"People are running, but where are they heading?” Disentangling the sources of electoral volatility

Abstract

Electoral volatility as measured by the Pedersen index is arguably one of the most popular indicators in political science, but its interpretation is far from clear. Volatility is produced by a mix of party-switching, differential turnout and generational replacement. However, there is virtually no empirical research on which, if any, of the main mechanisms leading to volatility tends to have the strongest net impact on election results. Furthermore, the presence of generational replacement and its relative impact on election results have been paid little attention to in studies of volatility. This paper develops several theoretical expectations concerning the strength that each of the three components of volatility is expected to exert on the latter. Subsequently, it estimates the net impact of each component on the results of 73 elections in six West European democracies using survey data. According to these estimates, party-switching produced 75% of the total amount of volatility, with differential turnout and generational replacement producing 17% and 8% respectively. Although the effect of these components may work against each other at times, on average only 11% of volatility was cancelled out this way. Findings provide, for the first time, a map of the components of volatility in established democracies and set the ground for further research on the topic.

Full text

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This is a post-peer-review, pre-copyedit version of an article published in Comparative European
Politics. The definitive publisher-authenticated version is available at doi:10.1057/cep.2015.22
“People are running, but where are they heading?”
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Disentangling the sources of electoral volatility
Author: Raul Gomez
Email: raul.gomez@liverpool.ac.uk
Abstract
Electoral volatility as measured by the Pedersen index is arguably one of the
most popular indicators in political science, but its interpretation is far from
clear. Volatility is produced by a mix of party-switching, differential turnout
and generational replacement. However, there is virtually no empirical
research on which, if any, of the main mechanisms leading to volatility tends
to have the stronger net impact on election results. Furthermore, the presence
of generational replacement and its relative impact on election results have
been paid little attention to in studies of volatility. This paper develops several
theoretical expectations concerning the strength that each of the three
components of volatility is expected to exert on the latter. Subsequently, it
estimates the net impact of each component on the results of 73 elections in
six West European democracies using survey data. According to these
estimates, party-switching produced 75% of the total amount of volatility, with
differential turnout and generational replacement producing 17% and 8%
respectively. Although the effect of these components may work against each
other at times, on average only 11% of volatility was cancelled out this way.
Findings provide, for the first time, a map of the components of volatility in
established democracies and set the ground for further research on the topic.
Keywords: volatility, Pedersen index, vote-switching, differential turnout, generational
replacement
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This sentence was reportedly said by Indian life coach Vikran Kalloo, who added: “It’s maybe just a stage, like
growing pains” (Hazlewood 2010).
ACKNOWLEDGEMENTS: I would like to thank Wouter van der Brug, Mark Franklin, Jose Ramon Montero, and all
the participants at the EPSA Conference in Dublin and at the EUI Colloquium for their very thoughtful comments.

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Introduction
Electoral volatility in the form of the Pedersen index (Pedersen 1979) is perhaps one of the most
widely known indicators in political science. Due to its ease of computation (it is only necessary to
have data on the results of two subsequent elections), it has been employed as dependent or
independent variable in a panoply of studies.
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Volatility is a good indicator of party system change,
but it is extremely difficult to assess what it really reflects in terms of individual voting behaviour.
As a consequence, scholarly work employing the Pedersen index must rely upon untested
assumptions concerning the behaviour of individual voters, which raises important questions of
interpretation. But, what is behind electoral volatility?
In principle, electoral volatility may be produced by three main mechanisms: party-switching,
differential turnout and generational replacement. However, to date there has been virtually no
attempt to assess the net impact of these factors on volatility at party- and election- level in a general
way. Moreover, generational replacement has been paid very little attention to in the literature on
party choice (van der Brug and Kritzinger 2012), and its net effect on volatility has, to the best of
my knowledge, never been fully assessed. This paper provides an analytical reasoning of the
mechanisms leading to volatility and tests several theoretical expectations concerning their relative
net impact on election results using data from 73 national elections in six West European
democracies. By doing so, it provides a general map of electoral volatility in several established
democracies and sets the ground for further research on the topic.
The study proceeds as follows. The first section defines electoral volatility and provides a review
of the most relevant literature on electoral instability. Next, the paper elaborates on the link between

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individual behaviour and aggregate volatility. It will be argued that, even though interpreting
volatility is always difficult without further investigation, there are a number of theoretical reasons
to argue that party-switching is likely to be the mechanism behind most of the net volatility seen at
elections. Subsequently, the research strategy and method followed in the paper are both explained.
An empirical evaluation of the mechanisms leading to volatility is then presented by focusing on
changes at party level first and then moving on to the election level. The paper then ends with a
conclusion.
2 Volatility and electoral change
The term ‘volatility’ is often used to refer to the total amount of electoral change that takes place
between two given elections. There is not a single way to measure aggregate volatility (see, for
example, Ascher and Tarrow, 1975; Przeworski, 1975; Rose and Urwin, 1970), but the most popular
indicator is the one introduced by Pedersen (1979), who defined it as ‘the net change within the
electoral party system resulting from individual vote transfers’ and suggested the following formula:
Volatility (Vt) =
∑∆
,




where volatility (Vt) may be interpreted as the gains of all winning parties in the party system
or, symmetrically, the losses of all losing parties.
2
The subscript i stands for each party, t stands for
the election year, and, therefore, 
,
corresponds to the percentage of votes gained by party i at
election t.

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The main advantage of volatility as an indicator is that it can be obtained for a great number of
countries and elections, which allows for large-n comparative analyses. Thus, this indicator has been
used in most of the comparative research on net volatility that has been published (eg. Bartolini and
Mair, 1990; Bischoff, 2012; Converse, 1969; Mainwaring and Zoco, 2007; Mair, 1993; Pedersen,
1979, 1983; Roberts and Wibbels, 1999; Rose and Urwin, 1970). This line of research has attempted
to explain volatility by emphasizing the role of variables such as the electoral system and parties’
socio-organizational bounds (Bartolini and Mair, 1990; Pedersen, 1983; Roberts and Wibbels,
1999), the timing of democratization and the party system (Mainwaring and Zoco, 2007;
Przeworski,1975; Tavits, 2005), patterns of mobilization (Huntington, 1968; Przeworski, 1975),
political cleavages (Heath, 2005; Tavits, 2005), economic voting (Remmer, 1991; Roberts and
Wibbels, 1999; Tavits, 2005), fiscal space (Nooruddin and Chhibber, 2008), etc.
A handful of scholars have refused to make inferences about the behaviour of voters from
aggregate measures of volatility, as they claim that the only thing that volatility certainly reflects is
party system change (eg. Rose and Urwin, 1970; Drummond, 2006). However, volatility is usually
taken by the literature employing the Pedersen index as an indicator of electoral instability,
assuming generally that this is somehow produced by a mix of voters switching parties and others
switching between voting and non-voting.
3
In spite of this, there is not a real sense of how these
different elements can really affect election results in empirical terms.
As Butler and Stokes (1974, p.185) pointed out, ‘electoral change is due not to a limited group
of ‘floating’ voters but to a very broad segment of British electors’. Election results may change
because of three mechanisms. One is party-switching, which involves an active behaviour on the

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side of voters that decide to choose different parties in consecutive elections. A second mechanism
is differential turnout, which is the joint effect of the mobilization of some voters and the
demobilization of others. Though ‘volatility’ often brings to mind the image of switching voters,
the role of differential turnout as a catalyst of change has been highlighted by several scholars.
Campbell et al. (1960), for instance, coined the term ‘peripheral electorate’ to refer to those voters
that only participate in some elections and whose erratic behaviour may undoubtedly affect the
results. For Boyd (1985, p.521), too, ‘the potential effect of abstention on election outcomes is quite
high, even in countries with high voting rates’. Nevertheless, the question of whether or not this
potential is generally translated into an empirical pattern has been contested. Särlvik and Crewe
(1983) find ‘switching by abstention’ to be the most common of the inconsistent vote patterns. In a
similar vein, Hansford and Gomez (2010) argue that irregular voters are less predictable than regular
voters, and show turnout variations to have quite a meaningful impact on election results. By
contrast, others have claimed the effect of differential turnout to be usually much smaller than that
of switching between parties (Boyd, 1985; Butler and Stokes, 1974), while the influence of turnout
on election results has been found by some to be negligible both in national (Bernhagen and Marsh,
2007) and in European Parliament elections (van der Eijk and van Egmond, 2007).
The third mechanism leading to volatility is generational replacement. Perhaps because it does
not really imply an active change of behaviour on the side of voters, generational replacement has
been ignored by most of the literature dealing with election-level volatility. However, as Przeworski
(1975) puts it, volatility might well be an indicator of the difference in the political preferences of
new voters compared to those of their elders. The generational renewal of the electorate may, thus,

