keeping the dimensionalityof
E
low.2.3.1 Data: Party Vote
We now turn to the atual spatial representations derived from the data.
A disussion of the involved diulties and the auray of the
representa-tionsisprovidedin2.6. Animportantonstraintofthespatialrepresentation
methodisthattheassoiationmatrixannotontainzeroentries.
6
This
on-straint is unlikely to be satised in eld experiments involving a reasonable
number of voters whenever many smallparties are available. In the
experi-5
The innovative part of Spatial ApprovalVoting is the behavioral model underlying
the voters' deision makingproess. One the model distanes are alulated, standard
estimation tehniques (multidimensional saling) are used to nd a representation; for
moredetailsontheexatproedureofobtainingaspatial representation,see 2.5.
6
Elseoneobtainsinnitelylargedistanes. SeeEquation(2.3)in2.5.
ment, itwas satised for Candidate Vote inboth Messel and Konstanz, but
not forthe Party Vote (inneither ase). To takle this problem,we deided
toexlude someof the smallerpartiesand reduethe set ofalternativestoa
manageable level. Sine the theory ofspatial voting determines the distane
between two alternatives solely on the basis of approvals reeived and the
assoiations between those two alternatives, we an restrit our analysis to
a subset of alternatives without loss of generality and still draw
meaning-ful and onsistent onlusions. The parties we analyze in Messel are: SPD
(soial-demorati),CDU (onservative), the Greens,FDP (marketliberal),
the Left (neo-ommunist),AnimalProtetion Party,the Family Party,REP
(Republians; extreme right),and NPD (also extreme right).
Table 2.1: Assoiation matrix for Parties,Messel.
Parties SPD CDU GRE FDP Left APP FAM REP NPD
SPD 517 88 266 91 91 46 54 6 2
CDU 88 429 67 242 12 36 43 21 21
GRE 266 67 347 70 59 40 40 4 1
FDP 91 242 70 313 15 27 30 13 10
Left 91 12 59 15 118 15 12 2 1
APP 46 36 40 27 15 92 22 3 3
FAM 54 43 40 30 12 22 92 6 5
REP 6 21 4 13 2 3 6 32 14
NPD 2 21 1 10 1 3 5 14 27
SPD= Soial Demorati Party, CDU= Christian Demorati Union, GRE=
Greens, FDP= Liberal Demorati Party, Left= The Left, APP= Animal Pr
ote-tionParty, FAM= FamilyParty,REP= Republians, NPD=NationalDemorati
Party.
Table2.1shows theorrespondingassoiationmatriesforthepartyvote
inMessel. Thenumbersonthediagonalaretheabsolutenumberofapprovals
reeived by the parties, the numbers o-diagonal are the number of
assoi-ations between two parties. The matrix is stritly positive, hene nding a
spatial representation is,in priniple, possible.
The smallest distane among the onsidered parties is the one between
the two extreme-right parties, NPD and REP. For that distane to be
pos-itive, we obtain the onstraint (see 2.5)
α ≥ 3.69
. Calibrating the model by setting a proper value forα
, however, is a umbersome proedure. Onthe one hand, the smaller
α
is, the larger will be the explained inertia ofthe lower-dimensional representation. In priniple, we ould set
α = 3.69
and arry out the analysis. On the other hand, setting a too low value for
α
reates diulties with the spatial representation and might result in an inaurate piture. A proper alibration provides an aurate piture withenough explanatory power of the lower-dimensional projetion. For
α = 4
weobtainanaurateeight-dimensionalrepresentationfromwhihareliable
three-dimensionalprojetion an beobtained (explainedinertia63%; see 2.6
for more details).
Figure2.1: Three-dimensionalprojetion oftheeight-dimensionalparty repr
esen-tation, Messel.
