See e.g. Erikson (1971); Mayhew (1974); Fiorina (1977); Ferejohn (1977).
2 See e.g. Krehbiel and Wright (1983); Gelman and King (1990); Cox and Morgenstern (1993);

Levitt and Wolfram (1997); Ansolabehere, Snyder and Stewart (2000); Lee (2008)2

explain the difference in levels. The evidence for partisanship as an explanation for changes in incumbency effects in the U.S. is more convincing but remains incomplete. For example, Krehbiel andWright (1983, p. 140) examine data on party identification and vote choice in the U.S., concludingthat “partisan dealignment accounts for little of the increase in incumbency voting”; Ansolabehere
et al. (2006) examine a change in the ballot format in Minnesota and conclude that incumbency
effects did not drop when voters were given stronger party cues (see also Ansolabehere and Snyder
2002). Ansolabehere et al. (2007) find evidence of a larger (and earlier) incumbency advantage
in U.S. primaries than in general elections; this pattern fits the partisanship view but could also
be due to differences between the primary electorate and the general electorate.3 Jacobson (2015)shows that the growth and decline of incumbency advantage in the U.S. is mirrored by changes inparty loyalty and split-ticket voting over the same period, but of course many other things changed
over the same period (e.g. financing and campaigning techniques, popular support for Congress)
that could be seen as alternative explanations. In general, the difficulty researchers face in empirically linking partisanship and incumbency effects is that most variation in the strength of partisan
preferences (e.g. across countries or over time within a country) coincides with variation in otherrelevant factors that potentially confound the analysis.
To address this problem, we study variation in incumbency effects within the U.K.’s multiparty
system, where the strength of the relevant partisan preferences varies depending on the identityof the top two parties while many other contextual factors remain constant. The theoretical basis
for a relationship between incumbency effects and partisanship is fairly straightforward: if incumbency status makes a candidate more attractive to voters (for whatever reason), this change inattractiveness will produce greater electoral benefits when a larger proportion of the electorate isrelatively indifferent between the incumbent and her competitors on partisan grounds. The multiparty U.K. system offers an attractive setting to test this theory because in some places incumbencychanges hands between the Conservatives and Labour, while in others it changes hands between
3 For example, it seems likely that the primary electorate is more aware of the incumbent’s

activities in office. Ansolabehere et al. (2007) also provide intriguing evidence of larger primary
incumbency effects in states with weaker intra-party factions, though they caution that this patternis based on a small number of states.

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the Conservatives and Liberals;4 we show using survey data that more voters are nearly indifferent
between the Conservatives and the Liberals than between the Conservatives and Labour, which
implies that the electoral implications of shifts in incumbency between Conservative and Liberals
should be larger than the electoral implications of a shift between Conservatives and Labour. In
line with the theory and this survey evidence, we find that incumbency effects are indeed larger
in Conservative-Liberal contests than in Conservative-Labour contests, and that this difference isrobust to controlling for other differences between the two types of contests. Our analysis of asingle political system thus produces unusually clear evidence that incumbency effects are larger
when party preferences are weaker.
Of course, one could offer alternative explanations for the variation we find in incumbency effects across partisan matchups. Notably, Gaines (1998) and Katz and King (1999) both assert that
Liberals experience larger incumbency effects in the U.K. because of strategic voting: briefly, their
explanation is that Liberal incumbency signals to Liberal supporters that the Liberal candidate islocally viable, which discourages Liberal supporters from strategically voting Labour or Conservative. Another alternative explanation is that there might be something different about Liberal
MPs that explains why incumbency is more consequential in Conservative-Liberal contests. We
test both of these alternative explanations with survey data and fail to find evidence for either. We
recognize, of course, that it is impossible to completely rule out all possible alternative explanations
for the patterns we see; we note, however, that some of these other explanations (such as the ideathat Liberals tend to be better at establishing connections with their constituencies) could instead
be seen as further results of the variation in partisanship we document.
Our results have several implications for the comparative study of elections. Most directly,
they provide evidence that incumbency effects are relatively small in the United Kingdom in part
because of the strength of voters’ partisan preferences: if partisan preferences in all constituencies
had been at the level of constituencies where Conservatives and Liberals vie for a seat, the effect of
4 We use the term “Liberals” to refer to Liberals, Liberal Democrats, Social Democrats, andcandidates running under the SDP-Liberal Alliance. Incumbency also changes hands in a smaller
number of cases between Labour and the Liberals; we focus on Conservative pairs both for simplicity
and for statistical power.

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incumbency on vote share in the post-World War II period would have been about twice as large
on average and considerably closer to U.S. levels. This insight may also be useful in explaining why
incumbency effects have risen (and, perhaps, fallen) in the U.S. and more broadly why incumbency
effects vary across countries and electoral systems. In light of our analysis, the comparative studyof incumbency effects is not just about what incumbents in various systems do to protect theirpositions; rather, it can shed light on broader questions about how electoral accountability andpartisan preferences vary both across and within political systems, as we explain further in the
conclusion.

2

Incumbency effects and party preferences in multiparty systems

In this section we clarify why incumbency effects might be expected to vary across party pairs ina multiparty system, emphasizing the strength of partisan preferences. Like much of the recent
literature since Lee (2008), our analysis of incumbency effects asks how a party’s performance ina constituency in a given election is affected by whether it won or lost the previous election in
the constituency, conditional on the previous election being close. For example, supposing theConservatives won in a constituency at time t − 1, how would the Conservatives’ result in that
constituency at time t have been different if instead the Conservatives had lost at time t − 1? The
difference between these two scenarios is the party incumbency effect for the Conservatives. As
noted by Lee (2008) and discussed further by Erikson and Titiunik (2015) and Fowler and Hall(2014), earlier work on U.S. elections focused on different estimands, including the benefit for anindividual of running as an incumbent (Erikson 1971) and the benefit for a party of fielding theincumbent candidate (Gelman and King 1990). The theoretical analysis and predictions of thispaper would apply to any of these approaches; we focus on the party incumbency effect (which wewill refer to simply as the incumbency effect in the remainder of the paper) because it has been thedominant approach in recent empirical research, including as the basis for estimates of individualincumbency effects (e.g. Erikson and Titiunik 2015; Fowler 2014).
We make two key assumptions about voter preferences and the role of incumbency in votechoice. First, we assume that voters care about two things when it comes to candidates for office:their party and their personal qualities, which we will refer to as “valence”. If a voter prefers
5party A over party B, she will vote for party A’s candidate if all candidates have the same valence,but she might vote for party B’s candidate if she perceives that candidate to be more capable orhard-working. Second, we assume that voters perceive incumbents to have higher valence than the
average candidate; this might be because voters value incumbents’ experience in office, or because
ineffective incumbents tend to retire, or for some other reason.5
Given these assumptions, how do incumbency effects depend on the strength of voters’ partisan
preferences? Consider first a system involving only two parties (say, Conservatives and Labour).
It follows from the assumptions stated in the previous paragraph that the magnitude of the incumbency effect will depend on two key factors: first, the difference in average valence between
incumbents and other candidates; second, the proportion of voters who are nearly indifferent between the Conservatives and Labour, such that a change in incumbency will change their preference
ordering. If the Conservatives won the previous election (and thus they are the incumbents), they
subsequently receive the support of all voters who prefer the Conservatives to Labour plus those
voters who narrowly prefer Labour but are swayed by incumbency; if the Conservatives lost theprevious election (and thus Labour are the incumbents), the Conservatives receive the support ofall voters who prefer the Conservatives to Labour except those voters who narrowly prefer theConservatives but are swayed by incumbency. Thus the incumbency effect for the Conservatives
depends on the proportion of voters who are nearly indifferent between the two parties, such thatthey vote for whichever candidate is from the incumbent party.6
The relationship between incumbency effects and partisan preferences becomes more complicated when we consider systems with more than two parties, such as the UK. The key featureof multiparty competition that we leverage in this paper is that the value of incumbency may
differ depending on what pair of parties is vying for incumbency: in our case, the electoral value
to the Conservatives of defeating a Liberal opponent may differ from the electoral value to theConservatives of defeating a Labour opponent. We define two distinct incumbency effects: the
5 All of our arguments would work in reverse if incumbency was on average a valence disadvan-

