Dissertation zur Erlangung des
akademishen Grades eines Doktors der
Wirtshaftswissenshaften (Dr. rer. pol.)
vorgelegt von
Grani¢, ura Georg
an der Universität Konstanz
Sektion: Politik-Reht-Wirtshaft
Fahbereih: Wirtshaftswissenshaften
Konstanz, 2013
Tag der mündlihen Prüfung: 12. Juli 2013
Referent: Professor Dr. Alós-Ferrer
Referent: Professor Dr. Ursprung
Konstanzer Online-Publikations-System (KOPS)
Introdutionand Summary 1
Einleitungund Zusammenfassung 4
1 Two FieldExperiments onApprovalVoting in Germany 8
1.1 Introdution . . . 9
1.2 Design of the Experiment . . . 13
1.3 Results . . . 17
1.3.1 PartiipationStatistis and Voting Behavior . . . 17
1.3.2 Eletion Results . . . 24
1.3.3 General Disussion . . . 30
1.4 Parliaments . . . 37
1.4.1 Results . . . 38
1.5 Approval Voting for Multi-WinnerEletions . . . 44
1.6 Conlusion . . . 47
1.7 Appendix: AdditionalTables. . . 49
2 Politial SpaeRepresentations with Approval Data 55 2.1 Introdution . . . 56
2.2 The Data Set . . . 60
2.3 Spatial ApprovalVoting . . . 62
2.3.1 Data: Party Vote . . . 63
2.3.2 Data: Candidate Vote . . . 70
2.4 Conlusion . . . 73
2.5 Appendix: Spatial ApprovalVoting . . . 76
2.6 Appendix: Auray of the Spatial Representations . . . 80
3 TheProblemof theDividedMajority: Preferene Aggregation Un-
der Unertainty 89
3.2.2 The Voting Game . . . 99
3.2.3 Nash Equilibriaand Strategi Voting . . . 100
3.3 Results . . . 103
3.3.1 Eletion Results . . . 103
3.3.2 Condoret-Eieny and Coordination Failures . . . . 105
3.3.3 Duverger's Law, CloseRaes, and Ties . . . 115
3.3.4 Individual Behavior . . . 119
3.4 Conlusion . . . 128
3.5 Appendix: Tables . . . 131
3.6 Appendix: ExperimentalMaterials . . . 145
3.7 Appendix: Pre-Test . . . 149
4 Choies and Preferenes: Evidene from Impliit Choies and Re- sponse Times 151 4.1 Introdution . . . 152
4.2 The Present Researh. . . 154
4.3 Experiment1: Ratingsof Holiday Destinations . . . 157
4.3.1 Method . . . 157
4.3.2 Results . . . 158
4.3.3 Disussion . . . 162
4.4 Experiment2: Rankings of HolidayDestinations . . . 164
4.4.1 Method . . . 164
4.4.2 Results . . . 165
4.4.3 Disussion . . . 168
4.5 General Disussionand Conlusion . . . 169
Referenes 171
1.1 Partiipation in the experiments. . . 18
1.2 Number of ballotsfor the dierent eletions. . . 22
1.3 Messel: Approval vs. Plurality Voting,Constitueny Vote. . . 25
1.4 Konstanz: Approval vs. PluralityVoting, Constitueny Vote. . 26
1.5 Messel: Approval vs. Plurality Voting,List Vote.. . . 28
1.6 Konstanz: Approval vs. PluralityVoting, ListVote. . . 29
1.7 AV results for dierent groups of voters. . . 36
1.8 Fititious parliaments. . . 46
1.9 Messel: Conditional Frequenies, ListVote. . . 49
1.10 Konstanz: Conditional Frequenies, List Vote. . . 50
1.11 Results for the List Vote in Messel and Konstanz in absolute terms. . . 52
2.1 Assoiation matrix for Parties, Messel. . . 64
2.2 Assoiation matrix for Parties, Konstanz. . . 68
2.3 Assoiation matrix for Candidates,Messel. . . 71
2.4 Assoiation matrix for Candidates,Konstanz. . . 72
2.5 Pereptual dierenes ofthedistanes between the modeland the representation, Messel, Party Vote. . . 81
2.6 Cosines of projetions, Messel, Parties. . . 82
2.7 Perentual dierene of the distanes between the modeland the representation, Konstanz, Party Vote.. . . 83
2.8 Cosines of projetions, Konstanz, Parties.. . . 84
2.9 Perentualdierenes of thedistanes between the modeland the representation, Messel, Candidate Vote. . . 85
2.10 Cosines of projetions, Messel, Candidates. . . 86
2.11 Perentualdierenes of thedistanes between the modeland the representation, Konstanz, Candidate Vote. . . 87
2.12 Cosines of projetions, Konstanz, Candidates. . . 88
3.2 Payo sheduleand indued preferene prole. . . 99
3.3 Sinere strategies, admissible strategies and Nash Equilibria (NEs). . . 101
3.4 Dierenesinoordinationfailureratesbetweenvotingmethods.108 3.5 Dierenes in Condoret-Eieny between voting methods. . 110
3.6 Ballotsast underAV. . . 120
3.7 Panel probitestimates withrandomeets atindividuallevel for AV. . . 122
3.8 Ballotsast underBC. . . 124
3.9 Panel probitestimates withrandomeets atindividuallevel for BC.. . . 125
3.10 Ballotsast underPV. . . 126
3.11 Panel probitestimates withrandomeets atindividuallevel for PV.. . . 127
3.12 Eletion resultsAVfor the dierent series. . . 131
3.13 Eletionsresults of the AVFI treatment, group level. . . 132
3.14 Eletionsresults of the AVII treatment,group level. . . 133
3.15 Eletion resultsBC for the dierent series. . . 134
3.16 Eletionsresults of the BCFI treatment,group level. . . 135
3.17 Eletionsresults of the BCII treatment, group level. . . 136
3.18 Eletion resultsPV for the dierent series. . . 137
3.19 Eletionsresults of the PVFI treatment,group level. . . 138
3.20 Eletionsresults of the PVII treatment, group level. . . 139
3.21 PairwiseWiloxon-Rank-Sum-Testsfordierenesbetweenvot- ingmethods.. . . 140
3.22 Cuzik's trend tests for learningeets withintreatments. . . 141
3.23 Wiloxon-Rank-Sum-Testsfordierenesbetweeninformation treatments. . . 142
3.24 Distributionof ties inall sixtreatments. . . 143
3.25 Duverger's Law and Close Raes. . . 144
