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On the mechanism of change and

stability in multiparty elections

B A C K G R O U N D P A P E R

Joost Smits, Political Academy, Amster dam (NL)

14 June 2014 1

ABSTRACT

Although scholars find a certain stability in the geographical distribution of election results, the question remained how

this related to the fluctuating outcome of elections. When Dutch voters are presented as being "adrift", or "floating",

what is the mechanism of change and stability in multiparty elections? It will not explain voters' motivations at the

individual level, but treat (aggregate) distributions of voters (constituencies, voting stations, individuals), relationships

between voter distributions, and how they can be measured. Which can provide context to individual level research. This

mechanism can back up survey outcome (based on sample data), or question the validity of such outcome.

This paper contains a more elaborate explanation of an analysis of the elections in Rotterdam (Smits 2014a). What is

uniform swing? When occurs spatial variability? When are parties competitors and when are they counterparts? When

do geographical distribution maps change, and why are they often stable? A logical mechanism will be presented that

allows empirical research, and divides possibilities and impossibilities. What is the practical use?

INTRODUCTION | ONE

Voting results can be presented as geographical distribution maps. The results of voting stations can be divided into

percentile groups, and coloured accordingly. When eyeballing such maps of different elections for a certain political

party, one gets a sense of the stability of the geographical origin of the electoral support for that party. Examples are

the maps for the Netherlands for the 2010 and 2012 elections on the website of the Dutch newspaper NRC Handelsblad

(Poort 2012), but can also be seen in geographical maps of elections in Rotterdam from 1998-2014 (Smits 2014a), and

in the atlas of Dutch elections between 1848 and 2010 (de Jong, van der Kolk, and Voerman 2011).

FIGURE 1: DISTRIBUTION MAP OF VOTING STATION RESULTS, PVDA (SOCIAL-DEMOCRAT PARTY), MUNICIPAL ELECTIONS IN ROTTERDAM,

2010 AND 2014.

Voting stations fluctuate in location and number. Green: highest quartile, blue: 2nd quartile, purple: 3d quartile, red: lowest quartile. Note

that in 2010 the party got 28.9% of all votes, and in 2014 only 16.4%.

1 Presented as background to a paper on disaggregation of voter results (Smits 2014b) at the 13th Dutch-Belgian Political Science

Conference (Politicologenetmaal) at Maastricht University, 12-13 June 2014, Workshop 4: Dealigned Electorates - Short-Term Vote

Choice Determinants. Chaired by Ruth Dassonneville and Joost van Spanje, discussant of the paper was Marc Hooghe. This 14 June

version contains minor improvements, and one extra chapter suggested by discussant.

On the mechanism of change and stability in multiparty elections

Can one infer conclusions about voters from this? Daudt wrote in his thesis in 1961: "It is, in fact, quite possible that, for

instance, 30 per cent of all enfranchised persons switch their preference between elections I and II, and 10 per cent between

elections II and III, and that this 10 per cent consists entirely of persons who did not belong to the 30 per cent of the time

before." (1961, 160) Indeed, that may be quite possible, but would it be possible to discover a mechanism that can give

some context to the range of possibilities?

We would need some more unambiguous statement than "eyeballing", and even go beyond pure observations. As Taylor

and Johnston (1979, 81) described, "eyeballing" is a very subjective way of testing a hypothesis, and they advocate the

use of inferential statistics. Indeed the use of for example linear correlation and regression allows to measure the

relationship between the results of two elections.

To learn about the mechanism of change and stability we need to find out what the different variables in such correlation

and regression mean.

UNIFORM SWING | TWO

A good starting point to investigate the mechanism would be with Butler and Stokes' "Evolution of electoral choice". They

provided a qualitative approach in describing "uniform swing" between elections (1974, 140–151). With "swing" being

the change in percentage points between elections for one of two parties. They describe that "evenness of swing" relates

to a low standard deviation of swing, which was 3 times as great in the United States between 1952 and subsequent

elections until 1960 as in Britain between 1950 and 1974 (1974, n. 1, p. 121).

However, this is only practical for two-party systems, since with multiple parties in elections, the change of one party

does not relate directly to one of the other contenders. Johnston (1983) compares the results per party in two elections. It

is important to note he does not plot the percentage change, but two elections against each other:

FIGURE 2: PERCENTAGE CHANGE PLOTTED AGAINST RESULTS

FIGURE 3: ELECTIONS PLOTTED AGAINST EACH OTHER

The benefit of this approach is that the statistical conformity of the regression line through the plotted results of the

elections can be measured. Although easier to "eyeball", a uniform swing (a straight line as in Figure 2) has no

correlation with the previous election.