tage.
6 Note that the incumbency effect for Labour will be the same: assuming just two parties, one
party’s loss is the other’s gain and thus the effect is symmetric.

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Conservative-Liberal incumbency effect is the effect on Conservative electoral outcomes of the Conservatives having won the previous election as opposed to the Liberals; the Conservative-Labour
incumbency effect is equivalently defined for the Conservatives and Labour. The question we ask
is how these two effects differ in magnitude and how this depends on partisan preferences. (Tobe clear, the same comparison could be made focusing on Labour or the Liberals instead of theConservatives, though as we will see the comparison we have chosen is the one we can best test in
the UK setting.)
In order to make progress on how incumbency affects voting outcomes in elections with morethan two candidates, we must make some assumptions about how voters decide on voting strategies.
We consider two possible extremes. In the pure strategic voting case, we assume that voters focus
entirely on the two parties vying for incumbency in a given setting; that is, when we are working
out the Conservative-Liberal incumbency effect, we assume that voters ignore Labour and vote
Conservative or Liberal depending on which candidate they prefer. Under this assumption, theConservative-Liberal incumbency effect can be analyzed as if it were a two-party system involving
only the Conservatives and Liberals; as in the two-party case above, what matters for incumbency
effects is what proportion of voters is nearly indifferent between the two relevant parties. Thus
assuming pure strategic voting, the Conservative-Liberal incumbency effect will be larger than theConservative-Labour incumbency effect if more voters are nearly indifferent between the Conservatives and the Liberals on partisan grounds than are indifferent between the Conservatives andLabour on partisan grounds.
The other extreme is the pure sincere voting case, in which voters simply vote for the candidate
they like best. Under this assumption the Conservative-Liberal incumbency effect consists of (a)the proportion of voters who narrowly prefer the Conservatives over the Liberals, or vice versa, andplace Labour last, such that they vote Conservative or Liberal depending on who the incumbent
is, and (b) voters who narrowly prefer Labour over the Conservatives and place the Liberals last,such that they vote for a Conservative incumbent and otherwise Labour. A similar statement
can be made for the Conservative-Labour incumbency effect. If we denote by AB the proportionof voters who vote for narrowly prefer party A over party B (such that they would vote B if B
were the incumbent) and rank party C last, the Conservative-Liberal incumbency effect is ConLib

7

+ LibCon + LabCon, while the Conservative-Labour incumbency effect is ConLab + LabCon +LibCon; the difference between them is ConLib - ConLab. Thus under pure sincere voting theConservative-Liberal incumbency effect will be larger than the Conservative-Labour incumbency
effect if there are more voters who narrowly prefer the Conservatives over the Liberals and place
Labour last than there are voters who narrowly prefer the Conservatives over Labour and place the
Liberals last.

Summary of implications
Assuming that incumbency boosts candidate valence, the size of electoral incumbency effects will
depend on the strength of party preferences both in two-party settings and in multiparty settings.
In a multiparty setting we can consider different incumbency effects for each party pair (e.g. theeffect of the Conservatives being the incumbent as opposed to Labour); whether we assume thatvoting behavior is purely strategic or purely sincere (in the sense defined above), the relative
magnitude of these incumbency effects will depend on the proportion of voters who are nearly
indifferent between the two parties. Under strategic voting, the Conservative-Liberal incumbency
effect is larger than the Conservative-Labour incumbency effect if more voters are nearly indifferent
between the Conservatives and the Liberals than are nearly indifferent between the Conservatives
and Labour; under sincere voting, the former effect is larger than the latter effect if more voters
are nearly indifferent between the Conservatives and the Liberals and place Labour last than are
nearly indifferent between the Conservatives and Labour and place the Liberals last.

3

Party preferences and expectations about incumbency effects in
the UKIn this section we use survey data from the UK to show that voters in recent decades have hadstronger preferences between the Conservatives and Labour than between the Conservatives andthe Liberals. In recent general elections, the British Election Study (BES) has asked voters to givea 0-10 score to each of the major parties, with 0 indicating “strongly dislike” and 10 indicating“strongly like”. As a rough indication of the proportion of voters who are nearly indifferent between