1.1 Perentageof voters whoapproved ofagiven numberofalter-
natives, both forConstituenyVote(Candidates)and forList
Vote (Parties).. . . 20
1.2 Fititious Parliamentsbasedonthe results ofthe oialele-
tions and experimentaldata. . . 53
1.3 Seat alloations aording to the oial method, Approval
Voting,and SAV. . . 54
2.1 Three-dimensional projetion of the eight-dimensional party
representation, Messel. . . 65
2.2 Three-dimensionalprojetionoftheten-dimensionalpartyrep-
resentation, Konstanz. . . 69
2.3 Three-dimensionalprojetion of the seven-dimensionalandi-
date representation, Messel. . . 86
2.4 Three-dimensional projetion of the four-dimensional andi-
date representation, Konstanz. . . 87
3.1 The fration of won eletionsineah of the six treatments. . . 104
3.2 Coordination failurerates over the ourseof the experiment. . 107
3.3 Coordination Eieny over the ourse of the experiment. . . 109
3.4 Staked umulativeperentage plots for AV. . . 112
3.5 The fration of won eletionfor eahalternativeunder AV. . . 113
3.6 Staked umulativeperentage plots for BC. . . 114
3.7 The fration of won eletionfor eahalternativeunder BC. . . 114
3.8 Staked umulativeperentage plots for PV. . . 115
3.9 The fration of won eletionfor eahalternativeunder PV. . . 116
3.10 The umulativeshare of votes for the rst ranked and seond
ranked alternative. . . 118
4.1 StandardizedratingspreadsinExperiment1forimpliitpairs
(a, b)
, pooled and onditional on the distane to the alterna-tives
h
,l
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1604.2 Average response times in Experiment 1 for all diret pairs,
pooled and onditionalon the distane within the pair. . . 162
4.3 RankingspreadsinExperiment2forimpliitpairs
(a, b)
,pooledand onditional onthe distane tothe alternatives
h
,l
. . . . . 1664.4 Average response times in Experiment 2 for all diret pairs,
pooled and onditionalon the distane within the pair. . . 168
This dissertation onsists of four self-ontained researh papers, all of
whihwere writteninfulllmentofthe Ph.D requirementsfor the `Dotoral
Programme in Quantitative Eonomis and Finane' at the University of
Konstanz. Eah paper makes up one hapter in this dissertation. Chapter
1, Chapter2, andChapter 3 fous onthe study of one promisingalternative
voting system alled Approval Voting. Chapter 4 is related to the study of
hoie-indued attitudehanges inPsyhology. In the following, I present a
brief overview of the four hapters summarizingthe main ndings.
Chapter 1, entitled `Two Field Experiments on Approval Voting in Ger-
many', is the results of joint work with Carlos Alós-Ferrer (University of
Cologne) and has been published in the Journal Soial Choie and Welfare,
Vol. 39, No. 1, June 2012 , pp. 171-205. To evaluate the empirial onse-
quenesofthe ApprovalVotingmethodinmasseletions,wearriedouttwo
largesale eldexperiments;the rstduringthe2008Hessianstate eletions
in the ommunity of Messel (with 967 partiipants) and the seond during
theBundestageletions2009inKonstanz(with1431partiipants). Wemim-
iked the oial eletionas losely as possible. After asting aballot in the
oialpollingstationsusingthe oialvoting method,theonstituentshad
the opportunity toast a seond vote using ApprovalVoting. The data ol-
letedduringthe twoeldexperimentsallowed ustoexaminethe dierenes
between the outomes of our titiouseletions and the voting system ur-
rentlyinuse. Insummary,ourdataraisethesuspiionthatthetypialimage
of the German politial sene might not faithfully reet voter preferenes,
and that the voting methodurrently employed mightbebiasing it. For in-
stane,inthe aseofKonstanz, the resultsoftheatualeletionandthe one
using ApprovalVoting were radially dierent. Whilein the atual eletion
the onservative CDU won on all fronts, under Approval Voting it was re-
vealed that theGreen Party enjoyed the largest approval, being approved of
their empirialproperties.
Chapter2isbasedonthe researhpaper`PolitialSpaeRepresentations
with ApprovalData'whihisjointwork withCarlos Alós-Ferrer(University
ofCologne)andisurrentlyintheproessofreviseandresubmitintheJour-
nalEletoralStudies. Theoretialmodelsofspatialompetitionoftenusethe
notion ofleft-rightpositioningof theompetingparties/andidatesin auni-
dimensional politial spae. Estimating the position of parties/andidates
based on mass survey, elite survey or roll all votes data has beome an
importantempirialtask. Reentpubliations providestrong evidenethat,
indeed,positioningoftheompetingatorsfromvariousountriesboilsdown
to a single, left-rightdimensional spatial representation. However, the liter-
ature has paid little attention to atual, i.e., revealed through hoie, data
other than pluralityvoting. Byonsidering spatialrepresentations based on
our ApprovalVotingballot data,we showthatanaurate projetion of the
politial spae requires more than one dimension. Voting methods oer a
piture of the politial opinionof a ountry, state,or ommunity, whih an
be taken as a snapshot of the opinion landsape of a demorati soiety at
a spei point intime. We arguethat suh informationalaspets (e.g., the
aurayofthe snapshot)shouldbetakenintoonsiderationwhenanalyzing
the meritsof dierent voting methods.