Johnston described the regression line with the equation , later improved by Aarts and Horstman (1991, 7)

to:

(1.1)

Where is the percentage that voted for party in election year and , respectively.

A regression line with coefficient , which intersects the x-axis at an angle of 45 degrees, is then called "uniform

swing". The degree of conformity between the regression line and the actual values can simply be calculated with

correlation coefficient R2. If it is 1, then Johnston considered the uniformity as not random, and if it is lower than 1 it was.

Johnston concluded that this approach is superior to others, since the spatial variation can be observed, which is much

greater than was assumed so far. Other analytical methods stress spatial stability. Johnston plotted regression lines for

the conservative, labour and liberal parties in England from 1955-1974. He noted that election swing closely related to

previous party strength in the region. Thus, where a party was big, the biggest changes were found, and where a party

was small had been the smallest changes. Even though the geographical distribution would be stable, most change was

not uniform, "adding another topic for analysis of the geography of electoral change". (1983, 58).

Aarts and Horstman took this up in 1991. They investigated different slopes. See their Figure 2, reproduced below as

Figure 4. It involves two elections, in regions A, B and C. In Option II, the results in both elections are the same. In Option I

0

0,5

1

1,5

2

2,5

020 40 60 80 100

Differe nce in %-points

Votes previous e lection (%)

"Uniform swing"

0

50

100

150

020 40 60 80 100

Votes curr ent election (%)

Votes previous e lection (%)

"Uniform swing"

On the mechanism of change and stability in multiparty elections

the party is winning, and in Option III it is losing. The coefficients of the lines of the options I, II and III are 1.50, 1.00

and 0.50, respectively. Aarts and Horstman add Option Ia, which like Option I indicates profits, but with equal numbers

by region (uniform swing). The line runs parallel to Option II, only at a higher level. All regions gained the same amount

of percentage points in Option Ia, contrary to Option II, where the party remained stable (did not gain), and Option I,

where the party gained more in popular regions.

FIGURE 4: CHANGE (figure 2 of Aarts and Horstman)

With Aarts and Horstman the lineair equation (1.1) acquired notions of vote gain ( ) and vote loss ( ). And

another important information bit: indicates the amount of uniform swing. When , (the intercept) is equal to the

average change in percentage points.2

FIGURE 5: PVV (DUTCH FREEDOM PARTY), PARLIAMENTARY

ELECTIONS 2012 COMPARED TO 2010

Voting station results were (roughly) aggregated by

neighbourhood (Statistics Netherlands classification, n=5544).

PVV lost votes, which is expressed by . The votes were

mainly lost relative to the popularity of the party ( , R2 close

to 1).

VARIABILITY AND CHANGE | THREE

Neither Johnston, nor Aarts and Horstman give much thought to the correlation coefficient R2. Johnston dichotomised as

random/not random: "That most of the R2 values are very large indicates that this non-uniform change is not random"

(1983, 58). Aarts and Horstman called it the "coefficient of determination" (1991, 7).

It can be demonstrated that R2 is much more important to indicate change than perceived before. And that R2 < 1 does

not relate to randomness, but to measurable influences.

2 Aarts and Horstman erroneously treat a "serious" flaw (1991, 7) of Johnston. They give meaning to , as indicator of uniform swing.

However, they say Johnston should not estimate the value of through regression analysis, but use the average change as intercept.

Which is not so. This can be seen with actual data (for example PvdA Rotterdam 2014), but also by calculating the intercept of the

regression line "Option III" in Figure 4. The average change is -20. The line should then have been drawn not through the origin, but

through (0,-20). Which Aarts and Horstmann obviously did not see fit themselves. It is only true when . Nevertheless, testing this

error and thinking about it, formed in large part the contents of this paper. And it is only a minor argument in Aarts and Horstman's

extension of Johnson's work. Also see (Smits 2014a, 5).