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lead to sustained changes in election results even if voters did not change their choice at all. Indeed,
this mechanism has been shown to play a major role in massive political realignments in periods
such as the New Deal in America and the post-World War II elections in the UK (Andersen, 1979;
Franklin and Ladner, 1995). But it is not necessary to focus on massive realignments and exceptional
elections to realize the contribution that it may also have on election results even in the short term.
Nevertheless, to the best of my knowledge there has been no serious attempt to estimate the net
impact of generational replacement in ordinary elections.
It is thus clear that volatility may be brought about by different mechanisms. The question is
whether the strength with which these mechanisms impact on election results can be said to follow
a certain pattern. If it does not –that is, if the net effect of these mechanisms is purely random–, then
any assumption concerning the general meaning of electoral volatility in established democracies
will simply be misleading. In the next section, I present some theoretical considerations that may
help us understand why we can expect most elections to follow a pattern where party-switching
plays the most relevant role in volatility.
3 Disentangling the meaning of volatility: theoretical considerations
From a theoretical point of view, there are a number of reasons to argue that party-switching should
be the prevailing mechanism leading to net volatility at most elections. The first of these reasons is
that any vote captured from party-switching is simultaneously one vote gained by a given party and
one vote lost by another (Boyd, 1985). In contrast, this is something that does not necessarily hold
true for differential turnout or generational replacement. As an example, let me compare the effect

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of party-switching with that of mobilization. Figure 1 shows different exemplary scenarios in a two-
party system. In the first scenario, five voters switch from party B to A. This, as can be observed,
produces in this example 5 points of volatility. The second scenario also involves the action of five
voters, but these are previous non-voters that become mobilized to support party A. When non-
voters decide to turn out at a given election, they provide their chosen party with an extra vote
without any other party directly losing a single vote as a result of their behaviour. It is easy to realize
that the effect of the same number of voters is much smaller in this example than it is in the switching
scenario (it produces 2.9 points of volatility in this particular example, as opposed to 5 points in
scenario 1). Moreover, if demobilization or any of the elements that conform generational
replacement were used instead, conclusions would remain the same, one switching voter having a
much stronger impact on volatility than any other kind of voter.
[TABLE 1 ABOUT HERE]
Alongside this mathematical reason, there is yet another factor that is bound to work in favour
of party-switching: the net effect of differential turnout and generational replacement on volatility
is distributional. In other words, their effect depends not only on the number of voters involved but
also on how these are distributed among the different parties. In the two scenarios presented earlier,
only one of the parties received votes from previous non-voters. Now, imagine that both party A
and party B received the same number of mobilized voters. In this case, the net effect of mobilization

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on net volatility would be zero. And again, the same also applies to the effect of demobilization and
to the different elements of generational replacement.
It is evident that these factors give party-switching a comparative advantage. Indeed, one can
argue that the effect of party-switching may also be cancelled out if the same number of voters
switching from party A to B decide to switch from party B to A. Though this is a correct statement,
as well as a likely possibility, differential turnout and generational replacement both are likely to be
subject to several sources of cancelling-out. Apart from the cancelling-out that comes from their
distributional nature, the effect of mobilized voters may also be counteracted by demobilized voters
changing in the opposite direction. Similarly, the effect of new voters may compensate for the
passing away of others, thereby leading to zero volatility. All these theoretical considerations
should, therefore, be enough to expect that the effect of party-switching will prevail over the rest.
This in turn implies that studies where the Pedersen index is used as a surrogate of net switching are
likely not to be misleading. As a consequence, most of the volatility observed in election results is
probably produced by the net effect of voters defecting from one party to vote for another.
When it comes to the other two mechanisms, generational replacement is likely to be subject to an
additional limitation coming from demographic dynamics. Variations in mortality and/or birth rates,
as well as electoral rules lowering the voting age, may indeed have an important impact on election
results by benefiting those parties with stronger attraction among the young at the expense of the
rest. But, as the average rate of replacement in the electorate of Western European countries tends
to be rather low, the net effect of generational replacement is likely to be relatively small in the short

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term as well. Thus, we should probably expect generational replacement to have the smallest effect
on volatility.
Conspicuous readers will nevertheless argue that there is still another possible type of cancelling-
out that takes place between (and not within) the three mechanisms of volatility. This kind of
cancelling-out comes about when the net effects of different mechanisms present opposing signs.
Thus, a party might, for example, obtain gains from switching voters but lose votes from differential
turnout and generational replacement, obtaining as a result exactly the same vote percentage as in
the previous election. As the effect of party-switching is expected to be stronger than the effect of
any other mechanism, we could perhaps expect that it will also be much more difficult for it to be
removed by the action of the other two. The extent to which volatility is reduced as a result of the
different components working against each other is an empirical question, but it also needs to be
assessed in order to better understand the processes behind electoral change.
With these theoretical considerations in mind, the next section focuses on the research strategy
that will be employed in this paper.
4 Disaggregating electoral volatility: data and technical issues
4.1 Data
Political scientists are prone to enlarging the variation in their data by including additional countries.
However, when the goal is to study political change, it may be more appropriate to maximize the
number of time-points over which change can be tracked, even though lengthy time-series are

10
available only for a few countries. Thus, the cases that are the focus of this study are established
Western European democracies for which a large number of national election studies are available.
This strategy will allow me to compare elections within countries and study the effect of the different
mechanisms of volatility over time. Moreover, recent record peaks of volatility have been reported
and generated much academic debate in Western Europe, which makes of these countries an
interesting case for study (eg. Bartolini and Mair, 1990; Drummond, 2006; Mair,
1989, 1993, 2005, 2008; Pedersen, 1979, 1983).
The countries selected for analysis are Denmark, Great Britain, Germany, Netherlands, Norway
and Sweden. These are the same cases used by the European Voter project (Thomassen 2005a).
Election surveys from that project were collected and examined, resorting to the original databases
when coding mistakes were present. Additionally, more recent National Election studies were
collected to extend the dataset until the 2000s.
4
In total, the whole dataset contains 73 national
election surveys in 6 countries
5
over an average time span of 50 years, as displayed in Table 2.
[TABLE 2 ABOUT HERE]
The resulting dataset provides sufficient variation over time, but also in terms of the different
electoral and institutional settings of the six countries. Not only do they have different electoral and
party systems, but they also show clear variations in volatility (see Figure 1). With an average level
of volatility of 6.1 and 6.5 respectively, Germany and Great Britain show the lowest levels in the
period analysed. The Netherlands is at the other extreme (14.22), with Norway (12.46) and Denmark

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(11.66) showing high levels too while Sweden (8.9) occupies an intermediate position. There are
also different trends over time. Sweden departed from one of the lowest levels of volatility in the
1960s (2.6 in 1964) and reached levels higher than 15 points in the 2000s. Volatility has also
increased in Germany after the 1990s, but changes have been very slow and relatively small, while
abrupt changes are found in the Netherlands and Norway. In Great Britain, volatility does not seem
to follow a clear trend, and in Denmark it remains high but is clearly lower than in the 1970s where
record peaks of over 17 points are found in three consecutive elections. Thus, the sample of elections
provide enough variation in order to have a representative idea of the patterns of volatility.
[FIGURE 1 ABOUT HERE]
In terms of operationalization, and besides the age of respondents, the survey questions employed
for the analyses are vote choice in both the last and the previous election. These are the standard
survey questions where respondents are first asked whether they voted or not and, if they did, they
are asked about the party voted for.
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4.2 Research strategy and methods
Different possible strategies can be followed to observe the relationship between volatility and the
different individual-level mechanisms leading to it. Given the aggregate nature of electoral
volatility, one of those strategies may indeed consist in the use of ecological inference (Brown and
Payne, 1986; Mannheimer, 1993; King, 1997), but important shortcomings make it inconvenient for
the purpose of this paper. For one thing, ecological inference necessitates from data collected at the
lowest possible level of aggregation, which entails problems of feasibility when it comes to studying