Chapter3,entitled`TheProblemoftheDividedMajority: PrefereneAg-
gregation UnderUnertainty',presentstheresultsofaseriesofexperimental
(laboratory) eletionsdesigned toassess and ompare the eletionoutomes
and the individual voting behavior under three voting methods (Approval
Voting, the Borda Count, and Plurality Voting) in a divided majority set-
ting. Divided majority problems are haraterized by an absolute majority
of voters being uniedin strongly opposing one partiular andidate. How-
ever, their support is divided between two (or more) other andidates. If
they fail to ombine eorts and onentrate their support behind one an-
didate, the emerging winner is the andidate they jointly onsider to be
leaders. Ourresults showthatmulti-votesmethodlike ApprovalVoting and
theBordaCountoutperformPluralityVoting,oordinationfailuresariseless
frequently. Another ruial feature of our design was a manipulationof the
underlying information struture. We departed from a perfet information
framework towards a more realisti setting, in whih (boundedly rational)
voters were only informed about the outomes of previous eletions. The
observed superiority of multi-votes methods is even stronger under inom-
plete information. Our results suggest that, in general, the responsiveness
towards the informationalstruture may serve asanother important dimen-
sion to evaluate the merits of voting methods and an further enrih the
understanding of these methods.
Chapter4,`ChoiesandPreferenes: EvidenefromImpliitChoiesand
Response Times', is the result of joint work with Carlos Alós-Ferrer (Uni-
versity ofCologne), FeiShi(Shanghai JiaoTong University),and Alexander
K. Wagner (University of Cologne) and has been published in the Journal
of Experimental SoialPsyhology, Vol.48,No.6,November2012, pp.1336-
1342. In Eonomis, hoies and preferenes are two sides of the same oin
and formstrong onepts. They are thought of asstable and onsistent. In
Psyhology however, preferenes are a muh softer onept. They merely
reetanindividual'sattitudetowards aset ofobjetsoranevaluativejudg-
mentinthe senseoflikingordislikinganobjet. TheFree-ChoieParadigm
is a lassial paradigm in Psyhology and has been used numerous times
to demonstrate that hoies an feed bak into and alter preferenes. Re-
ently, the Free-Choie Paradigm has been ritiized. It has been argued
that the observed preferene hange might be nothingbut a statistialarti-
fat reated by a self-seletion bias within the paradigm. We design a new
experimentalparadigmwhere hoie-indued preferene hange is measured
and whih improves upon the Free-Choie paradigm by avoiding the sele-
tion bias. Response time measurements in our experiments indiate that
reappraisal proesses are already triggered during deisionmaking.
DievorgelegteDoktorarbeitbestehtausviereigenständigenForshungsar-
beiten,dieihalsDoktorand imDotoralProgramme inQuantitativeEo-
nomis and Finane an der Universität Konstanz geshrieben habe. Die
einzelnen Forshungsarbeiten stellen jeweils ein Kapitel innerhalb der Dis-
sertation dar. Die ersten drei Kapitel beshäftigen sih thematish mit
der Untersuhung eines alternativen Wahlverfahrens,der sogenannten Wahl
durh Zustimmung. Kapitel 4 ist der aus der Psyhologie bekannten Un-
tersuhung von Einstellungsänderungen, welhe durh Entsheidungen her-
beigeführt werden, zuzuordnen. Es folgt eine kurze Zusammenfassung der
einzelnen Kapitel und der darin enthaltenen Resultate.
Kapitel 1, mit dem Titel Two Field Experiments on Approval Voting
in Germany,istdas Ergebnis einerZusammenarbeitmitCarlosAlós-Ferrer
(Universität zu Köln) und wurde in der wissenshaftlihen Fahzeitshrift
Soial Choie and Welfare, Vol. 39, No. 1, Juni 2012, pp. 171-205, veröf-
fentliht. Um dieempirishe Tragweite der Wahl durh Zustimmung besser
bewerten zu können, führten wir zwei groÿ angelegte Feldversuhe durh.
Der erste Feldversuh (mit 967 Teilnehmern) fand während der hessishen
Landtagswahl 2008 in der Gemeinde Messel statt, der zweite (mit 1431
Teilnehmern) während der Bundestagswahl 2009 in der Stadt Konstanz.
Dabei stelltenwir die Gegebenheiten der entsprehenden amtlihen Wahlen
so gut wie möglih nah. Im Anshluss an der Teilnahme an der amtlihen
Wahl hatten die Wähler Gelegenheit ein weiteres Mal (ktiv) zu wählen.
Bei dieser zweiten (ktiven) Wahl kam dann die Wahl durh Zustimmung
zum Einsatz. Die gesammeltenDaten ermöglihtenes uns, dieUntershiede
zwishendenErgebnissenderamtlihenWahlundunsererenktiven Wahlen
zu untersuhen. Summa summarum legen unsere Ergebnisse nahe, dass
das typishe Bild der deutshen Parteienlandshaft niht den tatsählihen
PräferenzenderWählershaftentsprihtunddassdieamtliheWahlmethode
der Erst- als auh bei der Zweitstimme die stärkste Kraft war, waren es
die Grünen, die die meiste Zustimmung auf sih vereinen konnten. Die
enorme Bedeutung dieser Beobahtungen stellt klar, dass die theoretishen
und empirishen Eigenshaften alternativer Wahlmethoden erst vollständig
verstanden werden müssen, bevor man sieder Gesellshaft letztendlih vor-
stellen kann.