0

10

20

30

40

50

60

70

80

90

100

020 40 60 80 100

Percentage results in second election

Percentage results in first election

OptionI

OptionII

OptionIII

OptionIa

y = 0,7128 x - 0,0088

R² = 0,9122

0%

10%

20%

30%

40%

50%

60%

0% 10% 20% 30% 40% 50% 60% 70%

Percentage results in 2012

Percentage results in 2010

On the mechanism of change and stability in multiparty elections

As mentioned above, when electoral globule maps and other distribution maps are created, they appear to be quite

similar from one election year to the next. How does the change of maps relate to the voter transition in Option I, II, III, Ia

of Figure 4?

Let's look at an example, referring to the geographical distribution maps of Figure 1. The voting stations in the highest

quartile were coloured green, the quartile below that blue, then purple and then red. Figure 6 shows that if R2 = 1, given

some values for the quartiles, given equation (1.1), voting stations do not skip between quartiles. Plotted is Option I, but

the same goes for the other regression lines, as long as R2 = 1. The voting stations with the lowest scores in the first

election, also will get the lowest scores in the second election. And the voting stations with the best scores in the first

election end up with the best scores in the second election.

FIGURE 6: DISTRIBUTION

Hence, if R2 = 1, or close to 1, there will not be respectively any or much change in the geographical distribution maps.

No spatial variability. All (R2 = 1) or most (R2 near 1) globules will have the same colour in election 2 as in election 1.

Independent of the values of and in equation (1.1).

Johnston found many values of R2 very close to 1 (1983, 57)3. Which means parties do not attract voters from new

regions. So, where then do these voters go to or come from?

COMPETITORS AND COUNTERPARTS | FOUR

Besides plotting election results on maps in a geographical distribution (Figure 1), or against the results of another

election (Figure 2-Figure 4), we can also sort the party outcome from high to low and put it in a curve:

FIGURE 7: CURVE OF SORTED OUTCOME FOR THE "BLUE PARTY"

The slope of the curve can be described with the "people's party index" (Smits 2012). A "people's party" scores high in

many voting stations. An "elite party" relies on lots of votes in a few voting stations. The index is calculated by counting

the number of voting stations that score higher than average, divided by the total number of stations, times 100%. If the

result is higher than 50% we have a "people's party", otherwise we consider it an "elite party". When all votes are

added, they can be equally large. A people's party has a very straight slope, and the "Blue Party" in Figure 7 is an

extreme example of an elite party. The stronghold, at the left, points to certain regions where the party is very popular.

Suppose there is a second party, the "Red Party", which is popular in regions where the Blue Party is not:

3 See (Smits 2014a) for Rotterdam 2010-2014. Figures for Netherlands between 2010 and 2012 were presented at the conference

"Feiten, feiten, feiten", in Zwolle on 13 May 2014, and will be repeated in further papers. R2 is usually close to 1.

0

10

20

30

40

50

60

70

80

90

100

020 40 60 80 100

Percentage result s in second election

Percentage results in first election

OptionI

=

3

2 + 0

most

less

few

very few

On the mechanism of change and stability in multiparty elections

FIGURE 8: CURVES OF BLUE AND RED PARTY

From the previous paragraph we know that when R2 is 1 or close to 1, regions with high scores in election 1 remain high

in election 2, and regions with low scores remain low. In that case voting stations in the left part of the blue curve, where

popularity for the Blue Party is high, will not turn massively to the Red Party. And voting stations in the left part of the

red curve, where the Red Party is unpopular, will not turn massively to the Blue Party.

The Blue Party and Red Party therefore are not competing for the same voters. They should be considered antipodes, or

counterparts.

Can Blue and Red attract new voters, even when R2 is 1 or close to 1? In multiparty systems, like the Netherlands, there

are usually more parties. See the curve of the "Green Party" in the next figure:

FIGURE 9: CURVES OF BLUE, RED AND GREEN PARTY

One can imagine that the Blue Party can acquire quite large amounts of Green voters within the bounds of equation

(1.1), and with R2 remaining 1 or close to 1. Blue and Green compete for the same voters. Red and Green hardly do.

Red and Green, Red and Blue are counterparts. Blue and Green are rivals, or competitors. A party's competitors are

parties whose constituencies overlap. Counterparts are parties with very different supporters' habitats.

FIGURE 10: CURVES OF LEEFBAAR ROTTERDAM (LR, LIVABLE ROTTERDAM), AND PVDA (SOCIAL

DEMOCRATS ROTTERDAM), MUNICIPAL ELECTION 2014

Voting station results were normalised and sorted, for LR from high to low, for PvdA from low to

high, to give a clearer picture. Analysis shows they are popular in different neighbourhoods, they are

not competitors but counterparts (Smits 2014a). Note LR is a "people's party" according to the

definition in this paper, with a straight slope, and PvdA is an elite party with strongholds.