8

two parties, we examine the proportion of voters whose scores for the two parties are within a given
amount; recognizing that voters may apply different implicit scales in assigning 0-10 scores toparties, we examine both the raw scores and normalized versions.
Figure 1 shows the basic patterns for the 2001, 2005, and 2010 BES data. The solid black
curve in the upper left plot indicates the (weighted) proportion of BES respondents who place theConservative and Labour parties within a given number of points on the 0-10 scale, where we vary
the gap from 0 to 10; the dashed black curve shows the equivalent values for the Conservativeand Liberal (Democrat) parties. (The gray curves will be explained shortly.) The plot tells us,
for example, that about 35% of respondents place the Conservative and Labour parties within
one point, compared to 45% for Conservative and Liberal; about 45% of respondents place theConservative and Labour parties within two points, compared to about 65% for Conservative andLiberal. This suggests that under the pure strategic voting assumption introduced above (i.e. voterschoose between the two parties vying for incumbency) the Conservative-Liberal incumbency effectwould be larger than the Conservative-Labour incumbency effect.
The top right plot of Figure 1 shows the same basic information with the extra condition thatthe two parties must be at the top of the respondent’s preference ordering. This plot tells us,
for example, that about 9% of respondents place the Conservative and Labour parties within two
points and above the Liberals, compared to about 19% who place the Conservative and Liberal
parties within two points and above Labour. This suggests that under the pure sincere voting
assumption introduced above (i.e. voters choose the candidate they like best) the ConservativeLiberal incumbency effect would be larger than the Conservative-Labour incumbency effect.
In the bottom plot of Figure 1, we present an alternative version in which we normalize each
respondent’s like-dislike scores such that the largest pairwise gap among the main three parties
for each respondent is 1.7 We then show the (weighted) proportion of respondents with a gap innormalized scores below a given value. The plot indicates that about half of respondents placed
the Conservatives and Liberals within half a point on the normalized scale, while only about 20%
7 Thus a respondent who gives scores of 2, 4, and 8 to the Conservatives, Labour, and Liberals

would have normalized scores of 0, 1/3, and 1, and a respondent who gives scores of 2, 3, and 4
would have normalized scores of 0, 1/2, and 1.

9Raw scores, party pairat top of preference ordering

0.2
0

2

4

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8

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Conservative−Liberal
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0.1

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Conservative−Labour

0.0

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Proportion w. party−pair difference
within gap at top of pref. order

Raw scores

0.0

Proportion w. party−pair difference within gap

Figure 1: Strength of party preferences by party pair, 2001-2010

100

Gap on 0−10 like/dislike scale

2

4

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Gap on 0−10 like/dislike scale

1.0
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Conservative−Liberal

Conservative−Labour

0.0

Proportion w. normalized
party−pair difference within gap

Normalized scores

0.0

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0.6

0.8

1.0

Gap on 0−1 normalized like/dislike scaleNote: The British Election Study asks respondents to rate each party on a 0-10 scale. In each plot
the black curves show the (weighted) proportion of all respondents who place each pair of parties
within a given interval, where the interval varies from 0 to the maximum possible value; the graycurves show the same information for respondents who live in constituencies where the given party
pair finished in the top two in the previous election. In the upper right plot we apply the extra
condition that the respondent ranks the other major party last. In the lower plot we normalize
each respondent’s scores such that the highest is 1 and the lowest is 0.
of respondents placed the Conservatives and Labour within the same margin. Because any gap
less than one indicates that a party pair was at the top of the respondent’s preference ordering,
this shows that whether we assume pure strategic voting or pure sincere voting (as defined in theprevious section), we should expect the Conservative-Liberal incumbency effect to be larger than10the Conservative-Labour incumbency effect.
The evidence presented so far in this section suggests that in the entire UK electorate the proportion of voters whose support for the Conservatives would depend on whether the Conservatives
or the Liberals hold a seat (the Conservative-Liberal incumbency effect) is larger than the proportion of voters whose support for the Conservatives would depend on whether the Conservatives orLabour hold a seat (the Conservative-Labour incumbency effect). An important complication toraise at this point is that we cannot credibly estimate these two incumbency effects for the entire
UK electorate or any other fixed set of voters: there are few if any constituencies in which we
can obtain a credible estimate of Conservative support under hypothetical Conservative incumbency, Labour incumbency, and Liberal incumbency. What we can do is focus on cases where
the Conservatives are in close competition with either Labour or the Liberals and use a regression
discontinuity design (Lee 2008) to estimate the incumbency effect separately for the ConservativeLabour cases and the Conservative-Liberal cases. Figure 2 shows the proportion of constituencies
in which a given party pair finished in the top two in the previous election since 1950.8 Early inthe postwar period, Labour and the Conservatives finished in the top two in the vast majority of
constituencies; over time, this proportion has dropped as the Liberals (a term we use inclusively,
as explained in footnote 4) regained some of the ground they lost earlier in the century. In particular, the Conservatives and the Liberals have been the top two parties in around 20% of races
we analyze since the mid-1970s. (The proportions look very similar if we consider only contests
where the previous election was close.) Our empirical analysis will use the Conservative-Liberalcases to estimate the Conservative-Liberal incumbency effect and the Conservative-Labour cases
to estimate the Conservative-Labour incumbency effect; extending the typical RDD, we will apply
statistical controls to allow for differences in the two types of cases (such as when they took place,
given the Conservative-Liberal contests tend to be more recent).
Given that we will be using different sets of cases to estimate the different incumbency effects,
it is worth looking at the party-pair preferences that are relevant to each type of battleground. The
8 Here as in the rest of the paper we omit cases where, due to boundary changes so significant

that the constituency’s name changed, we are unable to link a constituency to election results inthe previous election.

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1.0

Figure 2: Proportion of races according to the top two parties in the previous race
Other

0.4

0.6

Liberal−Conservative

Conservative−Labour

0.0

0.2

Share of races

0.8

Liberal−Labour

1950

1960

1970

1980

1990

2000

2010

Note: Figure indicates the proportion of races over time in which a given party pair finished in
the top two in the previous race. Each vertical dashed line indicates a general election. Races
are omitted when substantial boundary changes took place, such that the top two parties in theconstituency in the previous election cannot be determined.
gray curves in Figure 1 indicate the degree of indifference for a given party pair in constituencies
where that pair of parties finished in the top two in the previous election, i.e. where the incumbency effect for that pair will be estimated. In the top left plot, these gray curves are barely (if atall) distinguishable from the black curves, indicating that e.g. the intensity of preferences between
Labour and Conservative parties is similar in Labour-Conservative battlegrounds and in the entire electorate. The discrepancy is largest for the Conservative-Liberal pairing in the upper rightplot; not surprisingly, more voters place Labour last and are indifferent between the Conservatives
and Liberals in Conservative-Liberal battlegrounds than in Conservative-Labour battlegrounds,
which suggests that the Conservative-Liberal incumbency effect we find in Conservative-Liberal
battlegrounds will be larger than what we would hypothetically find in Conservative-Labour battlegrounds or for the electorate as a whole. There is a smaller discrepancy in the opposite direction
when we look at normalized scores in the bottom plot. The overall implication is that incumbency
effects in Conservative-Liberal contests should be larger than incumbency effects in ConservativeLabour contests; this is basically because of preference patterns that apply in the whole electorate,12