Kapitel2basiertaufder inZusammenarbeitmitCarlosAlós-Ferrer(Uni-
versitätzuKöln)erstelltenForshungsarbeitPolitialSpaeRepresentations
with Approval Data. Das entsprehende Manuskript bendet sih inÜber-
arbeitung und wird der Fahzeitshrift Eletoral Studies erneut vorgelegt
(revise and resubmit). Theoretishe Modelle räumlihen Wettbewerbs tr-
een häug die Annahme, dass sih im politishen Wettbewerb zueinan-
der stehende Parteien/Kandidaten in einem eindimensionalen politishen
Raum positionieren. DasShätzeneben dieserPositionenmitHilfevonUm-
frageergebnissen, Expertenmeinungen oder Ergebnissen amtliher Abstim-
mungenhatsihzueinerwihtigenempirishenAufgabeentwikelt. Neueste
Forshungsergebnisse bekräftigendietheoretishen Annahmen dahingehend,
dass sih der politishe Wettbewerb in vielen Ländern tatsählih auf nur
eine Dimension im politishen Raum beshränken lässt. Bei den meisten
Shätzungen spielendieeigentlihen Entsheidungender Wählerjedoheine
untergeordnete Rolle. Wir zeigen, dass eine akkurate Projektion des poli-
tishen Raums mehr als eine Dimension benötigt, wenn man für die tat-
sählihe räumlihe Darstellung Wahlentsheidungen heranzieht, die unter
der Wahl durh Zustimmung getroen wurden. Wahlmethoden bilden die
politishe Meinung eines Landes, eines Staates oder einer Gemeinshaft ab
und liefern uns konkrete Momentaufnahmen der Meinungslandshaft inner-
halb einer demokratishen Gesellshaft. Wir vertreten die Auassung, dass
solhe Aspekte (z.B. wie genau diese Momentaufnahmen ausfallen) bei der
Evaluierung von Wahlmethoden mitberüksihtigt werden müssen.
Kapitel 3, mit dem Titel The Problem of the Divided Majority: Pref-
dieentsprehend getroenen individuellenWahlentsheidungen dreierWahl-
methoden(WahldurhZustimmung,BordaWahl,Mehrheitswahl)miteinan-
der zu vergleihen. Der Fokuslaghierbeiauf den sogenannten Divided Ma-
jority Problemen. Dieselassensihwie folgtbeshreiben. Füreine absolute
Mehrheit anWählernstellt einbestimmter Kandidatdieeindeutig shleht-
este Lösung dar. Die Mehrheit ist sih jedoh niht darüber einig, welher
Kandidat die beste Lösung darstellt. Gelingt es der Mehrheit niht ihre
Anstrengungen zu bündeln und einen einzigen Kandidatenzu unterstützen,
gewinnt derKandidat, den siealseindeutig shlehteste Optionwahrnimmt.
Das Auftreten eines solhen paradoxen Ergebnisses (Kandidaten gewinnen
eine Wahl, obwohl sie für eine absolute Mehrheit an Wählern das shleht-
este Ergebnis darstellen) kann den demokratishen Prozess im Allgemeinen
behindern, da die politishe Legitimität der gewählten Kandidaten unter-
graben wird. Unsere Ergebnisse zeigen, dass Wahlmethoden wie die Wahl
durh Zustimmung oder die Borda Wahl die Mehrheitswahl in dem Sinne
dominieren,dass dieKoordinationsbemühungenderMehrheit seltenershei-
tern. EinweitererwihtigerAspektunseresExperimentsistdieexpliziteMa-
nipulation derzugrunde liegendenInformationsstruktur. Wirzeigen,dass in
einer realistisheren Umgebung, in denen Teilnehmern nur die Information
bezüglihvergangener Wahlen zur Verfügungsteht, diebeobahtete Domin-
anz sogar noh verstärkt wird. Unsere Ergebnisse legen nahe, dass die In-
formationsstrukturerheblihen Einuss aufWahlergebnissehaben kann und
somit dieInteraktionen zwishen Information und Wahlmethode einen weit-
eren wihtigen Aspektbeider Beurteilungvon Wahlmethoden darstellt.
Kapitel 4, Choies and Preferenes: Evidene from Impliit Choies
and Response Times, ist das Ergebnis einer Zusammenarbeit mit Carlos
Alós-Ferrer (Universität zu Köln), FeiShi (Shanghai JiaoTong Universität)
und Alexander K. Wagner (Universität zu Köln). Die Forshungsarbeit
wurde in der wissenshaftlihe Fahzeitshrift Journal of Experimental So-
ialPsyhology,Vol.48,No.6,November2012,pp.1336-1342,veröentliht.