PRACTICAL USE | FIVE4

The relevancy of this mechanism can be demonstrated with a few practical examples.

4 This chapter was added after discussion at the conference.

Percentage results vot ing stations (sort ed)

1. PvdA

2. LR

On the mechanism of change and stability in multiparty elections

a. Voter transition

A researcher may suspect that in an election party X mainly won because of transfer of votes from party Y. The

researcher can plot maps of the places where parties X and Y are popular in election 1 and 2, and calculate the

similarity between both parties' catchment areas. That gives clues to the competitiveness between party X and party Y. If

they are competitors, plotting a regression line with equation (1.1) should show that R2 is close to 1 for party X and if

party Y is supposed to have lost mainly to party X also party Y should have R 2 close to 1. If they are counterparts, the

regression should show a low R2. Further research can be done to learn more about voters' individual motivations.

b. Party decline (and ris e)

A researcher may see a party X lose (or win) votes, and wonder where these votes are going to (or coming from). Indeed

there are several techniques to calculate transition, but the logical mechanism provides extra information. First the

regression line with equation (1.1) can be calculated, to see if the decline is just because a competitor is gobbling up all

voters, or because an unexpected counterpart got hold of the voters. Which may be examined from perspectives

differing from an internal (party turmoil) or external (economy, natural disaster) crisis, or bad choice in candidates, a

bad campaign with unclear of undirected messages at voters, etc. Party rise can be examined along similar lines, and

research may want to look at that a party may gain votes in crisis, which are lost again when the crisis dissipates.

When R2 is known can be calculated which parties are competitors, or happened to compete. Maps can serve to point to

geographic problem areas. Which can inspire further research, on individual or aggregate level. Including conclusions

about the changing status of the party as "people's party" or "elite party".

c. Test individual l evel results

Individual level research may find that voters have equal preference for party X or party Y. That may lead to

conclusions that parties X and Y are competitors. Although individual level and aggregate level research can have quite

different outcome, it goes beyond say that in case of elections voters at some point go to voting booths, which aggregate

outcome should not be discarded because of its "aggregateness". If party X and party Y are true competitors there

should be some similarity in the aggregate outcome of the votes, or a very good explanation why that is not the case.

Also, if party X is supposed to have gained lots of votes mostly from party Y, and they are supposed to be competitors,

at least the R2 of the equation (1.1) of party X should be close to 1.

An example of individual level equal preferences that disappear at aggregate level: a researcher may interview low-

income shoppers about their inclination to choose between a supermarket with relatively high prices, and a discount

supermarket. And high-income shoppers about the same choice. That research may point out equal preferences. But in the

end the low-income shoppers on aggregate level may favour the discount supermarket, and the high-income shoppers

supermarkets the more expensive supermarket. Indeed they may be considered competitors at the individual level, but if

in the end they make different choices, what is the point of that qualification? These supermarkets are to be considered

counterparts.

Finally, a researcher must watch out that the inclination to participate in research does not disturb the validity of research

outcome for the entire population. Individual level research usually is based on population samples, where voting station

outcome contains the entire population (including abstainers, blank and invalid votes).

d. Micro-targeting

Micro-targeting is a marketing strategy for political parties which involves diversification in its campaign and messages,

tailor made to subgroups in the electorate. The mechanism could be used as the basis of disaggregation of voter results

to geographical levels below voting stations, for example neighbourhoods, streets or postal codes, using underlying

characteristics. More about that in (Smits 2014b).

Parties could calculate the "normal" competitors in municipalities or regions, to address voters in regions that may be

threatened by competitors with messages partly based on messages, achievements and errors of competitors. Or try to

attack competitors via their voters to gain more votes.

CONCLUSION

The logical mechanism of change in multiparty elections can be described through (at the moment) three procedures that

interlink, and which describe variables that can be measured and calculated.

The first is the geographical distribution map; election outcome in a spatial representation. This allocates geographical

co-ordinates to election results.

On the mechanism of change and stability in multiparty elections

The second procedure is a linear correlation and regression of election results on equal co-ordinates (or aggregated to

the same neighbourhood, constituency, town, region), as described by Taylor and Johnston (1979), Johnston (1983) and

Aarts and Horstman (1991).