but the difference may be exacerbated due to differences in preferences across different types ofbattlegrounds.
Figure 3 shows that the same pattern extends back to the 1970s, when we first have BES party
like/dislike scores: the left plot compares the proportion nearly indifferent between the Conservatives and Liberals and the proportion nearly indifferent between the Conservatives and Labour
using raw BES scores, both when we require that the party pair is at the top of the respondent’s
scores (in gray) and when we do not (in black); the right plot shows the same comparison for thenormalized scores. (See notes under the table for details on how indifference is defined.)
We can point to two reasons why voters in the period we examine held stronger preferences
between the Conservatives and Labour than between the Conservatives and the Liberals. First,
the Liberals were not in government during this period; to the extent that voters’ party preferences
come from feelings toward the government, it is unsurprising that the Liberals would not elicit
strong feelings.9 Second, the Liberals occupied an ideological middle ground throughout this period. The survey data clearly shows this back to the late 1970s, when voters were evenly split about
whether the Liberal Party was ideologically closer to Labour or the Conservatives.10 To be clear,
the Liberals’ centrism does not in itself ensure that Labour and the Conservatives would evoke thestrongest party preferences: after all, a voter in the ideological center might be most indifferent
between Labour and the Conservatives, both of which she dislikes but for different reasons, whilestrongly preferring the Liberals to either. The pattern of party preferences we document is consistent with a view that the Liberals occupy the center and most voters are to the left or right ofcenter such that they have a clear preference between Labour and the Conservatives and put the
Liberals either first or second.
9 Relatedly, to a strategic voter who cares about whether Labour or the Conservatives wins moreseats in Parliament, a vote in a Labour-Conservative contest is twice as consequential as an equallyclose contest between either party and the Liberals.
10 In the 1979 BES, 40% of respondents put the Liberals closer to the Conservatives and an equal
number put them closer to Labour.

13Figure 3: Indifference over party pairs since 1974 based in British Election Study

●
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0.8

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Indifferent Con−Lab & Lib last
Indifferent Con−Lib & Lab last●

0.6

Indifferent Con−Lab
Indifferent Con−Lib

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Relatively indifferent Con−Lab
Relatively indifferent Con−Lib

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Normalized scores

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1.0

Raw scores

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0.0

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1975

1985

1995

2005

1975

Election year

1985

1995

2005

Election year

Note: In the left plot, in black we show the (weighted) proportion of respondents who are nearly
indifferent between a pair of parties based on BES like/dislike scores (where indifference means
placing within two points on the 0-10 scale used from 2001 and within one point on the five-point
scale used before that); in gray we add the requirement that the respondent must rank the otherparty below both parties in the pair. In the right plot we use a relative measure of indifference:each respondent’s like/dislike scores are normalized such that the highest is 1 and the lowest iszero; we show the (weighted) proportion for whom the given party pair is within half a point on
this scale.

14

4Incumbency effects by party matchup

We now turn to assessing the variation in incumbency effects across party matchups: for Conservative candidates, is the electoral benefit of defeating a Liberal opponent larger than the electoral
benefit of defeating a Labour opponent? As explained above, we estimate incumbency effects usinga regression discontinuity design (Lee 2008). The fundamental idea behind RDD approaches toincumbency effects is to study the effect of election outcomes at time t − 1 on election outcomesin the same constituency at time t, focusing on close elections to minimize the endogeneity oftime t − 1 electoral outcomes. We first estimate the Conservative-Liberal incumbency effect andConservative-Labour incumbency effect separately; to address differences between ConservativeLiberal and Conservative-Labour battlegrounds, we then extend the RDD to include interactions
with covariates.

Comparisons based on separate RDD estimates
The basic RDD result for the 1950-2010 period appears in Figures 4 and 5, which show the Conservative vote share (Figure 4) and the Conservative probability of winning (Figure 5) at time t asa function of the margin between the Conservatives and their best competitor at time t − 1.11 In
each figure, the left plot shows this relationship for cases where the Conservatives’ best competitor
was Labour, while the right plot shows this relationship for cases where the Conservatives’ bestcompetitor was the Liberals. That is, to the right of the vertical dashed line in all four plots, theConservatives won the seat at time t − 1; to the left of the vertical dashed line in the left plot ofboth Figures 4 and 5 Labour won the seat, while to the left of the vertical dashed line in the rightplot of both Figures 4 and 5 the Liberals won the seat. The black dots show the average outcome
for all cases in 1 percentage point bins of the Conservative margin (e.g. between 0 and 1%, between
1% and 2%, etc); the blue solid line shows the local linear regression a triangular bandwidth set at
11 Thus when the Conservative wins, the running variable is the difference in vote share between

the Conservative candidate and the second-place candidate; otherwise, it is the difference in voteshare between the winner and the Conservative candidate.

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Figure 4: Regression discontinuity design (RDD) plot: the effect of Conservative victory at timet − 1 on Conservative vote share at time t, 1950-2010

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50Conservative vs. Labour−15 −10

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−15 −10Conservative margin, t−1

−5

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Conservative margin, t−1

Note: Black dots show binned averages; blue curves show local linear regressions and point-wise
95% confidence intervals.
0.75 times the Calonico, Cattaneo and Titiunik (2014) (henceforth CCT) optimal bandwidth12 ; theblue dashed lines show the point-wise 95% confidence interval for the local linear regression. The
jump in the outcome at the threshold measures the incumbency advantage for the Conservatives:
the effect of narrow victory at time t − 1 on electoral success at time t.
It is clear from Figures 4 and 5 that, consistent with the evidence on preferences in the previous
section, the benefit of incumbency for the Conservatives was larger in the period 1950-2010 when
the primary opponent was a Liberal than when the primary opponent was from the Labour Party.
The binned means closest to the threshold in Figure 4 indicate that when the Conservatives won aclose race over either Labour or the Liberals, they won on average about 45% of the vote in the next
election; when they lost a close race to Labour, they won 43% in the next election whereas when
they lost a close race to the Liberals they won only about 38% in the next election. If outcomesin close losses provide a good measure of what would have happened if narrow victories had been
turned into close losses, then these numbers imply an incumbency advantage for the Conservatives
12 All tables showing analysis based on CCT bandwidths are reproduced in the Online Appendix

using IK bandwidths (Imbens and Kalyanaraman 2012); the conclusions never depend on the
bandwidth used.