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several countries and elections. For another, and even more importantly, ecological models are, by
their own nature, based on the assumption that the population between two consecutive elections
remains exactly the same. This rules out the possibility of estimating the effect of generational
replacement and, therefore, of comparing its relative impact on volatility vis-à-vis the other
mechanisms. An alternative and more feasible strategy consists in combining aggregate and
individual data. Since election surveys including vote recall for at least two elections have been
conducted in several countries for decades now, there is no reason not to make use of them in order
to have an overall idea as to what the common trends might be. To be sure, such a strategy is also
far from perfect, as surveys do always contain some amount of measurement error. But, for the
reasons already expressed, it looks like the best strategy in this case.
In what follows, several sources of information are employed to test the arguments made in
previous sections. On the individual side, I will employ the pooled database of national election
surveys already mentioned in section 4.1. Although many of these surveys are not panel studies,
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which might perhaps give us more precise information, we may combine them with other sources
to try to approach a general picture of what is going on.
8
Together with the presence of misreports,
the other source of error of survey data is associated with non-response.
9
In order to deal with these
possible sources of error, this paper follows the literature on vote transitions and applies a weighing
procedure that takes into account the real proportion of non-voters and voters of each party in the
population (eg. Axelrod, 1972; Butler and Stokes, 1974; Särlvik and Crewe, 1983; Boyd, 1985;
Aimer, 1989; Granberg and Holmberg, 1991; van Egmond, 2007).
10
An Iterative Proportional
Fitting (IPF) procedure will be employed to weigh the data.
11

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One particularity of this paper is that it is also aimed at getting an estimate of generational
replacement, which requires combining more than two data sources. Certain voters came of age in-
between the elections analysed, and that has to be accounted for. Vote recall variables contain
information on who those voters were. This information was checked on the basis of their age to
prevent coding mistakes and, subsequently, weighed by the actual number of new voters at every
single election.
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By combining all these data, we could get information on voters who changed their behaviour as
well as on those who entered the electorate for the first time. This would enable us to calculate the
net effect of switching and differential turnout, but not of generational replacement, as information
on the voters who passed away is missing in the surveys. Generational replacement produces
volatiity if and only if the preferences of voters from older cohorts are different from those of new
voters. Since there is no way to know which of the voters from older cohorts died between two given
elections, a simulation was made in the following way:
a) First, using demographic statistics,
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the proportion of the population passing away between
elections (t and t+1) was calculated for three age cohorts: 50-59 year-olds, 60-69 year-olds and
people over 70 years old. Age cohorts refer to the year when the first of each couple of elections
(election t) took place.
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b) Second, voters that had passed away between elections are absent in the surveys in spite of
having voted at election t, and so it is necessary to create those cases artificially. Therefore, a group
of respondents within each of the age cohorts mentioned earlier was randomly duplicated

14
mantaining the vote distribution and turnout rates of their cohort counterparts at election t.
15
The
number of respondents to be created was determined on the basis of the proportions of people that
passed away between election within each age group.
c) Naturally, "deceased electors" were assumed to have only voted (or not) in the previous
election (election t) but not in the most recent one (t+1). Moreover, they were assigned a weight
corresponding to the actual percentage of individuals over 50 years old that passed away between
elections.
Despite not being a perfect measure, this strategy has the advantage of producing approximate
estimates of the effect of deceased voters on volatility. Of course, it does not account for the small
amount of younger people who die between elections, nor does it take into consideration that the
distribution of preferences of deceased voters may be different from those of voters who are still
alive even if they belong to the same cohort. The latter is likely the case with manual workers, whose
higher mortality rates will probably affect the vote of labor, socialist and communist parties
somewhat more than is predicted by this method. However, with regard to deaths of younger
individuals, it must be borne in mind that these are, by definition, much less likely to be related to
the ageing process and, as a consequence, cannot be directly linked to generational replacement.
Moreover, since the passing away of younger voters is likely to have a larger random component,
its impact on election results, if any, is bound to be very marginal. So, aside from a certain amount
of measurement error, this approximation method is far from problematic given our complete lack
of information and the fact that the overall proportion of deceased voters is relatively small.

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Once all the weights have been applied, vote recall questions can be used to calculate the
percentage of votes gained or lost by each party as a result of party-switching. This is done by
keeping only those respondents who voted at both elections and cross-tabulating the data election
by election. For each party, the amount of voters that left for other parties can then be subtracted
from the amount of voters gained from competitors. A similar strategy (albeit including non-voters)
can be employed to compute the net percentage of votes gained/lost by each party as a result of
voter mobilization, which is then subtracted from the percentage of votes gained/lost from
demobilized voters. Lastly, in order to calculate the impact of generational replacement, the amount
of votes gained/lost by each party when new voters are added must be subtracted from the amount
gained/lost as a result of older voters passing away.
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The procedure was carried out and then repeated for each election in order to produce an estimate
of how the different parties were affected by each mechanism. Results were then stored and put
together in a pooled dataset.
Following this strategy, if switchers are set not to have switched, demobilized voters are set to
have voted for the party that they did in the previous election, mobilized voters are set not to vote,
young voters are set as missing and diseased voters are set to have voted in the way they presumably
did, we can perfectly wind back from the most recent actual results to the results of the previous
election. It is, therefore, perfectly possible to simulate how much is added when different groups of
voters come into play and how that affects the electoral prospects of every single party in all of the
73 elections.

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5 What lies behind: analyses of electoral volatility in six countries
5.1 Analysis at party level
a) Mapping out the impact of the three components
Even though electoral volatility tends to be measured at election level, it is at party level that net
election change really takes place. Different parties lose and gain electoral support between
consecutive elections, and volatility is only a measure of how much of the percentage changed
hands.
As explained earlier, in spite of being an acummulation of processes that happen primarily at the
individual level, volatility is a net outcome. This implies that the effect of the underlying processes
leading to it can potentially be cancelled out and have no observable impact on election results. As
a consequence, volatility cannot be fully comprehended unless we take a step up in the ladder of
aggregation. For that reason, the strategy followed in this paper consists in aggregating individual-
level data at party level in order to simulate the process that takes place between elections leading
to changes in election results
17
.
Following the procedure explicated in section 4.2, the net effect of party-switching, differential
turnout and generational replacement was calculated for each party and election using survey data.
The result is shown in Figures 2-3. These figures show the percentage of votes that each party lost
or gained in each election as a result of the three mechanisms of volatility.

17
As can be seen, party-switching is by far the component of volatility that produced stronger
changes in the support of most parties (Figure 2). Although the range of losses and gains for each
party varies across countries, switching caused average changes of about 1.8 percentage points for
the parties analyzed. Overall, there seems to be a small centripetal tendency in many elections
whereby a small number of parties tend to attract voters from a range of parties (332 winning cases
versus 290 losing cases). Of all the parties under study, the one that suffered the greatest losses was
the Dutch labour party (PDVA) in 2002, with a net loss of almost 10.6% of the votes due to
switching. Not surprisingly, this was precisely the year that Pim Fortuyn's populist right party
managed to get the highest number of switching voters in the sample (11.34% of net gains from
switching) and to be the second most voted party in the Netherlands. Clearly, switching voters were
responsible for much of the changes that occurred in the most dramatic election in Dutch history to
date.
[FIGURE 2 ABOUT HERE]
Differential turnout, on the other hand, produced an average change in party support of 0.51%
of the vote share (Figure 3). This is 2.5 times less than the estimated average change produced by
switching, which lends support to the expectation that switching is by far the most important of the
mechanisms leading to electoral volatility - at least it is at party level. The party that managed to
lose the highest vote share by the relative demobilization of its voters (2.9 per cent) was the British
Labour party in 1970. Although most opinion polls prior to the election had predicted Labour Prime
Minister Wilson's victory, the final result was a fall of 4.9 percentage points in Labour's vote share

18
(Abrams 1970). In light of these estimations, it seems that more than half of this fall could be
explained by the effect of differential turnout. The other extreme is, once again, represented by Pim
Fortuyn's party in the 2002. Not only did the party manage to attract voters from their main
competitors, but also it obtained about 5.46% of extra votes thanks to the relative mobilisation of
its voters vis-à-vis its competitors.
[FIGURE 3 ABOUT HERE]
Lastly, the effect of generational replacement (Figure 4), although important, is the smallest
among the three components. On average, this component produced a change of 0.34 percentage
points in party support (4.3 times less than switching). The maximum amounts of votes gained and
lost by a party due to generational replacement are both found in the 1972 German election. The
stronger sympathy towards Chancellor Willy Brant among younger voters seems to have helped the
former to win his second consecutive federal election, giving the SPD an extra 2.12% of votes
mostly at the expense of the CDU/CSU, which lost 2.14 percentage points from generational
replacement. The reasons for the popularity of Willy Brant are not the focus of this paper. However,
it might be partly related to the development of the Ostpolitik, which in effect recognised the
Democratic Republic of Germany as an independent country and was relatively less popular among
those aged over 60 (Irving and Paterson 1972).
It is worth noting that generational replacement also appears to be one of the main factors helping
many Green, Populist and Radical Left parties to emerge in several countries. Examples of this are