(a) Axes1and 2 (b) Axes1and 3
Figure 2.1 shows the latter three-dimensional representation of the
po-litial spae for the parties in Messel. In all gures below, we inlude a
hypothetial Left-Right Line (more properly, a pieewise linear urve) for
better visual orientation. This line is onstruted onneting the loations
of the parties whih are traditionally pereived as having a lear left-right
orientation. The line starts at the position of the Left (far-left party) and
ontinues to the average position of the SPDand the Greens. The reasonis
that, in Germany, the SPD and the Greens have built the traditional
left-ist government oalitions. The third point is the average position of CDU
and FDP, for the analogous reason that these two parties have historially
built the right-winggovernment oalitions. The fourth point is the average
positionof the two extreme-right parties,REP and NPD.
To a ertain extent, the rst axis in Figure 2.1 reets the standard
one-dimensional ategorizationofthe parties intoleft and right(ompare to
the Left-Right Line). The extreme-right parties REP and NPD are loated
far right, the German Soial Demorati Party (SPD), the Greens and the
Left (neo-ommunist)party onthe left,the onservativeparty CDUand the
liberal party FDP inbetween. The enter of the rst axis is overed by the
issue-orientedAnimalProtetion Partyandthe FamilyParty. Thisleft-right
ordering of the parties does not stem from any distributional assumption,
but is endogenously determined by measuring the overlap of the dierent
eletorates.
Examination of Figure 2.1, however, indiates that a redution of the
politial spae to one dimension only would be misleading. The set of
par-ties' positions is far away from being on a line. There are marked party
dierenes along the seond and third axes. As it is often the ase in
mul-tidimensional politial spae studies, the interpretation of these axes is not
unambiguous. Fortheseondaxis,theupperpartontainstheextremeright
parties, aswellas the extremeleft party, and isopposed tothe liberalparty
FDPand onservativePartyCDU. Theformer ingeneralsupportastronger
state with broader ompetenies for the government and more intervention
in the market system, while the latter prefer a liberal market system
with-out intervention by the state. A possible interpretation of the seond axis
is thus that it reets the dierent standpoints market liberalism vs. state
intervention.
It should also be remarked that even the three-dimensional projetion
mightinduesomemisinterpretation. Forexample,thepositionoftheFamily
Party in the three-dimensional projetion should not be trusted (see 2.6).
Examinationof thefull, eight-dimensionalrepresentation reveals that thisis
thepartylosesttotheNPDandREP.OneofthemajortopisoftheFamily
Party is the strengthening of the family and the preservation of traditional
family values. Apparently, voters who approved of parties from the right
end of the politial spetrum also ared for family poliy issues, espeially
preserving traditionalfamilyvalues.
The representation also delivers other interesting insights. For instane,
we observe a strong lustering of the major parties. The distanes between
theSPD,theGreenPartyandtheLeftarealmostofthesamemagnitude,but
muh larger than the distanes towards any other party. The party losest
to the onservative CDU is the liberal FDP and vie versa. Interestingly,
the distane between the far-right party NPD and the onservative CDU is
only slightly larger than that between the CDU and FDP. Of all the major
parties, the CDU exhibits the smallest distane towards the extreme right
partiesREPandNPD. ThisfatmightreetthepolitialsituationinHesse
at the time ofthe eletion. Mr.Koh, the party-leader of the Hessian CDU,
stressed some popular right-wing topis during his eletion ampaign. He
was pleading, for instane, for stronger penalties for delinquent adolesene
that have a strong migration bakground.
7
The distane between the CDU
and SPD, the parties who were in the federal government in Germany the
dayoftheexperiment(theso-alledgrandoalition,Sarrow,2012),isvery
large. In fat, the far-left party the Left and the market-liberal party FDP
are loserto eahother than the parties of the grand oalition.
Let us turn to the data from Konstanz. The threshold value for
α
suhthat allmodeldistanes arepositiveisequalto3.72. Weset
α = 3.85
,allow-ingforareliableten-dimensionalrepresentation(see2.6). Theorresponding
three-dimensionalprojetiononly explainsabout 56%of the inertia.