16

Figure 5: RDD plot: the effect of Conservative victory at time t − 1 on Conservative victory attime t, 1950-2010

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Note: See notes to Figure 4.
of 2 percentage points in close races against Labour and up to 7 percentage points in close races
against the Liberals.
The difference between the Conservative-Labour incumbency effect and the Conservative-Liberal
incumbency effect is even larger when we look at the probability of Conservative victory at time
t in Figure 5. In that figure, the binned means closest to the threshold suggest an incumbency
advantage in close races against Labour of perhaps 10 percentage points (though the shape of theconditional expectation function implies that the true effect at the threshold is smaller), while theadvantage in close races against the Liberals is around 45 percentage points.
Figure 6 shows point estimates and confidence intervals for the RDD-based party incumbency
effect separately for each outcome (Conservative vote share in the left plot; Conservative winningprobability in the right plot) according to whether the close election involved the Conservatives andLabour or Conservatives and the Liberals. Note that these estimates improve on the comparisonof means on either side of the threshold both because they are based on the comparison of theconditional expectation function immediately above and below the threshold and because they
incorporate the bias correction of Calonico, Cattaneo and Titiunik (2014). For both outcomes,
the difference in the two incumbency effects is statistically significant. For the vote share-based
measure, the Z-statistic on the difference between the two incumbency effects is 2.03 (implying a17

Figure 6: Bias-corrected estimates of incumbency advantage, by party pair
Effect of Conservative incumbency on
Conservative vote share0

Effect of Conservative incumbency on
probability of Conservative victoryConservative−Labour

Conservative−Labour

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2

Conservative−Liberal

Conservative−Liberal

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4

6

8

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0.2

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0.8

Note: Point estimates incorporate CCT bias-correction; gray lines show both the conventional
95% confidence intervals (wider lines) and the robust confidence intervals (narrower lines).
two-sided p-value of .04) when we use conventional standard errors and 1.78 (implying a two-sided
p-value of .08) when we use the CCT robust confidence intervals. For the victory-based measure,the corresponding Z-statistics are 2.81 (.004) and 2.39 (.016).
In the Online Appendix we extend Figure 6 to examine the incumbency effect for all party
pairs, including the Labour-Liberal incumbency effect and the Liberal-Labour incumbency effect(i.e. the effect of victory in a Labour-vs.-Liberal contest on each party’s subsequent success). The
estimates are noisy for the Liberal/Labour pairs, but for the most part we find larger effects in any
pairing involving in the Liberals than in Conservative and Labour races.

Comparisons based on local linear regressions with interactions
Although the difference we have documented between the Conservative-Labour incumbency effectand the Conservative-Liberal incumbency effect is consistent with the theory and evidence presented
in the previous two sections, there are of course many possible reasons for this difference. For
example, it could be that incumbency effects are smaller in urban constituencies, and close elections
involving Conservative and Labour candidates are more common in urban places; it could be thatincumbency effects are larger in recent elections, and close elections involving Conservative andLiberal candidates are more common in recent elections. To address these possibilities we extend
the standard RDD approach. In particular, we begin with the local linear approach to RDD

18

estimation, which fits a model like
Yit = β0 + β1 ConMargini,t−1 + β2 ConWoni,t−1 + β3 ConMargini,t−1 × ConWoni,t−1+ it , (1)where Yit is the Conservatives’ electoral outcome (vote share or an indicator for victory) at time t ,ConMargini,t−1 is the margin between the Conservative and the Conservative’s strongest competitor
at time t − 1, and ConWoni,t−1 is an indicator that takes the value 1 if the Conservative’s margin
is positive at time t − 1 and 0 otherwise; the effect of incumbency conditional on a tied election
at time t − 1 is indicated by β2 . (The regression model uses a triangular kernel that places thelargest weight on observations where the margin at time t − 1 is zero, with the weights linearlydecreasing to zero where the absolute margin is equal to the chosen bandwidth; see Imbens andKalyanaraman (2012) and Calonico, Cattaneo and Titiunik (2014) on the use of triangular kernels
for RDD estimation.) We first extend this model by adding an indicator for the Conservative’s
opponent at time t − 1 being a Liberal and interacting it with each element of Equation 1:

Yit = β0 + β1 ConMargini,t−1 + β2 ConWoni,t−1 + β3 ConMargini,t−1 × ConWoni,t−1β4 LibOpponenti,t−1 + β5 LibOpponenti,t−1 × ConMargini,t−1 +
β6 LibOpponenti,t−1 × ConWoni,t−1 +β7 LibOpponenti,t−1 × ConMargini,t−1 × ConWoni,t−1 + it .


+

(2)

In this first extension of the model, the Conservative-Labour incumbency effect is measured byβ2 and the difference between the Conservative-Liberal incumbency effect and the ConservativeLabour incumbency effect is measured by β6 . We then extend the model further by also including

19

covariates Xit and their interaction with ConWoni,t−1 :
Yit = β0 + β1 ConMargini,t−1 + β2 ConWoni,t−1 + β3 ConMargini,t−1 × ConWoni,t−1β4 LibOpponenti,t−1 + β5 LibOpponenti,t−1 × ConMargini,t−1 +
β6 LibOpponenti,t−1 × ConWoni,t−1 +β7 LibOpponenti,t−1 × ConMargini,t−1 × ConWoni,t−1 +Xit γ + ConWoni,t−1 × Xit ψ + it .


+

(3)

In this second extension of the model, the effect of incumbency is also allowed to vary acrossvalues of Xit , e.g. over time or between urban and rural constituencies. Our question is whether
the difference between the Conservative-Liberal incumbency effect and the Conservative-Labour
incumbency effect, as measured by β6 , is robust to allowing the incumbency effect to vary withother attributes in Xit that might differ between the cases in which Conservatives have closeelections with Liberals and cases in which they have close elections with Labour.
Column 1 of Table 1 shows the baseline analysis of Equation 1. The top panel indicates thatwhen we estimate Equation 1 with Conservative vote share as the outcome, our estimate of β2 (thecoefficient on ConWinit ) is 1.911, indicating that conditional on a close election at time t − 1 theConservatives win almost 2 percentage points more in support at time t as a result of narrowly
winning the time t − 1 election as opposed to narrowly losing it. As indicated above the top panel,
the CCT bandwidth for the triangular kernel used in this regression is 16.34, meaning that cases
where the previous margin was above 16.34 percentage points are completely ignored and the weightassigned to the remaining case is linearly decreasing in the previous margin, with the largest weightgoing to essentially tied elections. (The total number of observations receiving positive weight isslightly over 4,000.) The bottom panel indicates that conditional on a close election at time t − 1,a narrow Conservative win increases the probability of a Conservative win at time t by .17; inthis case the bandwidth chosen is about 10 percentage points, resulting in fewer elections being
considered. In both cases we can reject the null hypothesis of no incumbency effect at the .001
significance level.