19
the German Grüne (Greens), the Norwegian FRP-ALP (right-wing populist) and SV (Radical Left),
the Dutch Pim Fortuyn (right-wing populist), or the Danish SF (Green/Radical Left).
[FIGURE 4 ABOUT HERE]
b) Analyzing changes in party support
So far, the paper has analyzed the estimated impact of net switching, differential turnout and
generational replacement on the electoral prospects of parties separately. However, actual changes
in election results are the consequence of an aggregation that occurs when the effects of the three
components of volatility are summed up, and so the total percentage of votes that is lost or gained
by each of the parties at a given election equals the following equation:
Total change i = s
i
+ t
i
+ g
i
,
where s is the net effect of party-switching for each party (i), t is the net effect of differential
turnout, and g is the net effect of generational replacement.
So, in order to study how each of these three mechanisms (in what follows, they will also be
called components) impacts on volatility, it is necessary to analyze the relationship between their
effects and total vote changes at party level. In other words, what needs to be assessed is the
relationship between the gains and losses in party support that are produced by each of the
components and the total percentage of votes that parties lose or gain between elections. This way,

20
it will be possible to assess which of the three components, if any, presents the strongest relationship
with total change in parties' support. As previously mentioned, switching voters are expected to
have the largest effect on net volatility, while generational replacement should the smallest effect.
Correlations between the effect of each of the components and total change at party level are
shown in Table 3. Looking at correlations is a useful strategy; if, for example, parties gain votes
regardless of whether they attract or lose switching voters, then switching cannot be deemed to be
a good indicator of volatility (or the other way around).
As can be seen, there is a very strong relationship between the net effect of switching and actual
changes in party support (see first row in Table 3). This indicates that the effect of switching is not
only large but also cancelled out to a lesser extent than the effect of the other components. The
correlation is .97 when all six countries are considered and, when split by country, it is actually
equal or higher than that in five of them. Only in Germany does switching explain a little less of the
variance of actual results (Pearson’s r = .88), although the range of variation is also much smaller
than in any other country. So, on average, it is possible to get a very accurate idea of the actual
amount of volatility by looking only at the net effect of switching on each party’s results. In fact,
regressing the effect of switching on total change in party support yields a coefficient of 0.75,
indicating that 75% of volatility is produced by switching voters.
18
[TABLE 3 ABOUT HERE]

21
As expected, the picture is somewhat different with regard to the other two components. The
correlation between the net effect of differential turnout and total change at party level (second row
of Table 3) shows a more erratic pattern. The relationship is strong in most countries, but in no case
does it reach the levels found with switching. This is especially true in Germany, where the net
effect of turnout only explains 18% of the variance of total change (Pearson's r = 0.43), and so it
can hardly be used as an accurate indicator of the latter. Regressing the effect of differential turnout
on total change in party support yields a coefficient of 0.17, indicating that 17% of volatility is
produced by this component.
19
The net effect of generational replacement, on the other hand, shows an even weaker correlation
with total change in every one of the six countries (third row in Table 3), which indicates high levels
of cancelling out between this and the other two components (in other words, parties often gain or
lose votes regardless of the effect of generational replacement). Actually, in both Great Britain and
Germany the correlation is particularly low (0.36 and 0.39 respectively). Finally, regressing the
effect of generational replacement on total change in party support suggests that 8% of volatility is
produced by this component.
20
Findings support the expectation that switching is the most important cause of changes in party
support, followed by differential turnout and generational replacement. Having said that, it is
necessary to keep in mind that total changes in party support are the sum of the changes caused by
the three components. Therefore, components may have contradicting effects, with parties being
able to benefit from one of the components while they lose from another. With this in mind, there
may be two interrelated reasons for the strong correlation between switching and changes in party

22
support: either switching produces the stronger impact (which, as shown in the previous subsection,
it does) and/or the effect of the other two components is more likely to be cancelled out by the action
of switching voters. In other words, it might well be that differential turnout and generational
replacement benefit different parties from the ones that are benefitted from switching.
To investigate the presence of cancelling-out between components, we need to look at the
correlation between their effects individually (Table 4). As can be appreciated, correlations between
components of volatility are overall moderate in the six countries. Indeed, the positive signs show
that, most of the time, the gains and losses of electoral support caused by the three components take
place in a rather coordinated fashion. Parties that lose support from defection to other parties tend
to also lose support from differential turnout and generational replacement, and the opposite seems
to work for parties that gain support. Thus, the forces that lead individuals to help or damage the
electoral prospects of particular parties seem to act in a similar direction regardless of the path we
look at. Nevertheless, the fact that the relationships are not very strong also shows that there is in
fact some degree of cancelling-out between the different components of volatility. The cases of
Germany (where correlations do not even reach statistical significance at p<.05) and Great Britain
(where there is only a highly significant correlation between the effects of party-switching and
differential turnout) provide clear evidence in this direction, suggesting that losses from one
component may often be compensated with gains from another.
[TABLE 4 ABOUT HERE]

23
In order to estimate the total amount of cancelling-out that takes place between components, it
is necessary to aggregate their effects at election level. This is what the next section deals with.
5.2 Analysis at election level: taking account of cancelling-out between components
The total amount of volatility that vanishes as a result of cancelling-out between components can
be better analysed by looking at what would happen were there no cancelling-out between
components. With this aim, we must first calculate the amount of ‘intra-component volatility’at each
election. This is done by applying Pedersen’s (1979) formula separately to the effect of each of the
components as shown in Table 5. The total sum of these effects at election level (the "flux of
volatility") is the amount of net volatility that would be found if no cancelling-out took place
between components (in the table, as well as in most real-world cases, that amount is higher than
actual net volatility).
It is also possible to calculate the percent contribution of each component to the total flux of
volatility produced by the three of them together. Note that this is not the average contribution of
each component to actual volatility (which was shown in the previous section) but the contribution
that the components would have if there was no cancelling out between them. In the example shown
in Table 5, the contribution of generational replacement to the flux of votes is 12.5%, while party-
switching and differential turnout represent 62.5% and 25% respectively.
[TABLE 5 ABOUT HERE]

24
Moving on to the data, Figure 4 shows the estimated contribution of each component to the total
flux of volatility in the 73 elections under study. As can be appreciated, switching is clearly the
component that generates most of the net flux of votes between elections. Even though there is
variation in this pattern, only in two cases is the effect of party-switching surpassed by that of
another component. One is the exceptional election of 1990 in Germany (the first after
reunification), where differential turnout clearly had a bigger effect (45% compared to 38% of
switching) due to the high levels of mobilisation among CDU/CSU supporters.
21
The second
exception is Great Britain in 1966, when the extraordinary low effect of switching (only 1.5% of
the vote share, the smallest amount in the sample) resulted in a higher contribution of turnout (54%
versus 36% of switching).
[FIGURE 4 ABOUT HERE]
On average, party-switching would represent 66% of volatility if there was no cancelling-
out between components, whereas differential turnout and generational replacement would
represent 20% and 14% respectively. This distribution contrasts with the figures on the amount of
actual change in party support caused by each component that were explained in the previous
section. The difference between them should give us an idea of how much the effect of each
component is weakened or reinforced by the effect of the other two components. As expected, the
presence of net switching is reinforced to a greater extent than the other components by the

25
cancelling-out between them (from 66% before cancelling-out to 75% of actual change in party
support, an increase of 9 points). Moreover, this reinforcement seems to happen at the expense of
both of the other two components. While the effect of differential turnout is reduced by 3 points
(from 20% to 17%), the contribution of generational replacement decreases by 6 points (from 14%
to 8%) after cancelling-out is taken account of.
Finally, to analyse how much volatility is cancelled out by the effect of the three components
working against each other, we can simply compare the amount of volatility without cancelling-out
between components (i.e. the total flux of volatility) with the Pedersen index as in Table 6. As can
be seen, the average amount of volatility in the sample would have been 1.32 percentage points
higher if no cancelling-out between components had taken place. In other words, we can argue that
about 11.5% of volatility is lost as a consequence of this process.
[TABLE 6 ABOUT HERE]
.
6 Concluding remarks
Which are the mechanisms more likely to be behind electoral volatility? This paper has provided
several answers to this question. First, it has developed a series of theoretical expectations about
which of the mechanisms leading to changes in election results is expected to have a more prominent
presence in aggregate volatility. Second, patterns of volatility have been analysed across 73
elections in 6 countries over an average time span of 50 years employing survey data, demographic
data and election records. The main finding is that, in spite of some variation, net volatility can be