Appro-priately representing some ofthe partiesrequires morethan vedimensions.
Nevertheless, the tehnique employed to obtain a spatial representation is
suh that taking into aount an additional dimension does not aet the
oordinates of the parties on the previously analyzed dimensions. When it
7
This strategy isnotnew. Theeletion polls in 2003foreastadramati derease in
termsofshareforMr.Kohandhisparty. Hethenstartedaerelydebatedandpolarizing
eletion ampaign. Mr. Koh wasritiizedfor fuelinghatred againstforeigners. Atthe
end, hispartyreeivedanabsolutemajorityofseats.
omes to interpretation of the politial spae, the onlusions based on the
relativepositionsalongagivendimension,asthosegivenbelow,remainvalid
although aparty might not be well represented. However, the distanes
be-tween ertain parties might not be aurately represented. Therefore, we
will refer to the full set of dimensions (ten in the ase of Konstanz) when
interpreting distanes between parties.
Table 2.2: Assoiation matrix for Parties,Konstanz.
Parties GRE SPD CDU FDP PIR Left APP ödp VIO REP NPD
GRE 831 516 208 173 219 198 124 84 40 3 4
SPD 516 677 155 130 137 141 86 52 18 2 2
CDU 208 155 593 364 65 22 50 39 9 10 3
FDP 173 130 364 519 79 27 48 26 5 8 5
PIR 219 137 65 79 298 93 51 30 19 5 6
Left 198 141 22 27 93 263 47 21 16 5 6
APP 124 89 50 48 51 47 175 42 18 2 2
ödp 84 52 39 26 30 21 42 106 14 2 2
VIO 40 18 9 5 19 16 18 14 44 2 3
REP 3 2 10 8 5 5 2 2 2 19 6
NPD 4 2 3 5 6 6 2 2 3 6 15
GRE= Greens, SPD= Soial Demorati Party, CDU= Christian Demorati
Union, FDP= Liberal Demorati Party, PIR= The Pirates, Left= The Left,
APP= Animal Protetion Party, ödp= Eologi Demorati Party, VIO=The
Vi-olets, REP= Republians, NPD=National Demorati Party.
Again we redue the set of parties to obtain a restrited but stritly
positive assoiation matrix. The parties we analyze in Konstanz are: SPD,
CDU, the Greens, FDP, the Left, AnimalProtetion Party, ödp (Eologial
DemoratiParty,environmentalist),theVioletParty(whihpursuesasoial
order based on self-awareness through individual spirituality), the Pirate
Party(issue-oriented,supports the preservationof urrentivilrightsonthe
Internet), REP,and NPD.The orrespondingassoiationmatrixisshown in
Table 2.2.
tation, Konstanz.
(a) Axes1and 2 (b) Axes1and 3
Figure 2.2 shows the three-dimensional representation of the politial
spae for parties in Konstanz (inluding a Left-Right Line generated as
ex-plained above). In ontrast to the ase of Messel, the interpretation of the
rst axis is not so lear. The ideologially-related parties NPD and REP
exhibit again the smallest distane, being loated farthest right on the rst
axis. Nexttothem,wendthe Leftand theVioletParty. Itishardtoargue
that partiipants approving both of extreme-left and extreme-right parties
are ideologially motivated. One possible explanation for the loseness
be-tween the German extreme right-wingers and extreme leftist is preferenes
towards extreme parties or, to put it plainly, protest voters. The enter is
oupied by the Pirate Party and the ödp. The large parties are loated at
the left. Hene, itseemsthatthe rstaxisdistinguishesthe largetraditional
parties from smaller and extreme parties.
8
We still observe lustering as in
the ase of Messel. The CDU has the smallest distane with the FDP and
vie versa, the SPD is losest tothe Greens, reeting traditionaloalitions
in Germany. The parties with the smallest distane to the Greens are the
Animal Protetion Party and the ödp, quite naturally as all three parties
8
We haveto pointoutthat the City ofKonstanzwasruled bya Greenmajor atthe
timeof theexperimentandthat theGreenPartythereismuhstrongerthanintherest
ofGermany,sotheGreenPartytsintothepitureofamoretraditionalparty.
emphasize environmental issues, but they are losely followed by the SPD.