20

Table 1: How the effect of incumbency for Conservatives depends on the opponent (CCT bandwidths, 1950-2010)(1)

Conservative win at t − 1
Conservative win at t − 1 ×
Liberal opponent

Conservative win at t − 1
Conservative win at t − 1 ×
Liberal opponent

(2)
(3)
(4)
(5)
(6)
(7)
(8)
Outcome: Conservative vote share at t (N = 4,030, CCT BW = 16.34)
1.911∗∗∗
1.644∗∗∗
1.642∗∗∗.603
1.788∗∗∗
1.591∗∗∗
1.899∗∗∗
1.938∗∗∗(.489)(.408)(.464)(.811)(.446)(.410)(.450)(.490)
1.782
1.687†
2.013∗
1.891
1.988†
2.078†
1.985∗(1.181)(1.006)(.849)(1.191)(1.168)(1.174)(.993).170∗∗∗(.044)

Outcome: Conservative win at t (N = 2,423, CCT BW = 9.99).133∗∗∗.290∗∗∗.014.131∗∗∗.137∗∗∗.127∗∗∗(.034)(.039)(.074)(.037)(.034)(.038).308∗∗.384∗∗∗.384∗∗∗.308∗∗.314∗∗.309∗∗(.100)(.088)(.079)(.101)(.100)(.100)

Covariates (and their interaction with indicator for Conservative win at t − 1) included:
Margin at t (running var.)
X
X
X
X
X
X
X
Decade dummies
Year dummies
X
Borough (v. county)
X
Country
X
Country × borough.293∗∗∗(.043).388∗∗∗(.088)

X

X
X

X
X
X

X
X
X

Note: Column 1 reports the coefficient and standard error for β2 from our estimate of Equation 1.
Column 2 reports β2 and β5 (the interaction) from our estimate of Equation 2. Columns 3-8 report
β2 and β5 (the interaction) from our estimate of Equation 3 including different covariates and theirinteraction with the indicator for Conservative victory at t − 1. Regressions use triangular kernel
weights with CCT bandwidths reported above each panel. *** - p < .001, ** - p < .01, * - p < .05,
† - p < 0.1.

21

Column 2 of Table 1 reports the results when we interact an indicator for “Liberal opponent”
with the indicator for Conservative victory at time t − 1 (as well as the running variable and theinteraction between them), as in Equation 2. When the outcome is Conservative vote share (toppanel), the estimated Conservative-Labour incumbency effect (given by the “main effect” in the
top row) is 1.644, which is slightly lower than the average effect given in Column 1; the interaction
indicates that the Conservative-Liberal incumbency effect is estimated to be about 1.8 percentage
points higher, or around 3.5 percentage points overall. (The interaction in this specification is not
significant at the p<.1 level.) When the outcome is Conservative victory (bottom panel), the results
are somewhat starker (consistent with the graphical evidence in Figure 5): the Conservative-Labour
incumbency advantage is estimated at .133, while the interaction implies that the ConservativeLiberal incumbency advantage is around .45. (The interaction in this specification is significant at
the p<.01 level.)
In Columns 3-8 of Table 1 we report results for the main effect and interaction when we alsointeract the indicator for Conservative victory with other covariates, as in Equation 3, thus allowing the incumbency advantage to vary along with other characteristics that might vary between
Conservative-Labour and Conservative-Liberal matchups. When the outcome is the Conservative
vote share (top panel), the estimate of the interaction remains fairly stable between around 1.8 and2.3 percentage points, indicating a Conservative-Liberal incumbency effect that is around twice theConservative-Labour incumbency effect. Three of the interaction coefficients are significant at thep<.05 level; two others are significant at the p<.1 level. When the outcome is Conservative victory(bottom panel), the estimate of the interaction varies between about .3 and .4, indicating an effectof Conservative incumbency on the probability of subsequent Conservative victory that is between
two and three times larger when the opponent was a Liberal. All of these interaction coefficientsare significant at the p<.01 level.

Tests of RDD validity and other falsification checks
The validity of the sharp regression discontinuity design depends on the assumption that potential
outcomes are continuous across the threshold at which treatment is applied; in this setting, thisassumption essentially requires that we can use the Conservatives’ narrow losses to infer what would

22

Figure 7: Continuity in the density of Conservative vote margin, by party pairing (McCrary (2008)
test)

0.020
0.000

0.010

Estimated density

0.020
0.010
0.000

Estimated density

0.030

Conservative−Liberal races

0.030

Conservative−Labour races−30 −20 −10

0

10

20

30

−30 −20 −10

Conservative margin

0

10

20

30

Conservative margin

Note: Continuity in the density of the running variable across the threshold suggests the key
assumption of RDD is met.
have happened to narrow Conservative winners if they had actually lost. Although this assumption
is not directly testable, we can perform several indirect tests, including both standard tests andtests that are tailored to the specific research design used above to compare incumbency effects
across party pairings (Eggers et al. 2015).
The continuity assumption may be violated if some parties or candidates can precisely manipulate their margin of victory – for example, if Conservatives could disproportionately win closeelections. Figure 7 addresses this possibility. Each of the panels of Figure 7 shows the density of
the Conservative vote margin, estimated separately on each side of the threshold separating cases
where the Conservatives won and lost; the left and right panels apply to cases where the Conservatives’ main competitor was Labour and Liberal, respectively. The standard McCrary (2008) test
for manipulation of the running variable checks for a discontinuity in the density at the threshold.
As suggested by the plots, we fail to reject the null hypothesis of no jump at the threshold in bothcases, as well as for both sets of cases combined,13 which is consistent with the assumption thatnarrow Conservative wins and losses are comparable.
As another indirect test of the continuity assumption, we check whether pre-treatment covariates
are continuous at the threshold separating narrow winners and losers. We test this assumption by
13 The three Z-statistics are -.12, -.96, and -.49.

23

Figure 8: Continuity in the proportion of elections taking place in boroughs, by party pairing(falsification test)

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Note: Both plots show the proportion of elections taking place in boroughs as a function of theConservatives’ vote margin in the previous election. Constituencies are divided according to thewhether the top two parties in the previous election were the Conservatives and Labour (left plot)or the Conservatives and the Liberals (right plot).
estimating the “effect” of Conservative victory at time t − 1 on outcomes determined before periodt − 1: an indicator for whether the constituency is a borough or a county (a measure of urban-ness),an indicator for whether the constituency is in England, the year of the election, and three measuresof the Conservative performance at time t − 2 (margin, vote share, and an indicator for victory).
If the continuity assumption required for RDD is valid, these falsification tests should show null
effects. For example, Figure 8 shows the RDD plot for the “effect” of Conservative victory at timet − 1 on an indicator for whether the election took place in a borough. The plot confirms thatclose Conservative-Labour contests were more common in urban areas (as indicated by the higher
overall proportion of elections taking place in boroughs in that subset), but within each subset close
Conservative victories and losses appear to be equally likely to take place in boroughs.
Extending Figure 8, we report estimated effects of Conservative victory on pre-treatment covariates separately by party pairing in the first two columns of Table 2. Each entry is the RDD estimate(with bias correction) of the effect of Conservative victory at time t − 1 on the pre-treatment covariate listed at the left; we estimate these separately for cases where the Conservative’s opponent
was Labour or Liberal. None of the “effects” is significant, which is what we would expect if the24Table 2: Falsification tests: effect of Conservative incumbency on pre-treatment covariates (CCT
bandwidths, 1950-2010)