26
claimed to be, by and large, an indicator of net switching. On average, party-switching produced
75% of the net volatility in the sample of elections analyzed, while differential turnout produced
17% and generational replacement 8%.
Though parties may, in principle, lose votes from one of the three mechanisms and gain votes
from another, this type of cancelling-out is demonstrated to have a very modest average effect.
Moreover, the small percentage of volatility that is absorbed by it (11% in the sample of elections
analyzed in this paper) tends to negatively affect both differential turnout and generational
replacement at the expense of vote-switching.
These findings have important implications. In spite of being one of the most popular variables
in political science, research trying to elucidate what exactly volatility (as measured by the Pedersen
index) reflects in terms of individual-level changes is absolutely scarce. This piece of research has
contributed to clarify this subject and, therefore, to alleviate, at least in part, the interpretation issues
of this aggregate indicator. Overall, research employing the Pedersen index can rest assured that
volatility is by and large reflecting the net effect of party-switching.
Having said that, the effects of both differential turnout and generational replacement cannot be
disregarded, as both of them account, on average, for 25% of volatility. Moreover, the effect of
generational replacement is larger that what should probably be expected given the low birth and
mortality rates of established democracies, which highlights the importance of taking account of
differences in the political preferences of different cohorts. Generational replacement was found to
produce an average 8% of party volatility, which is not little for a component that does not even
require any changes in voting behaviour in order to produce volatility.

27
In spite of its small effect, the potential of generational replacement to produce electoral change
over time in the long-term should not be overlooked. This is especially true for those parties that
have seen a steady decline in support over the past few years. In many of those cases, part of the
answer to their electoral decline could be found in the natural replacement of the electorate. For
example, the conservative party has lost over 11 percentage points in support from 1958 to 2010 in
Great Britain.
22
On average, generational replacement has cost the party about 0.9 points every
election year since the 1964 election, which amounts to almost 12 percentage points over the whole
period (partly compensated by the effect of other components of volatility). The opposite could be
said for the German Green Party. From 1980 to 2005, generational replacement granted the party
an average of 0.85 percentage points at every election. As a consequence, almost 67% of its votes
in the 2005 election were due to the replacement of older voters over a 25-year period with new
voters more sympathetic with the green cause. This is consistent with Franklin and Rudig's (1992)
finding that Green voters were overwhelmingly young at the time of the study.
This paper sets a stepping stone for further research, although there is still much work to be done.
The empirical analysis presented in this study is limited to six West European democracies. There
is arguably enough variation in volatility both across countries and over time in this sample so as to
make findings representative of most established democracies. However, there are reasons to think
that patterns of volatility might be different in other cases, especially in those countries that have
recently transitioned to democracy and where differential turnout or even generational replacement
might play a more important role. Studying the variations in the presence and strength of different
components of volatility should definitely be part of the agenda of scholars working on political

28
change. Moreover, the relative impact of some of the components of volatility may have changed
over time, which opens an extremely interesting avenue for further research.
Endnotes

29
1
Despite being the most widely used indicator of electoral instability, the Pedersen index is not the only one that
has been proposed. For example, Rose and Urwin (1970), suggested other indicators such as elasticity, variability
and persistence of party support. Ascher's (1975), on the other hand, suggests using "fluidity", which is measured
as the total pool of voters that might eventually be prone to change from and towards a given party. By contrast,
Ascher and Tarrow (1975) separated net change from total change, the latter resembling the notion of "gross
volatility" that measures the aggregate proportion of voters that switch parties between two elections.
2
Note that changes in the party system pose no particular problem for this formula. Parties that disappear are losing
parties, while new parties are considered winning parties. Following Bartolini and Mair (1990), party splits and mergers
are treated as if they all continued to be the same party at both elections t and t+1. This is because voters of those parties
cannot be considered to be switching voters.
3
For some examples, see the works cited in the previous paragraph.
4
In total, the surveys employed are the following: European Voter dataset of election studies (Thomassen, 2005b),
British Election Studies 1969-1987 (Heath, 1989), British Election Study 1997 (Heath et al., 2000), British Election
Study 2002 (Sanders et al., 2002), British Election Study 2005 (Clarke et al., 2006), British Election Study 2010
(Sanders et al., 2010), Danish Election Study 2001 (Andersen et al., 2002), Danish Election Study 2005 (Andersen et
al., 2005), Danish Election Study 2007 (TNS Gallup, 2007), Dutch parliamentary election study 1981-1984-1986
(van der Eijk et al., 1997b), Dutch parliamentary election study 1986-1989 (van der Eijk et al., 1997a), Dutch
parliamentary election study 1989-1994 (Anker and Oppenhuis., 1997b), Dutch parliamentary election study 2002-2003
(Irwin et al., 2005b), Dutch Parliamentary Election Study Cumulative Dataset, 1971-2006 (Aarts et al., 2010), German
Election Study 1998 (Schmitt and Wessels, 1998), German Election Study 2002 (Wessels and Schmitt, 2002), German
Election Study 2005 (Wessels, 2005), Norwegian Election Study 2001 (Valen and Aardal, 2008a), Norwegian Election
Study 2005 (Valen and Aardal, 2008b), Swedish Election Study 2002 (Holmberg and Oscarsson, 2004), and Sweden
Election Study 2006 (Holmberg and Oscarsson, 2008).
5
Note that national election surveys in the UK only include Great Britain.
6
Fortunately, wording of party choice questions is rather stable over time and no major issues have been identified.

30
Also, the questions were asked in a similar way across countries. Note, however, that in Germany two votes are
cast and so respondents are asked about both the candidate and the party list they chose. The vote choice variable
in this paper refers only to the latter.
7
The exception is the Netherlands. Most of the respondents in the Dutch parliamentary election surveys (with the
exception of years 1981 and 1986) had also been interviewed at the previous election and their past responses were
employed in the vote recall question in order to reduce error (Anker and Oppenhuis., 1997a; Aarts et al., 1999; Irwin et
al., 2005a; Todosijevic et al., 2010). It is important to mention that conclusions remain generally the same after
comparing Dutch results with the rest.
8
The main difference between panel data and cross-sectional surveys that has been found in the literature in this regard
is over-reported vote stability in the latter, as some respondents tend to declare current party preference rather than their
past choice (Waldahl and Aardal, 1982, 2000). In this paper, a weighting procedure based on actual election results will
be employed, as explained later, in order to deal with this problem. As Schoen (2011) argues, panel data are ‘neither
abundant nor without their own problems’, and cross-sectional studies are, despite their shortcomings, the best data
available to date for the purpose of comparing volatility across a vast number of elections and/or countries (eg. Anderson
et al., 2005; Carrubba and Timpone, 2005; Clark and Rohrschneider, 2009; Dalton, 2000; Hobolt, 2009; Schmitt et al.,
2009; Trystan et al., 2003).
9
In the sample, though, there is a moderately low number of missing cases (6.7% of missing cases for vote choice in
the last election and 8.8% regarding the previous election, with 4.4% of respondents giving no information on either
variable).
10
In this case, weighting seems more adequate than other methods that deal with missing data, particularly multiple
imputation. Multiple imputation is used to get more accurate standard errors from imputed data and what is required
here are simple point estimates.
11
IPF, also known as raking, is a well-established technique that can be used to calibrate estimation by integrating
disaggregated data from one source with aggregated data from others (Wong, 1992; Kalton and Flores Cervantes, 2003).
IPF may be useful for the reduction of bias associated with non-response, non-coverage and measurement error