In the equation , refers to the uniform swing: the percentage point change all voting stations experience.

refers to variable swing. When the party generally loses votes, when the party wins. When there

is uniform swing.

If the conformity of the regression, R2, is 1 or close to 1, geographical distribution maps do not change, and parties only

gain voters in regions they were popular before. They will not attract many voters from competitors, or in new regions.

Maps of the same party in subsequent elections only show major differences when R2 is far from 1. R2 not being 1 should

not be seen as "random", but only means that the linear equation apparently does not fit the swing between elections. A

party may have put a candidate on the bill that is attractive to voters of another party, or, a party may have adopted

non-party specific political ideas, etc.

The third procedure involves the correlation between parties. Are they popular in the same voting stations or regions, or

in different stations or regions? Are they competitors, or counterparts? This enables proper assessment of changes,

beyond observations of the fluctuation of the final outcome, and beyond surveys of what voters believe themselves about

the competition between parties. And subsequent conclusions of researchers about the flow of voters between parties

based on those surveys.

For example, if a party gains votes, it is logical that these come from a party competing for the same voter habitat. That

habitat must share common characteristics, with a common geographical pattern. Except when R2 is far from 1.

If a researcher was to claim that two parties compete for the same voter group, without a similar vote distribution over

voting stations or geographical areas, he must show that for one or the other R2 was far from 1, or provide some

common characteristic that explains the geographical spread, that fits the logical mechanism.

SUGGESTIONS FOR FURTHER RESEARCH

A "people's party" is less prone to lose voters to competitors than an "elite party".

LITERATURE

Aarts, K., and R. Horstman. 1991. ‘Political Change And The Electoral Geography Of The Netherlands’. In ECPR Joint

Sessions of Workshops, Essex.

Butler, D., and D. Stokes. 1974. Political Change in Britain: The Evolution of Electoral Choice. 2nd ed. London: Macmillan.

Daudt, H. 1961. Floating Voters and the Floating Vote: A Critical Analysis of American and English Election Studies. Kroese.

http://books.google.nl/books?id=imuGAAAAMAAJ.

De Jong, R., H. van der Kolk, and G. Voerman. 2011. Verkiezingen op de kaart 1848-2010: Tweede Kamerverkiezingen

vanuit geografisch perspectief. Utrecht: Matrijs.

Johnston, R.J. 1983. ‘Spatial Continuity and Individual Variability: A Review of Recent Work on the Geography of

Electoral Change’. Electoral Studies 2 (1): 53–68. doi:10.1016/0261-3794(83)90106-3.

Poort, A. 2012. ‘Wat Stemden Uw Buren? Bekijk de Uitslag per Stembureau (i.s.m. J. Smits)’. NRC Handelsblad.

http://www.nrc.nl/verkiezingen/2012/10/03/wat-stemden-uw-buren/.

Smits, J.H.F. 2012. Kamerverkiezingen in Rotterdam - Observaties (in Opdracht van de Stadskrant van de Gemeente

Rotterdam). Berkel en Rodenrijs.

http://www.politiekactief.net/files/Observaties%20Rotterdam%20TK2012.pdf.

———. 2014a. De Onvermoede Stabiliteit van de Rotterdamse Verkiezingen - Observaties. Berkel en Rodenrijs: Stichting

Politieke Academie. http://www.politiekactief.net/files/Observaties%20Rotterdam%20GR2014.pdf.

———. 2014b. On Disaggregation of Voter Results. Amsterdam/Berkel en Rodenrijs: Stichting Politieke Academie.

http://www.researchgate.net/publication/263089862_On_disaggregation_of_voter_results.

Taylor, P.J., and R.J. Johnston. 1979. Geography of Elections. New York: Holmes & Meier Publishers.

http://books.google.nl/books?id=pUOFAAAAMAAJ.

Van Gent, W.P.C., E.F. Jansen, and J.H.F. Smits. 2014. ‘Right-Wing Radical Populism in City and Suburbs: An Electoral

Geography of the Partij Voor de Vrijheid in the Netherlands’. Urban Studies 51 (9): 1775–94.

doi:10.1177/0042098013505889.

BIOGRAPHY

Joost Smits (1965), MA in Public Administration (University of Twente), researcher at Political Academy (Amsterdam),

works on PhD (University of Twente (2011-2013), now at Political Academy).

Recent publication: (van Gent, Jansen, and Smits 2014)

joost@politiekeacademie.eu www.politiekeacademie.eu