OutcomePr(Borough)Bias-corrected, by matchup
LabourLiberalopponent
opponent.013-.039(.044)(.132)

Local linear, w. interaction
Main
Lib.
effectinteraction
-.001
-.035
(.030)(.085

Pr(England).003(.027)-.052(.103).007(.018)

-.072
(.051

Year of election.586(1.849)-4.509(3.908).078(1.172)-4.660(3.403

Conservative margin t − 2.540(1.017).002(2.643).665(.610).204(1.789Conservative vote share t − 2-.074(.409).216(.992)-.115(.273).140(.786

Conservative victory t − 2.076(.057).015(.113).097∗(.038)

-.023
(.115

Note: In columns 1 and 2, each entry is the RDD estimate (robust standard error in parentheses)of the effect of Conservative victory at time t − 1 on the pre-treatment covariate listed at left.
In columns 3 and 4, each entry is a coefficient (standard error in parenthesis) from a local linear
regression like Equation 2 in which the outcome is the pre-treatment covariate listed at left; coefficients shown relate to the treatment (Conservative victory at time t − 1) and the interaction
between the treatment and an indicator for Liberal opponent. Significance levels as in Table 1.
continuity assumption is met.
In the last two columns of Table 2 we present another falsification test that complements theanalysis in Table 1. In Table 1 we used an interaction term to test whether the effect of incumbency
on subsequent Conservative performance depends on whether the Conservatives’ opponent wasLabour or Liberal. In the last two columns of Table 2 we use the same approach, this timeusing pre-treatment covariates as the outcome; this allows us to check whether the difference inincumbency effects we found with this approach in Table 1 could be due to differences in covariatebalance across types of battlegrounds. The last column of Table 2 reports the coefficient on theinteraction from each regression; none of these is close to statistical significance, suggesting thatdifferences in covariate imbalance do not explain why incumbency effects are estimated to be larger

25

in Conservative-Liberal matchups.14

5Additional alternative explanations

The difference between the Conservative-Labour incumbency effect and the Conservative-Liberal
incumbency effect that we have shown is consistent with the pattern of preference intensity documented earlier: all else equal, we would expect a larger incumbency effect in Conservative-Liberalcontests given the larger proportion of voters who are nearly indifferent between the main parties
in those contests. The extended-RDD analysis in the previous section addressed a few alternative
explanations for this pattern based on time period and constituency characteristics. In this section
we consider two additional alternative explanations.

Does strategic voting explain the larger incumbency effect for Liberals?
As noted in the introduction, previous studies of incumbency effects in the U.K. noted that incumbency seemed to matter more for the Liberals than for other parties (Gaines 1998; Katz and King
1999). This is what we would expect given the pattern of partisan preference intensity documented
above: incumbency should matter more for Liberals because there are more voters whose rankingof the Liberals might depend on small valence shocks. But previous studies interpreted this finding
differently: both Gaines (1998) and Katz and King (1999) suggest that Liberals have larger incumbency effects because of strategic voting. The key idea expressed in both papers is that incumbency
has extra value for Liberals because it signals the local viability of the Liberal candidate to party
supporters who may be inclined to vote strategically for another party; incumbency is assumed toplay this role to a lesser extent for Labour and the Conservatives because voters who favor thoseparties simply assume their party is viable and vote for their top choice. Thus as Gaines notes(185), “the bonus of incumbency for Liberal candidates is not merely that they acquire whatever
normal advantages office-holding confers, but also that it lets them overcome an electoral logic
plaguing their party.” If there is a substantial pool of strategic voters who only vote for the Liber14 We do find a significant main effect for the last outcome (an indicator for lagged Conservative

victory); inspection of the RD plots suggest that this is because of under-smoothing, i.e. curvaturein the conditional expectation function that causes bias in the local linear regression.
26

als when there is a Liberal incumbent because they otherwise assume the Liberals are not viable,
then this could be enough to explain both Gaines (1998) and Katz and King (1999)’s finding thatincumbency matters more to the Liberals and our finding that incumbency matters more to theConservatives when they face a Liberal incumbent. The strength of partisan preferences need not
be a factor at all.
The key element of this alternative explanation is that incumbency must signal viability for
Liberals: we should find that the perceived viability of the Liberals is higher when they won theprevious election in the constituency than when they lost, all else equal. We might also expect this tobe true for the Liberals when they compete against the Conservatives, but not for Labour when they
compete against the Conservatives. To assess this, we use BES data from 2005 and 2010 to assess
how narrow victories and losses for the Conservatives affect voters’ perceptions of likely outcomes insubsequent elections. The BES asked respondents how likely it was that each of the major parties
would win the election in their constituency.15 The left plot suggests that voters perceive Labour
as more likely to win when Labour narrowly won the last election than when the Conservatives
narrowly won, suggesting that Conservative incumbency may reduce the perceived viability ofLabour in Conservative-Labour contests; the result is not statistically significant, however, once weapply the bias correction and associated confidence intervals.16 The right plot shows no effect inConservative-Liberal contests: there is no evidence in the plot or in hypothesis tests17 that voters see
the Liberals as more viable on average when there is a Liberal incumbent, all else equal. Although
this falsification test is somewhat underpowered (with 656 observations in the relevant bandwidth
for Conservative-Labour contests but only 203 for Conservative-Liberal contests), it does cast doubt
on an alternative explanation in which incumbency matters more in Conservative-Liberal contests
because it signals the viability of the Liberal candidate.18
15 The precise wording of the question was, “On a scale that runs from 0 to 10, where 0 meansvery unlikely and 10 means very likely, how likely is it that #{PARTY} will win the election in#{RESPONDENT’S CONSTITUENCY}?”
16 The coefficient is -1.07, with a robust standard error of .76.
17 The bias corrected estimate is 1.14 (i.e. the opposite sign from expectations, with a robust
standard error of 1.07.
18 In the Online Appendix we also use our interaction approach to show that incumbency effects
are larger in Conservative-Liberal contests even controlling for the extent to which there might be27

Figure 9: How does Conservative incumbency affect voters’ expectations of their opponents’ electoral viability?