All three distanes are of omparable magnitude. As a last omment, our
analysis shows that the right-wing parties NPD and REP are muh more
dierent than a usual one-dimensional, left-right,representation would
sug-gest. The Republians are more aepted (and therefore muh loser in the
representation) amongst the onservative voters who approved of CDU and
FDP than the NPD. On the other hand, the NPD is loserto parties whih
are about environmental issues, suh as the Greens and the ödp, than to
theREP.Insummary,therepresentationseemstodeliverinterestinginsights
whih were not immediately obvious before the experiment, but whih are
far from arbitrary. In our view, observations as these validate the possible
value of spatial representation tehniques based on approval voting data to
provide anaurate snapshot of voter preferenes.
2.3.2 Data: Candidate Vote
The snapshot we obtain fromthe andidate vote an potentially dierfrom
the one derived from the party vote. First, the andidate eletion in the
mixed-memberproportional representation onerns the distritleveland is
qualitatively dierent from the party eletion, whih onerns the federal
level. That is, the available andidates aspired to represent the loal
dis-trit level, while party votes where aggregated at the federal level. Seond,
during the analysisof the data,we enountered frequent ases ofvoters who
approved of a partiular andidate, but did not approve of the
orrespond-ing party, and vie versa. Voters may pereive a andidate as a worthwhile
reipientoftheirapproval,withoutagreeingwiththegeneralpartyposition.
9
Table 2.3 shows the assoiation matrix for the andidates in Messel. It
is stritly positive, hene we an represent the full set of andidates. A
value of
α = 4.45
allows for aseven-dimensionalrepresentation and a three-dimensional projetion thereof with an explained inertia of 69% (see 2.6).The latter isshown inFigure 2.3, where again we inlude aLeft-Right Line
9
Of ourse, oneanexpet a high orrelation betweenthe evaluation of aparty and
that ofitsleader. SeeWagnerandWeÿels(2012).
Candidates SPD CDU GRE FDP Left FRV REP NPD
SPD 557 95 250 92 76 35 10 4
CDU 95 402 42 210 13 26 21 20
GRE 250 42 302 59 47 26 5 2
FDP 92 210 59 291 8 28 14 8
Left 76 13 47 8 100 13 5 3
FRV 35 26 26 28 13 71 8 1
REP 10 21 5 14 5 8 37 14
NPD 4 20 2 8 3 1 14 27
SPD= Soial Demorati Party, CDU= Christian Demorati Union, GRE=
Greens, FDP= Liberal Demorati Party, Left= The Left, FRV= Free Voters,
REP= Republians, NPD= NationalDemorati Party.
as avisualaid. The rst axis distinguishesLeft-wing and Right-wing
andi-dates. The enter of this axis isempty. Comparingthe party and andidate
representations,theandidatevoteseemstobemorepolarizedthantheparty
vote. The far ends of the representation move loser together. Nevertheless,
we observe the same pattern of lustering of the major andidates that we
observed for parties. The SPD, the Left, and the Greens andidates form
one luster,the andidates ofthe CDU andthe FDP anotherone. The SPD
exhibits the smallest distane to the Greens and vie versa. The same is
true for the andidates of CDU and FDP. Again, reduing the spae to one
dimension ismisleading. The distane between the enter-rightandidate of
the CDUandtheenter-leftandidateofthe SPDislargerthanthe distane
between the far-left and far-rightandidates of the Left and the NPD.