31
(Battaglia et al., 2009; Flores Cervantes and Brick, 2008), especially when this is random with respect to the joint
distribution of vote for the two elections considered (Boyd, 1985, p.527). IPF consists in putting together actual
information on the margins of a distribution with individual survey data. Hence, what the iteration procedure does is
repeat calculations following a specified algorithm until they converge to adjust marginal information from different
sources keeping the cross-product ratios constant so that all the interactions that exist in the data are maintained (Bishop
et al., 1975; Simpson and Tranmer, 2005). The advantage of this method is that it produces good estimates of vote
transitions assuming that no or very little systematic bias is present that affects all the parties.
12
Demographic statistics come from the following sources: Danmarks Statistikbank (Denmark), Statistisches
Bundesamt (Germany), Centraal Bureau voor de Statistiek (Netherlands), Statistisk sentralbyrå (Norway), Statistika
centralbyrån (Sweden) and Office for National Statistics (Great Britain). Modifications of the voting age were taken
into account to calculate the number of new voters.
13
Mortality statistics come from Eurostat together with the sources mentioned in previous footnote.
14
This is a reasonable assumption in the light of demographic statistics. On average, people who died over 50 years old
between elections represented 92% of all deaths (standard deviation = 0.015).
15
The sample of "deceased electors" was randomly selected. If the data were not weighed by the actual election
results, this could potentially lead to random error, just as in a survey there is error produced by random sampling.
However, applying all weights after the "deceased electors" were created prevented that from happening and
ensured that the vote distribution in the survey mirrored actual election results and turnout rates.
16
The latter is computed by looking at how the results of the previous election change when deceased voters are
excluded. This mimics the process by which older voters' deaths affect election results in real life.
17
It is common practice to calculate the Pedersen index grouping very small parties into a category labelled "Others"
(for a discussion, see Bartolini and Mair, 1991). This strategy has been followed here when supporters of very
small parties were categorised as "Others" in the surveys. While some surveys did provide information on the
Scottish National Party and the Welsh nationalist party Plaid Cymru in Great Britain, these have been
systematically included into the "Others" category in the analyses - in fact, they are the only parties in such

32
category in most elections, as surveys for the United Kingdom do not include Northern Ireland. Owing to the
regional nature of these parties, including them in the same group does not impact results because vote transfers
between them are impossible.
18
The coefficient corresponds to a regression model using total vote change as dependent variable and the net effect
of switching as independent variable. This coefficient can be interpreted as "every point of total change in party
support corresponds to 0.75 points of change caused by switching". In other words, switching provides 75% of
every point of total change. The model uses fixed effects by party and country as the amount of changes in party
support might vary across these. Results are not shown but are available upon request.
19
See footnote 18. Results are not shown but are available upon request.
20
See footnote 18. Results are not shown but are available upon request.
21
Note that Eastern German voters were excluded from the sample, as the amount of volatility caused by these cannot
be attributed to any of the three components but to extraordinary reasons associated to that election. Note, too, that
election results and volatility in 1990 correspond to Western Germany only.
21
In the whole UK the decrease has actually been somewhat larger: about 13 percentage points.

33
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39
FIGURES AND TABLES
Table 1: The effect of switching on net volatility vs. other types of behaviour. Exemplary
scenarios.
Scenario 1
(switching): 5 voters switch parties.
Number of voters
Percentage of votes
Election t
Election t+1
Election t
Election t+1
Difference
Party A
40
45
40.0%
45.0%
5.0%
Party B
60
55
60.0%
55.0%
-
5.0%
Total voters
100
100
Volatility:
5
Scenario 2 (mobilization): 5 previous non-voters support A.
Number of voters
Percentage of votes
Election t
Election t+1
Election t
Election t+1
Difference
Party A
40
45
40.0%
42.9%
2.9%
Party B
60
60
60.0%
57.1%
-
2.9%
Total voters
100
105
Volatility:
2.9

40
Table 2: Countries and elections included in the analysis.
Country Election years
Denmark 1971 1975 1977 1979 1981 1984 1987 1988 1990 1994 1998 2001 2005 2007
Great Britain 1964 1966 1970 1974(a) 1974(b) 1979 1983 1987 1992 1997 2001 2005 2010
Germany

1965 1969 1972 1976 1980 1983 1987 1990

1994 2002 2005
Netherlands 1972 1977 1981 1982 1986 1989 1994 1998 2002 2006
Norway 1965 1969 1977 1981 1985 1989 1993 1997 2001 2005
Sweden 1960 1964 1968 1970 1973 1976 1979 1982 1985 1988 1991 1994 1998 2002 2006
(a) February, (b) October

Excludes Eastern Germany

41
Figure 1. Volatility (Pedersen index) over time in the six countries.
Source: own elaboration from Peter Mair's file of electoral volatility.
0 5 10 15
5 10 15 20
5 10 15 20
0 10 20 30
0 5 10 15 20
0 5 10 15
1955
1965
1975
1985
1995
2005
1955
1965
1975
1985
1995
2005
1955
1965
1975
1985
1995
2005
1955
1965
1975
1985
1995
2005
1955
1965
1975
1985
1995
2005
1955
1965
1975
1985
1995
2005
GB Denmark Germany
Netherlands Norway Sweden
Volatility (Pedersen index)
year

42
Figure 2: Estimated impact of vote switching on parties' electoral support.
Legend: Great Britain. LAB = Labour, CONS = Conservatives, LDem = Liberal Democrats; Denmark. SD = Socialdemocrats;
DRV = Radical Liberal Party; DKF = Conservative People's Party; CD = Centre Democrats; DanRets = Liberal Justice Party; SF =
Socialist People's Party; Grønne = Green Party; DHP = Humanists Party; SAP = Socialist Workers' Party; LibAll = Liberal Alliance;
DKP = Danish Communist Party; LC = Centre Liberal; Minorit = Minority Party; DF = Danish People's Party; KF = Christian
People's Party; APK = Communist Workers' Party; SP = Party of Schleswig; DU = The Independents; V = Liberals; VS = Left
Socialists; FP = Progressive Party; EL = Red/Green Union List; FK = Common Course; DemoForn = Democratic Renewal .
Germany. SPD = Social Democratic Party. CDU/CSU = Christian Democratic Union / Christian Social Union; FDP = Liberal Party;
Grünen = Greens; PDS = Party of Democratic Socialism; REP = The Republicans; Schill = Schill Party; Graue = Grey Party.
Netherlands. PVDA = Labour Party; CDA = Christian Democratic Appeal; KPD = Catholic People's Party; ARP = Anti-
Revolutionary Party; CHU = Christian Historical Union; VVD = People's Party for Freedom and Democracy; D66 = Democrats 66;
CPN = Communist Party of the Netherlands; PPR = Political Party of Radicals; PSP = Pacifist Socialist Party; DS70 = Democratic
Socialists '70; SGP = Reformed Political Party; GPV = Reformed Political League; BP (RVP) = Farmers' Party; RKPN = Roman
Catholic Party of the Netherlands; RPF = Reformatory Political Federation; EVP = Evangelical People's Party; CP (CD) = Centre
Party; SP = Socialist Party; GL = Green Left; ChrUn = Christian Union; PimFort = Pim Fortuyn. Norway. RV = Red Party; NKP =
Communist Party of Norway; SV = Socialist Left; DNA = Labour Party; V = Liberal Party; KRF = Christian Democratic Party; SP
= Centre Party; DLF = Liberal People's Party; H = Conservative Party; FRP/ALP = Progress Party; KP = Coastal Party. Sweden.V
CONSO thers LDemLAB
OthersCONSLDemLAB
LDemLAB CONSOthers
LABLDem
LDemOthers
CONS
LAB
Others
CONS
OthersLDem CONSLAB
CONSOthers LDemLAB
LABLDemCONSOthers
CONSOthersLDem LAB
LABOthersCONS LDem
OthersCONSLDemLAB
CONSLDemLAB Others
Others CONSLDemLAB
SDDan RetsSFDKFSPDRVDULC DKPVSV KF
CD DKPFPDKFDan RetsVSSF SDDRV KF V
V OthersCDFPKFDKPDRV DKFSDSF VSDanRets
CD DKFVSDanRetsDRVVFP SDSFOthersDKPAPKKF
FP APKVKFSD SAPDKPDRVDanRets CDSFDKFVS
SDSFDanRetsCD KFAPKVSV DKFDKPDRVSAPFP
GrønneDKF SFV DRVDKPFKDHPDanRetsSD FPSAPCDVSKF
FKVS SDVDRVDHPGrønneSFKFDKPDKFDanRetsCD FP
DanRetsELDRVCDFKSF VS VF POthersDKPGrønneKF SDDKF
VDKFSDDRVKFGrønneOthersFPFKDanRetsCDSF EL
VFP KFO thersELDKF CD DFSFDRVDemFornSD
CD DFOthers VKFELFPSF DRVSD DKF
MinoritOthersSDELSFDFKFDKFCD DRVV
LibAll SFKFDRV VELCDDFDKFSD
CDU/CSUSPDFDP Others
SPDOthersFDP CDU/CSU
CDU/CSUSPDOthers FDP
Others
CDU/CSU
FDPSPD
OthersGrünenCDU/CSU FDPSPD
SPD OthersFDP Grünen CDU/CSU
GrünenFDPOthersSPDCDU/CSU
GrünenF DPCDU/CSUSPD OthersPDS
FDP Other sPDSGr ünenCDU/CSU SPD
SchillREPOthers FDPSPD PDS Grünen CDU/CSU
FDPCDU/CSUNPDOther sG RAUEREP PDSGrünenSPD
PSP VVDCPNDS70SGPOthersD66 ARPKVP GPVBP(RVP)PPRRKPNCHU PVDA
DS70PPRPSPSG PCPNRKPN CDAGPVBP(RVP)D66 PVDAOthersVVD
DS70GPVPSPCP(CD)RPF D66SGPCDACPNRKPNVVDBP(RVP)PPRSPOthersEVPPVDA
GPVPPRPSPPVDAOthersEVPDS 70CP (CD)CDAD66 VVDSPRPFCPNBP(RVP)SGPRKPN
EVPSGPCP (CD)PSP D66PVDAOthers CDAPPRCPNVVD GPVRPF
D66CDAPVDAGPVEVPVVD SGPOt hersCP(CD)RP FGLSP
GPV D66CP(CD)PVDA RPFCDA VVDSGP OthersGLSP
RPF PVDAOthers GLCP (CD)D66 CDA SP VVDGPVSGP
ChrUnCP(CD)SGPSPD66 CDAGLVVDPVDA Others PimFort
GL ChrUnSGPD66PimFortCDA SPVVDPVDA Others
NKPSPHKRF SVDNA V
SPH DNAKRFNKPVSV
HKRFNKPSV DNARVSPFRP-ALPV OthersDLF
OthersSVNKPFRP-ALPVDLFKRFSPDNA RV H
SPDLFKRFFRP-ALPH RV DNAOther sSVV NK P
KRFH RVSPDNA Others FRP-ALPV SVNKP
VSV SPFRP-ALPH KRFRV DNAOthers
H NKPDNA KRFSVSP RVO thersV FRP-ALP
SVKRFSP RVDNA OthersFRP-ALP HV
DNAOthersSV FRP-ALPSPH KRF VRVKP
FPM SAPVCOthers
M FPSAP CV KDO thers
CV M SAPFP KDOthers
FPM VSAP COthersKD
SAPKD MCOt hersFP V
OthersVKD F PMCSAP
SAPKDVC FP MOthers
KDFP MGV MOthers SAPC
SAPVMGCKD F PM Others
MGSAPV KDCOthersM F P
C OthersSAP MVFP MG KDNyD
V SAPKD MNyD COthersMGFP
KDOthersC MFPSAP VMG
OthersM MG FPCKD SAPV
VKDSAPFP MG MOthersC
1964
1966
1970
1974
1975
1979
1983
1987
1992
1997
2001
2005
2010
1971
1975
1977
1979
1981
1984
1987
1988
1990
1994
1998
2001
2005
2007
1965
1969
1972
1976
1980
1983
1987
1990
1994
2002
2005
1972
1977
1981
1982
1986
1989
1994
1998
2002
2006
1965
1969
1977
1981
1985
1989
1993
1997
2001
2005
1960
1964
1968
1970
1973
1976
1979
1982
1985
1988
1991
1994
1998
2002
2006
-10 -5 0 5 10 -10 -5 0 5 10 -5 0 5
-10 -5 0 5 10 -5 0 5 10 -5 0 5 10
GB Denmark Germany
Netherlands Norway Sweden