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Note: Both plots show the perceived viability of the Conservatives’ main opponent in the constituency (Labour at the left, the Liberals at the right) among BES respondents as a function of
the Conservatives’ vote margin in the previous election. Constituencies are divided according to
the whether the top two parties in the previous election were the Conservatives and Labour (leftplot) or the Conservatives and the Liberals (right plot).

Are Liberals better incumbents?
Another alternative explanation is that Liberal incumbents may be better able to take advantage ofincumbency than MPs from other parties. In explaining why the Conservative-Liberal incumbency
effect is larger than the Conservative-Labour incumbency effect, we have emphasized the differencein partisan preferences across different party pairs, but clearly the effect of incumbency on perceived
valence could also vary across party pairs. One particularly simple mechanism that would produce
this variation is if Liberal MPs are systematically better than Labour MPs at converting incumbency into valence benefits, for example because they tend to put more effort into constituency
service or are more effective at claiming credit for their efforts. This would provide a particularly
straightforward explanation for the variation in incumbency effects we find – an explanation that
may have nothing to do with the strength of partisan preferences.
In fact, a simple cross-sectional analysis of BES survey data from 2005 and 2010 is consistent
with this possibility. The 2005 and 2010 BES asks respondents to say how much they agree withcoordination problems in the constituency.

28

the statement, “My member of parliament tries hard to look after the interests of people wholive in my constituency.” Focusing on constituencies with Conservative-Liberal and ConservativeLabour matchups, the average effort rating of Liberal MPs is significantly higher than that of bothLabour and Conservative MPs; if Liberal MPs are simply better than other MPs at making use ofincumbency, this could explain why Conservative-Liberal incumbency effects are larger. A closer
look at the survey data casts doubt on this explanation, however: the difference in perceived effort
between Liberal MPs and others disappears when we focus on cases where the MP was narrowly
elected. Figure 10 shows the average level of perceived effort for MPs in Conservative-Labour
and Conservative-Liberal constituencies, as a function of Conservative vote margin in the previous
election. If Liberal MPs were simply better than others at winning voters’ approval, then in theright plot (Conservative-Liberal contests) we might expect the average perceived effort to drop
down at the threshold when a Conservative is elected instead of a Liberal; if anything it is thereverse. (Similarly, the left plot indicates that Labour and Conservative MPs appear to receive
the same effort rating, conditional on a close election.) If Liberal MPs are not perceived to exerthigher effort than Conservative MPs conditional on a close election, there would seem to be little
reason to think that fundamental differences between Liberal MPs and others could explain thelarger Conservative-Liberal incumbency effect.
Figure 10: How does Conservative incumbency affect voters’ evaluations of MP effort?

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Note: See note to Figure 9; the outcome here is the perceived effort level of the local MP among
BES respondents.

29This survey evidence on MPs’ perceived effort does point to an intriguing pattern that weview as complementary to our main argument about how partisan preferences and incumbency
effects are related. A simple cross-sectional comparison shows that BES respondents who live inconstituencies where the top two parties in the previous election were Conservative and Liberal givesignificantly higher evaluations of their MP’s effort than BES respondents who live in constituencies
where the top two parties were Conservative and Labour; this is true whether we focus on cases
where the previous election was close or not. Thus while Figure 10 suggests that voters do not
perceive a difference in effort level between Conservative and Liberal MPs (conditional on a closeelection), they do perceive a difference between the effort level of, on the one hand, Conservativeand Liberal MPs in close races and, on the other, Conservative and Labour MPs in close races. To
the extent that such a difference exists, and to the extent to which greater MP effort leads to larger
incumbency effects (all else equal), this pattern would tend to produce higher incumbency effects
in Conservative-Liberal contests than in Conservative-Labour contests. This could be viewed as
an alternative explanation, in the sense that variation in MP effort is the proximate cause of thedifference in incumbency effects. But ultimately we view this variation in MP effort as itself an effectof the variation in the intensity of partisan preferences. That is, even if MP effort levels were fixed
across party pairings, we expect larger incumbency effects in Conservative-Liberal contests; because
MPs are strategic and understand that the rewards of additional effort are larger in ConservativeLiberal contests, we expect MP effort levels to be higher in contexts where partisan preferences are
weaker, which would tend to amplify the ceteris paribus effect.

6

Conclusion

In this paper, we have studied multiparty elections in the U.K. to shed light on the relationshipbetween incumbency effects and the strength of voters’ partisan preferences. Previous work pointed
toward an important role for partisanship in explaining incumbency effects, but most existingfindings are open to alternative explanations in part because variation in partisanship tends tocoincide with variation in other relevant factors that affect incumbents’ chances. Our approachis to compare incumbency effects across partisan matchups in the U.K., showing not only thatincumbency effects vary in the way we would expect but that this variation cannot easily be
30explained by other factors that vary across matchups. Of course, we cannot account for all possible
alternative explanations of the patterns we observe,19 but many of these explanations (e.g. thegreater focus of Liberals on “community politics”) could also be seen as strategic responses tothe difference in strength of partisan preferences that we document. At any rate, it is likely byaccumulating several studies with different designs in different settings that we will develop a clearerview of how partisanship, incumbency effects, and electoral accountability are related.
When we view incumbency as a shock to candidate valence whose electoral impact depends on
the strength of partisan preferences, it becomes clear that the study of incumbency effects may yieldinsight into a broader set of issues than has previously been supposed. The dominant view seems
to be that studying incumbency effects provides two main payoffs: understanding the degree towhich incumbents are insulated from electoral accountability, and assessing how much incumbents
do for their constituents (e.g. King 1991; Cox and Morgenstern 1993; Uppal 2009). When we
recognize that incumbency effects reflect not just incumbent actions but the strength of voters’
partisan preferences, it becomes clear that comparative studies of incumbency effects could also
yield insights into the extent to which political systems are candidate-centered as opposed to partycentered, which is in turn likely to depend on e.g. the electoral system, the legislative process, andpolarization at the elite and mass level. Similarly, although our focus has been on how the strengthof partisan preferences affects voters’ response to incumbency, the logic applies more broadly to how
voters respond to any differences among candidates, including differences in perceived corruption,
capability, or policy positions; in that sense, the study of incumbency effects can speak to a broader
set of questions about accountability and its relationship with partisan preferences, a question thathas been examined in a completely different way by Kayser and Wlezien (2011) and others in theliterature on economic voting. Thus while the study of incumbency effects began with concerns
about incumbent re-election rates specific to the U.S., the development of comparative work on
the topic promises to yield much broader insights into how electoral accountability and partisan
competition vary across political systems.
19 An anonymous reviewer noted that voters may vote against incumbents from the government’s

party; this would tend to reduce the electoral advantages of incumbency in Conservative-Labour
contests more than in Conservative-Liberal contests because Liberals are not in government.
31

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