ein viel weiheres Konzept. Präferenzen reektieren hier lediglih die Ein-
stellung eines Individuums gegenüber einer Menge an Objekten oder eine
wertende Beurteilung eben dieser. Mit Hilfe des Free-Choie Paradigmas
in der Psyhologie wurde shon häug demonstriert, dass Entsheidungen
Rükkopplungseekte auf Präferenzen ausüben und diese sogar beeinussen
undändernkönnen. InletzterZeitwurdedasFree-ChoieParadigmaoftkri-
tisiert. DiedurhEntsheidungenherbeigeführtenÄnderungenderPräferen-
zen sollen nihts weiter als ein statistishes Artefakt sein, welhe durh
Selbstselektionsprozesse, dieim Paradigmaselbst verankert sind, verursaht
werden. Wir haben diese Kritikpunkte aufgegrien und unsererseits ein
verbessertes Paradigmakonstruiert,welhesSelbstselektionsprozesse vermei-
det undindem Präferenzänderungentrotzdem gemmesenwurden. Die Mes-
sung vonReaktionszeiteninunserem Experimentdeutetdaraufhin,dass die
fürdieNeubewertungzuständigendieProzesseshonwährenddereigentlihen
Entsheidungsndung aktiv sind.
in Germany
1.1 Introdution
SoialChoieisadismalsiene. Inanyintrodutorysoialhoieourse,the
young,naïveundergraduateisdeliveredatleasttwoheavyblows. First,heor
sheistoldthatArrow'sImpossibilityTheorem(Arrow,1963)establishesthat
there exists no non-ditatorial voting method satisfying a few mild-looking
onditions. Seond, the student is shown that the Gibbard-Satterthwaite
Theorem (Gibbard, 1973; Satterthwaite, 1975) implies that any reasonable
voting method is manipulable by strategi voters. Afterwards, he or she
mightbeonfronted withaseletionofsomeofthe many otherimpossibility
results whih have been established, while the positive results oered as a
ompensation will typially require stringent assumptions, as e.g. severely
restrited preferene domains.
Few of these fatsseem to have perolated to the generalpubli, and in-
deeddisussionsonthedesignofatualvotingmethodstouseinthepolitial
arenararely involvesoialhoie theorists. One possiblereasonissimplythe
bluntness of the message arriedby impossibilityresults. If all methods are
awed, manyyoungundergraduatesreason,soialhoiehasnothingtooer
to soiety.
Of ourse, some methods are more awed than others, and arguments
havebeen putforwarde.g. fortheBordaCount(Saari,1994)ontheaount
that it (very roughly) minimizes the amount of paradoxes within ertain
sets of votingmethods. OtherargumentsfavorApprovalVoting(Bramsand
Fishburn, 1978), whih is the objet of study in this paper. Again, few of
these arguments have transpired to atual politial eletions. Most of the
eletions inthe western world are run aording toslightly pathed variants
of the plurality voting system, whih an probably be argued to be one of
the most awed systems in existene.
Under plurality voting, eahvoter isonstrained toast a singlevote for
his or her preferred andidate. This way, voters annot express any part of
their preferenes ortastes butanalleged maximum,whihmakes itpartiu-
larly easyfor paradoxesto appear. Insome atual eletions, suh paradoxes
have been partiularly transparent and have resulted in soialand politial
turmoil. One infamous example ourred in the 2002 Frenh presidential
eletions, where right-extremistJean-MarieLe Pen tookseond plaein the
rst round of the presidential eletions although 80% of voters in the se-
ond round voted against him; arguably, the rst-round outome resulted in
adistorted imageofthe Frenhpolitiallandsapeatthe internationallevel.
Another often-ited example is the ase of the 1998 governor eletions in
Minnesota, where the former professionalwrestler Jesse `the body' Ventura
won, although, allegedly, 64% of voters atually preferred any of the other
two major andidates.
Whether the problems with plurality voting have been understood at a
formal or merely at an intuitive level, some ountries have sought to avoid
these problems by either modifying the eletoral rules, or introduing other
voting systems. Forexample, run-o ballotsinFrane and multiple votes in
Germany (see below) represent attempts by these ountries to give voters a
furtheropportunitytoexpresstheirwisheswhileessentiallykeepingavariant
of pluralityvoting. A prominentexample of analternativevoting methodis
the Australian ase, where the `Single Transferable Vote' (or Instant Run-
o) method is employed. In this system the voters provide a omplete list
in ranking order of their preferred andidates. The results are determined
through an algorithm that progressively eliminates the weakest andidates
until an absolute majority is reahed. However, omplex voting methods
bringnewproblems oftheirown,andithasbeen arguedthattheymighte.g.
make the hanes for strategimisrepresentation ofvoters' preferenes more
obvious, exaerbating the problem identied in the Gibbard-Satterthwaite
Theorem.
In this paper, we are onerned with (the empirial testing of) a very
simple voting method, whih from a sienti point of view oers a viable
alternative to plurality voting. This method is known as `Approval Voting'
(as introdued by Brams and Fishburn, 1978) and is for example used for
the eletionofthegeneralseretaryofthe UnitedNations. InApprovalVot-
ing, the voters may vote for as many andidates asthey wish. To alulate
the eletionresult, the numberof votes for eah andidate are ounted. Ar-
guments have been put forward in the literature that the Approval Voting
methodprovidesanauratereetionofvoters'wishesandisnotvulnerable
to voter manipulation (see Brams and Fishburn, 1978; Fishburn, 1978a,b;
Brams and Fishburn, 2005; Wolitzky, 2009).
1
Additionally, the Approval
Voting method is more likely to lead to a onsensus vote than polarizing
the eletorate. It also redues the risk of `smear ampaigns' (Brams and
Fishburn, 1978; these often arise in eletions in the U.S. and are beoming
moreprevalentinEurope), beausetheandidatesarealsodependentonthe
approval by voters who alsosupport other politial parties.