43
= Left Party; SAP = Social Democratic Party; C = Conservative Party; FP = Liberal People's Party; M = Moderates; KD = Christian
Democrats; MG = Green Environmental Party; NyD = New Democracy.
Figure 3: Estimated impact of differential turnout on parties' electoral support.
See legend in Figure 2.
CONS Other s LDemLAB
OthersCONSLDem LAB
LDemLAB CONSOthers
LABLDem
LDemOthers
CONS
LAB
Others
CONS
OthersLDem CONSLAB
CONSO thers LDemLAB
LABLDem CONSOthers
CONSOthersLDem LAB
LABOt hersCONS LDem
Others CONSLDemLAB
CONSLDemLAB Others
OthersCONSLDemLAB
SDDanRetsSFDKFSPDRVDULCDKP VSV KF
CDDKPFP DK FDan RetsVSSF SDDRVKF V
V Others CDFPKFDKPDRVDKF SDSFVSDanRets
CDDKFVSDanRetsDRV VFP SDSFOthers DKPAPKKF
FPAPKV KFSD SAPDKPDRVDanRets CDSF DKFVS
SDSFDanRet sCD KFAPKVSV DK FDKPDRVSAPFP
GrønneDKF SFVDRVDKPF KDHPDanRetsSD FPSAPCDVSKF
FKVSSD VDRVDHPGrønneSFKFDKP DKFDanRetsCD FP
DanRetsELDRV CDFKSFVS VFP OthersDKPGrønne KF SDDKF
VDKFSD DRVKFGrønneOt hersFPFKDanRetsCDSF EL
VFPKFOthersELDKF CD DFSFDRVDemFornSD
CDDFOthers VKFELFPSF DRVSD DKF
MinoritO thersSD ELSF DFKFDKFCD DRVV
LibAll SFKFDRVV ELCD DFDKF SD
CDU/CSU SPDFDPOthers
SPDOthersFDPCDU/CSU
CDU/CSU SPDOthers FDP
OthersCDU/CSU FDPSP D
OthersGrünenCDU/CSU FDPSPD
SPDOthersF DPGrünenCDU/CSU
GrünenFDP Ot hersSPDCDU/CSU
Grünen FDPCDU/CSUSPD OthersPDS
FDPOthers PD SG rünenCDU/CSU SPD
SchillRE POthersFDPSPD PDSGrünenCDU/CSU
FDPCDU/CSU NPDOthersGRAUEREP PDSGr ünenSPD
PSPVVDCPNDS70SGPO thers D66ARPKVP GPVBP(RVP) PPRRKPNCHUPVDA
DS70PPRPSPSGPCPNRKPNCDAGPVBP(RVP)D66 PVDAOt hersVVD
DS70GPVPSPCP(CD)RPFD66SGPCDACPNRKPNVVDBP(RVP)PPRSPO thersEVPPVDA
GPVPPRPSPPVDAOthersEVPDS70CP(CD)CDAD66 VVDSPRPFCPNBP(RVP)SGPRK PN
EVPSGPCP(CD)PSPD66PVDAOt hersCDAPPRCPNVVDGPVRPF
D66CDAPVDAG PVEVPVVDSGPOthersCP(CD)RPFGLSP
GPV D66CP(CD)PVDARPFCDA VVDSGP Ot hersGLSP
RPFPVDAOthers GLCP(CD) D66CDA SPVVDGPVSGP
ChrUnCP(CD)SGPSPD66 CDAGLVVDPVDA Others PimFort
GLChrUnSGPD66PimFortCDA SPVVDPVDA Others
NKP SPHKRF SVDNA V
SPHDNAKRFNKPVSV
HKRFNKPSV DNARVSPFRP-ALPVOthersDLF
OthersSVNKPFRP-ALPVDLFKRF SPDNA RV H
SPDLFKRFFRP-ALPH RV DNAOthersSVVNKP
KRFH RV SPDNA Others F RP-ALPV SVNKP
VSV SPFRP-ALP H KRFRVDNA Others
HNKPDNA KRFSVSP RVOt hersV FRP-ALP
SVKRFSPRVDNA OthersF RP-ALP HV
DNAOt hersSV FRP-ALPSPHKRF VRVKP
FPM SAP VCOther s
M FPSAPC VKDOthers
CV M SAPFPKDOthers
FP MVSAP COthersKD
SAPKDM COthersF P V
OthersVKDFPM CSAP
SAP KD VCFP MOt hers
KDF P MGVMOthers SAPC
SAP VMGCKD FPMOthers
MGSAPV KDCOthersMFP
C OthersSAP MV FPMG KD NyD
V SAPKDMNyD COthersMGF P
KDO thersC MF PSAP VMG
OthersM MG FPCKD SAPV
VKDSAPFP MG MOthersC
1964
1966
1970
1974
1975
1979
1983
1987
1992
1997
2001
2005
2010
1971
1975
1977
1979
1981
1984
1987
1988
1990
1994
1998
2001
2005
2007
1965
1969
1972
1976
1980
1983
1987
1990
1994
2002
2005
1972
1977
1981
1982
1986
1989
1994
1998
2002
2006
1965
1969
1977
1981
1985
1989
1993
1997
2001
2005
1960
1964
1968
1970
1973
1976
1979
1982
1985
1988
1991
1994
1998
2002
2006
-4 -2 0 2 4 -2 -1 0 1 2 -3 -2 -1 0 1 2 3
-2 0 2 4 6 -2 -1 0 1 2 -2 -1 0 1 2
GB Denmark Germany
Netherlands Norway Sweden