Table 2.4 shows the assoiation matrix for the andidates in Konstanz,
whih is stritly positive and hene enables us to represent the full set of
andidates. A value of
α = 3.35
allows for a very aurate four-dimensional representation of the model distanes (see 2.6). All parties are wellrepre-sented in the lower-dimensional projetion. In fat, with three dimensions
Parties GRE SPD CDU FDP Left NPD
GRE 723 420 177 137 175 4
SPD 420 665 184 126 124 2
CDU 177 184 644 333 21 2
FDP 137 126 333 482 27 6
Left 175 124 21 27 249 5
NPD 4 2 2 6 5 14
GRE= Greens, SPD= Soial Demorati Party, CDU= Christian Demorati
Union, FDP= Liberal Demorati Party, Left= The Left, NPD=National
Demo-rati Party.
we explain about 90% of the inertia. It is an striking result that the
three-dimensional projetion yields suh an aurate piture of the overall
dis-tanes. However, aredution toonlyone dimensionwouldexplain only44%
of the inertia.
At rst glane, the number of available andidates is muh smaller than
in the appliations before. Yet, there is no obvious reason to assume that
a smaller set of alternatives inreases the preision of the lower-dimensional
projetions. The ruial point is that four dimensions are enough to nd a
good representation of the overall piture. Obviously, the more dimensions
are required for an aurate representation, the poorer will be the
lower-dimensionalprojetions. Presumably,thepartiularitiesofthevotingdistrit
Konstanz play animportantrole here.
Thethree-dimensionalrepresentation forthe andidate vote inKonstanz
is shown in Figure 2.4 (the far-right position in the Left-Right Line
orre-sponds tothe NPD andidate only, beausethere was no REPandidate in
Konstanz). Similarlytoourobservationsfromthe partyvoterepresentation,
the rst axis does not distinguish the left-wing from the right-wing
andi-dates. Thedistane betweentheLeftandidateandtheright-wingandidate
of the NPD isatually thesmallest. Althoughthe party vote andthe
andi-date vote onstitute twodistint idiosynrati eletions, we an transfer our
ndings for the representation fromthe former to latter. The overlap in the
eletorate for the two traditional oalitions an also be observed here with
the further addition that the Left needs to be plaed into the same luster
as the SPD and Greens as the distanes among those three parties are of
similar magnitude.
Again, examination of the representation reveals interesting insights on
the loal politial landsape at the time of the eletion. For example, we
alreadyemphasized inthe analysisforthe PartyVotethat theoverlap ofthe
eletorate between the NPD and parties orientated towards environmental
issues is similar to the overlap between the REP and onservative voters.
This observation is even stronger for the Candidate Vote in the sense that
the NPDandidate isloatedlosertotheGreenandidatethan heistothe
CDU andidate.
2.4 Conlusion
This paper presents new evidene on the spatial representation of politial
landsapesusingauniquedatasetwhihontainsapprovaldatafortwoparty
eletions and two andidate eletions in Germany. Our study is the rst to
estimate a politial landsape for partieson the basis of suh data. We use
the datatoobtainspatialrepresentationsof partiesandandidatesinan
en-dogenously determined politial spae. This is made possible by tehniques
developed in Laslier (2006). This model delivers an interesting method for
obtaining spatial representations of politial positions, whih uses data not
available under e.g. Plurality Voting. The researher observes the approval
data inan experiment,and uses these data toestimatethe distanes among
parties. Thenheobtainsalow-dimensionalspatialrepresentationalibrating
a salieneparameter (whihmodels the importaneof the andidate's
prox-imitytoavoter'sidealpointandinuenesthequalityanddimensionalityof
representation). The objetive is to obtain an aurate representation with
as lowadimensionalityas possible. Further, the dimensionsare endogenous
and need not orrespond toexogenously deided variables.
We ompute spatial representations for all four eletions, whih in some
ases are already reliable with a relatively low number of dimensions; one
dimension, however, never sues. Thisprovidesuswith politialsnapshots
of the eletorate's preferenes at the moment of the orresponding eletion.
The representations also serve as eient ways of organizing the data and
The representations also serve as eient ways of organizing the data and