There is, however, no universal agreement among soial hoie theorists
as to whih alternativemethod should be put forward as a replaement for
plurality voting. Insofar as analytial results are onerned with rational
deision makers who perfetly understand the involved methods and their
onsequenes, pratial objetions are likely to be raised at any theoreti-
ally solid reommendation. In our opinion, the debate is likely to remain
onstrained to the aademi world unless the sienti ommunity is able
to provide empirial results on the performane of possible alternatives in
real-world voting situations. In other words, we advoate the use of eld
experiments in order to obtain hard data on the outomes and proedural
diultiesoftheoretiallydesignedvotingmethodsunderrealistionditions
(or, toborrowa linefrom psyhology,eologiallyvalid onditions).
Approval Voting has meanwhile been adopted by a number of sienti,
engineering, and professional soieties. This has generated a fair amount
of data on small-saleeletions, whih have been reported on in e.g. Brams
and Fishburn (1988) (Mathematial Assoiation of Ameria), Brams and
Fishburn (2001) (Soial Choie and Welfare Soiety), and Brams and Kil-
gour (2010) (Game Theory Soiety); see Brams and Fishburn (2005) for a
more general perspetive. Movingto politialeletions, Laslier and Van der
Straeten (2004; 2008) and Baujard and Igersheim (2009, 2010) onduted
two eld experiments onApproval Voting during the 2002 and 2007 Frenh
presidential eletions.
1
However,regardingmanipulabilityorstrategy-proofness,ApprovalVotinglearlybe-
longs to a dierent formal framework, and hene not to the domain of voting methods
overedbytheGibbard-SatterthwaiteTheorem (Gibbard,1973;Satterthwaite,1975).
The empirial evidene olleted in those studies has provided new in-
sights into the atual funtioning of the Approval Voting method, and ad-
ditionally shown that the urrently used voting methods an lead to results
that do not represent the real wishes of the eletorate. For example, whilst
the oial voting methodgave LePen seondplaeinthe 2002 Frenhele-
tions,theApprovalVotingmethodgavehimonly12thplae. Thusaording
to this method, Le Pen would not have been a serious ontender for pres-
ideny, a onlusion whih might have been more in aordane with the
atual wishes of the eletorate asexpressed in the seond round of the 2002
eletions.
Inthis paper,wereportontwoseparateeld experimentswhihwe have
onduted in Germany. The partiularities of the German eletoral system
allowedustosimultaneously olletdata ontwoqualitativelydierentvotes
per experiment. Germany uses a mixed-member proportional representa-
tion system in whih voters are asked to ast two distint votes, one for a
andidate and one for a party. Thus the only natural way to ondut the
experiments was to alsoask voters toprovide approval ballots both for dis-
trit andidates and state or federal parties. Hene we olleted data for a
total of four eletions. This has provided us with a unique data set with
two observations per voter, inludingdata on the performane of Approval
Voting forparty eletions, aontextthe methodwasnot originally designed
for.
The rst experiment took plae in the town of Messel during the 2008
state eletions in Hesse, while the seond one was onduted in the ity of
Konstanz during the 2009 federal eletions. These eld experiments have
provided uswith a number of insights,whih an beorganized in three at-
egories. First, the experiments themselves serve to establish the pratial
appliability of a given voting method in large eletions. In partiular, it is
importanttoondut experimentsindierentountriesand witheletorates
whihareused todierentvoting systems. Seond, by omparingtheresults
in our experimentsto the ones of the simultaneous, oial eletions, we ob-
tain arediblemeasureofthe degreeofdistortionduetotheoialeletoral
system. Third, the results serve to establish the empirial validity of vari-
ous theoretialarguments onthe advantages and disadvantagesof Approval
Voting.
The paper isstrutured as follows. Setion1.2desribes howthe experi-
ments were onduted. Setion 1.3presents the data, omparingthe experi-
ments'resultstotheresultsoftheoialvote,restritedtotheonstituenies
we olleted data in. Setion 1.4 then presents titious Parliaments built
aording to our experimental data as a straightforward, graphial way to
examinethepossibleimpliationsofApprovalVoting. Setion1.5brieydis-
usses theimpliationsfortheSatisfationApprovalVoting methodreently
proposedby Bramsand Kilgour(2010). Setion1.6onludes. Inaompan-
ion paper (Alós-Ferrer and Grani¢, 2012a), we use our dataset in order to
obtain spatial representations of parties and andidates in an endogenously
determined politial spae, following the method of Laslier (2006).
1.2 Design of the Experiment
In ooperation with the ompetent state and federal authorities, we devel-
oped a design for the experiments ensuring an absolutely undisturbed and
regular oial eletion. Further, we tried to mimi the oial eletion as
losely as possible. We established one experimentalpolling station ineah
of the preseleted polling stations. Our titious polling stations were set
up in the immediate viinity of the oial ones, i.e. they were loated in
the same buildings, but in separate rooms. In eah of our stations, ballot
boxes were provided by ourtesy of the ommunities. Before the eletion,
all registered voters reeived a letter in whih the methodwas explained to
them and inwhih they were invitedtopartiipateinthe experiment. After
asting a ballotin the oial polling stations, apaper slipwas handed over
to the voters by the polling lerks whih qualied them for partiipation in
the experiment. This proedure ensured that voters' deisions in the o-
ial eletion were not inuened by our presene, and also that only those
onstituents who atually went to the polls ould take part in the titious
vote. Assistants fromthe University of Konstanz were assignedto eah one
of our stations. Theirtask was toollet the partiipationpapers, hand out
the titiousballot papers, and olletthem bak after the voters had lled
them in. Before the eletion, the ommunities provided us with an oial
ballot paper, so that the same parties and andidates were available in the
experimentsas inthe oialeletions andwere namedand desribed in the
same way.