44
Figure 4: Estimated impact of generational replacement on parties' electoral support.
See legend in Figure 2.
CONS OthersLDemLAB
OthersCONSLDemLAB
LDem LABCONS Others
LABLDem
LDemOthers
CONS
LAB
Others
CONS
OthersLDemCONS LAB
CONS Others LDemLAB
LABLDemCONS Others
CONS O thersLDem LAB
LABOthersCONS LDem
OthersCONS LDemLAB
CONS LDemLAB Others
OthersCONS LDemLAB
SDDanRetsSFDKF SPDRVDULCDKPVSV KF
CD DKPFPDKFDanRetsVSSFSD DRVKF V
V OthersCD FPKF DKPDRVDKF SDSFVSDanRets
CD DKFVSDanRetsDRVV FPSD SFOthersDKPAPKKF
FPAPKV KFSD SAPDK PDRVDanRetsCD SFDKFVS
SD SFDanRetsCDKF APKVSV DKFDKPDRVSAPFP
GrønneDKF SFV DRVDKPFKDHPDanRetsSDFPSAPCD VSKF
FKVSSDV DRVDHPGrønneSFKFDKPDKFDanRetsCDFP
DanRetsELDRVCDF KSF VSVF P Ot hersDKPGrønneKF SDDKF
VDKFSD DRVKFGrønneOthersFP FKDanRetsCD SFEL
VFP KFOt hersELDKF CDDFSFDRVDemFornSD
CDDFOthersVKF ELFP SFDRVSDDKF
MinoritOthersSD ELSFDFKFDKFCD DRVV
LibAllSFKFDRVV ELCDDFDKFSD
CDU/CSUSPDFDPOthers
SPDOthersFDPCDU/CSU
CDU/CSU Others FDP
OthersCDU/CSUFDPSPD
OthersGrünenCDU/CSU FDP
SPD
SPD OthersFDP
Grünen
CDU/CSU
FDPOthersSPDCDU/CSU
GrünenF DPCDU/CSU SPDO thersPDS
FDPOthersPDS
Grünen
CDU/CSUSPD
SchillREPOthersFDP SPDPDS GrünenCDU/CSU
FDPCDU/CSU NPDOthersGRAUEREPPDSGrünenSPD
PSPVVDCPNDS70SGPO thersD66ARPKVPGPVBP(RVP)PPRRKPNCHUPVDA
DS70PPRPSPSGPCPNRKPNCDA GPVBP(RVP)D66 PVDAOthersVVD
DS70GPV PSPCP(CD)RPF D66SGPCDA CPNRKPNVVDBP(RVP)PPRSPOthersEVPPVDA
GPVPPRPSPPVDAOthersEVPDS70CP(CD)CDAD66 VVDSPRPFCPNBP(RVP)SGPRKPN
EVPSGPCP(CD)PSPD66PVDAOt hersCDA PPRCPNVVDGPVRPF
D66CDAPVDA GPVEVPVVDSGPO thersCP(CD)RPFGLSP
GPV D66CP(CD)PVDA RPFCDA VVDSGPOthersGLSP
RPFPVDAOthers GLCP(CD)D66CDA SP VVDGPVSGP
ChrUnCP(CD)SGPSPD66CDA GLVVDPVDA Others PimFort
GLChrUnSGPD66PimFortCDA SPVVDPVDAOthers
NKPSPHKRF SVDNAV
SPH DNAKRFNKPV SV
HKRF NKPSVDNARVSPFRP-ALPVOthersDLF
OthersSVNKP FRP-ALPVDLFKRF SPDNA RVH
SP DLFKRF F RP-ALPHRVDNAOt hersSVVNKP
KRF H RVSPDNA Others F RP-ALPV SVNKP
V SVSPFRP-ALPHKRF RVDNA Ot hers
H NKPDNA KRFSVSP RVOthersV FRP-ALP
SVKRFSP RVDNA OthersFRP-ALPHV
DNAOthersSV F RP-ALPSPH KRFVRVKP
FPM VC Others
M FP
SAP
C V KDOthers
CVM SAPF PKD Others
FP M VSAPC OthersKD
SAPKDM COthersFP V
OthersVKDFPM CSAP
SAPKD VCFPM Others
KDFP MGVMOthersSAPC
SAPVMGC KD FPMOt hers
MGSAPVKDC OthersM F P
C OthersSAP MVFP MGKD NyD
VSAPKD MNyDC OthersMGFP
KDOthersC MFPSAP VMG
OthersM MGF PCKD SAP V
VKDSAPFP MGMOthersC
1964
1966
1970
1974
1975
1979
1983
1987
1992
1997
2001
2005
2010
1971
1975
1977
1979
1981
1984
1987
1988
1990
1994
1998
2001
2005
2007
1965
1969
1972
1976
1980
1983
1987
1990
1994
2002
2005
1972
1977
1981
1982
1986
1989
1994
1998
2002
2006
1965
1969
1977
1981
1985
1989
1993
1997
2001
2005
1960
1964
1968
1970
1973
1976
1979
1982
1985
1988
1991
1994
1998
2002
2006
-2 -1 0 1 -2 -1 0 1 -2 -1 0 1
-2 -1 0 1 2 -2 -1 0 1 2 -2 -1 0 1
GB Denmark Germany
Netherlands Norway Sweden

45
Table 3: Correlations between the impact of the three components of switching on parties'
electoral support change between elections.
All
Countries
Denmark
Great
Britain Germany
Netherlands
Norway Sweden
net vote switching 0.97 0.98 0.98 0.88 0.98 0.97 0.98
differential turnout 0.78 0.72 0.90 0.43 0.84 0.87 0.76
generational replacement 0.53 0.55 0.36 0.39 0.66 0.63 0.54
N (parties) 626 175 52 60 130 95 114
All correlations are significant at p<0.01

46
Table 4: Zero-order correlations between the net effect of the components of volatility at party
level.
Great Britain Denmark
n=52 Switching Diff. Turnout
n=175 Switchi
ng
Diff. Turnout
Diff. Turnout 0.85*** 1 Diff. Turnout 0.59***
1
Gen. Rplmt 0.24* 0.17 Gen. Rplmt 0.43***
0.37***
Germany Netherlands
n=60 Switching Diff. Turnout
n=130 Switchi
ng
Diff. Turnout
Diff. Turnout 0.04 1 Diff. Turnout 0.74***
1
Gen. Rplmt 0.05 0.23* Gen. Rplmt 0.55***
0.51***
Norway
Sweden
n=95 Switching Diff. Turnout
n=114 Switchi
ng
Diff. Turnout
Diff. Turnout 0.75*** 1 Diff. Turnout 0.66***
1
Gen. Rplmt 0.46*** 0.59*** Gen. Rplmt 0.41***
0.48***
*** p<0.01, ** p<0.05, * p<0.1

47
Table
5: Net
switching, differential turnout
and
generational
replacemen
t
and their
corresponding
contribution
to
the flux of
v
olatilit
y
.
party-switching
differential turnout
generational replacement
Party A
-4 2 -1 -3
Party B
-1 0 1 0
Party C
5 -2 0 3
Total volatility:
3
a
b
c
Total (a+b+c)
Component effect
5 2 1 8
Contribution
62.5% 25% 12.5%
Note: Figures in the upper table stand for losses or gains of vote share.

48
Figure 5:
Relative
contribution
of each
comp
onen
t
to the flux of volatilit
y
(stac
k
ed
areas).
0 50 1000 50 100
1965
1970
1975
1980
1985
1990
1995
2000
2005
2010
1975
1980
1985
1990
1995
2000
2005
1965
1970
1975
1980
1985
1990
1995
2000
2005
1975
1980
1985
1990
1995
2000
2005
1965
1970
1975
1980
1985
1990
1995
2000
2005
1960
1965
1970
1975
1980
1985
1990
1995
2000
2005
GB Denmark Germany
Netherlands Norway Sweden
net switching differential turnout generational replacement
% of the total flux of volatility
year

49
Table 6:
Average volatility (Pedersen index) and total flux of volatility and paired t-test of the
difference
Mean S.E.
Volatility (Pedersen Index) 10.15 (0.63)
Total flux of volatility 11.47 (0.63)
Difference -1.32*** (0.11)
N (elections) = 73
*** p < 0.01
Word count: 7,593
Date: 7/3/2015