Germanfederal eletions, andmost of thestate ones,are idiosynrati in
that voters are asked to ast two dierent votes. The rst, for the distrit
eletion(Wahlkreisstimme fortheStateEletioninHesseandErststimme
forthefederalEletioninGermany,respetively)isgiventoaandidate,and
theresultsaredeterminedbythewinner-takes-allproedurewithsimplema-
jority. We will refer to this rst vote as the Constitueny Vote. That is,
eahdistriteletsonememberofparliamentindependentlyofotherdistrits.
Before the eletion, eah parliament has a theoretial number of seats; half
of those seats are alloatedthrough this method (diret seats). The seond
vote, (the Landesstimme for the State Eletion and the Zweitstimme for
the FederalEletion),determines (following aproportionalsystem) the per-
entage of the total seats in the parliament tobe alloatedto eah dierent
partywhihreahesatleast5%ofthevotes.
2
Eahpartyprovidesadditional
andidates(omplementingthediretseats)outofapredeterminedlist,until
the total number of seats it should reeive aording to the seond vote is
reahed. This an atually ause ompliations whih might lead to minor
adjustments in the eetive size of the parliament.
3
We will refer to this
seond vote as the List Vote. The partiularities of the German eletoral
systems allowed ustoolletdata onfoureletionswiththe helpoftwoeld
experiments. Further, in sharp ontrast to the Frenh presidential eletion
experimentsin2002(LaslierandVanderStraeten, 2008)and2007 (Baujard
and Igersheim, 2009, 2010), we ould adopt and test a variant of Approval
Votingwithinaparty-based,proportionalrepresentationframework. Tobest
2
Ifapprovalvotingwouldbeusedinsteadoftheoialmethod, therewouldbequali-
tativelydierentpossibilitiesforthedenitionofsuhthresholds. SeeSetion1.4.
3
Diulties appearifapartymanagestoapturealargernumberofdiretseatsthan
the total perentagewould allow it to have, or if aparty whih does not reah the 5%
barrierobtainssomediretseats. Theseproblemsareessentiallydealtwithbyinreasing
thenumberofseatsin parliament.
of our knowledge, this possibility has reeived no or very littleattention in
the literature up to this point (Bramsand Kilgour 2010 is a notable exep-
tion). Hene,althoughApprovalVoting istypiallyonsideredforandidate
eletionsonly,itwasnatural,inoursetting,toaskvoterstoprovideapproval
ballots both for distrit andidates and state/federal parties.
OialballotsinGermanyare large sheetsof paperdividedvertially in
twoparts,onefortheConstituenyandonefortheListvote. Theandidates
and parties are listed aordingto the ranking ofthe parties inthe previous
eletion, i.e.the partieswhih obtained the most votes in the previous ele-
tions are at the top of the list. Voters hand in their votes for parties and
andidatessimultaneously,althoughtheyan ofoursedeideindependently
whihpartyand whihandidatetosupport. Forour experiments,the om-
petent authorities requested us not touse exat reprodutions of the oial
ballots in order to avoid any possible onfusion. We agreed to use separate
sheetsofpaper(ofdierentolors)forConstituenyandListvotes,buteah
voter was given both sheets of paper simultaneously and requested to hand
them in within a single envelope. Our experimental ballots were otherwise
identialtothe oialones, downtotheir graphialdesign. Candidatesand
parties werelisted inthesame orderasinthe oialballot,weprovided the
exat same information on parties and andidates (name, address, oupa-
tion), et. The main dierenewas that, ontop of the experimentalballots,
the word Zustimmungsverfahren (Approval Voting)was printed.
Forourrstexperiment,weseletedtheGermanstateofHesse. The2008
eletionsinthisstatewereexpetedtobeverylose,whihmadetheeletion
espeially interesting.
4
Indeed, afterthe eletions, the involved parties were
unable to form a new government and new eletions had to be alled for
almost exatlyone year later.
The experiment was arried out in the relatively small German town of
Messelonstateeletionday,January27 th
2008. Thisommunityisloatedin
South Hesse and belongsto the voting distritDarmstadt-DieburgI. It on-
4
For instane, aording to a survey with 1000 partiipants onduted by the rm
infratest-dimap on January 14-16, 2008 for the German national television, 38% of the
votersplannedtosupportSPD,while37%expressedanintentiontovotefortheCDU.See
http://www.wahlreht.de/umfragen/landtage/hessen.htm,lastaessedMarh14,2011.
tains three separate polling stationsthat we willrefertoas Messel I, Messel
II, and Messel III.
5
The lastone orresponds to asmall, nearby dependeny
loatedoutside the town.
WiththeexpliitpermissionandfriendlysupportoftheHessianMinistry
for the Interior and for Sport, the head eletion organizer (Mr. Wolfgang
Hannappel), the mayor of the Messel distrit (Mr. Udo Henke), and the
eletionommissioner(Mr.DieterLehr), weinstalledseparate votingbooths
in eah of the three dierent voting areas in the Messel distrit. A total
of 3017 eligible voters, of whih 1909 personally took part in the oial
eletion,were dividedamongstthe threevotingstationsMessel I,II,andIII,
with 1326, 1401 and 290 registered voters respetively.
The seond experiment was arried out on September 27 th
2009 during
the nationwide GermanFederaleletionsinKonstanz,a ityinthe southern
GermanstateofBaden-Württembergwhihispartofthedistritofthesame
name. As in Konstanz itself and most of Germany, the onservative party
(CDU)wasexpetedtoreeiveasimplemajoritybothforthedistriteletion
and the party-list eletion. The relatively large number of registered voters
(57727), fored us to restrit our study to a few of the total 65 polling sta-
tions. Withthe help of the loalauthorities,we identied 6polling stations
that we onsidered as pratial for our purposes (on the basis of represen-
tativeness and pratial riteria) with a total of 5526 registered voters, of
whih2879tookpartintheoialeletionpersonally. Wewillrefertothese
pollingstationsasKonstanzI toKonstanzVI; they had856, 728,810, 1010,
1157, and 965 eligiblevoters respetively.
6
Withthe expliit permissionand
friendly support of the federal eletion organizer (Mr. Roderih Egeler), the
state eletion organizer (Mrs. Christiane Friedrih), the eletion organizer
in the DistritOe (Mr. Manfred Roth), and the eletion ommissionerof
Konstanz (Mr. Raphael Wiedemer-Steidinger), we installed separate voting
booths ineah of the six pre-seleted voting areas in Konstanz.
Before we report on the results of our experiments, we would like to re-
5
TheatualnamesofthestationsareHausderVereine,Kindergarten,andGrube
Messel,respetively.
6
TheatualnamesofthestationsareRathaus,WallgutshuleI,WallgutshuleII,
WallgutshuleIII,ParkstiftRosenau andGeshwister-ShollShule,respetively.
markthat, asin any othereld experiment, the emphasis wasplaed onob-
taining data underrealisti onditions. Foravoting experiment,this means
arrying out the experiment with atual voters on an atual eletion day.
Hene, we neessarilyhave towork with animpliitwithin design, i.e.our
experimental subjets voted aording to the oial method before taking
part in our experiment. Ideally, one would like to work with a between-
subjet design wherepartiipantsare randomlyassigned toone orthe other
voting method. While this is learly not possible in a eld experiment on
voting (if ondutedon anatualeletion day), between-subjet designs are
perfetly feasible in the laboratory. On the other hand, laboratory exper-
iments have lear disadvantages with respet to eld experiments, e.g. a
smaller number of partiipants and a lower level of external validity. For
these reasons, we vieweld and laboratory experimentsas omplementary.
1.3 Results
1.3.1 Partiipation Statistis and Voting Behavior
All registered voters were informed by a letter about the experiment that
was going to take plae during the Eletion Day on January 27 th
, 2008 in
Messel, respetively onSeptember 27 th
, 2009 inKonstanz, and were invited
to partiipate. The statistis for the partiipation in the experiments are
presented in Table 1.1. Sine only the urn voters are onsidered as being
potential experiment partiipants, we exluded those voters who registered
in order to ast a vote per post (292 in the ase of Messel and 1308 in the
ase ofKonstanz) fromall oialstatistis.
Insummary,of the 1909 voters who atually wenttothe pollsinMessel,
967 partiipants (50.7%)took their time toast their approval ballotin our
experiment. A totalof 6invalidvotes were ast intheexperiment'seletion,
sothat 961ballots areavailableforthe desriptiveanalysisof the results. In
Konstanz, of the 2879 voters who atually went to the polls, 1431 (49.7%)
partiipated in the experiment. Only two invalid ballots were ast for the
Constitueny Vote and one for the List Vote. Our sample thus onsists of
Table 1.1: Partiipation in the experiments.
Regis- Oial Eletion Approval Voting Eletion
Station tered Parti. Invalid Parti. Invalid %
Messel I 1192 847 20/28 461 4/4 54.4%
Messel II 1256 902 19/20 407 2/2 45.1%
Messel III 277 160 5/5 99 0/0 61.9%
TOTAL 2725 1909 44/53 967 6/6 50.7%
KonstanzI 605 409 3/2 234 0/0 57.2%
KonstanzII 570 389 5/9 165 0/0 42.4%
KonstanzIII 617 376 0/1 218 0/0 58.0%
KonstanzIV 784 532 7/11 261 1/0 49.1%
KonstanzV 860 649 8/8 301 1/1 46.4%
KonstanzVI 782 524 7/10 252 0/0 48.1%
TOTAL 4218 2879 30/41 1431 2/1 49.7%
Invalid: the rstnumber denotesthe invalid votes forthe List Vote, the seond for
the Constitueny Vote. The perentage indiates the share of voters in the oial
eletion who tookpartin the experiment.
1429 observations for the Constitueny Vote and 1430 observations for the
ListVote. Thisrelativelylargedatasetensures statistialsignianeforthe
omparison between our results andthe oialresults inMessel. Compared
to the eld experiments onduted in Frane, our partiipation rates are
lower. In the 2002 experiment (see Laslier and Van der Straeten, 2008), the
partiipationratewas77.6%,inthe2007experiment(BaujardandIgersheim,
2009, 2010), the rate was 61.6%. The dierenes an mainly be attributed
to the fat that, in addition to the information letter and the artile in
the muniipal bulletin, information meetings were sheduled in eah town
the experimentswere onduted in,whihunfortunately was notfeasible for
our purposes. The 2007 experiment further made use of information spots
transmitted via loal radio and national TV. A stable phenomenon aross
both the eld experiments in Frane and our two eld experiments is the
fat thatthe rates of spoiled ballotsare extremely low(stritly smallerthan
0.7% for allfour eld experiments).
Theommunitiesthemselvesaretoosmalltodrawsigniantimpliations
for the whole (federal) state. In the following, whenever the oial results
areomparedtothoseoftheexperiment,andwheneveronlusionsaremade
fromonetotheotherorpolitialimpliationsaredrawn, theywillbealways
madefortheommunityitself,ortobemorepreise,tothesetofurnvoters,
not the (federal) state.
7
,
8Twooftheobjetivesofourexperimentsweretotesttheappliabilityand
thegeneralaeptaneofApprovalVotingamongthepopulation. Compared
to the oial voting method,Approval Voting gives voters more options to
express their will. For instane, with six andidates for the Constitueny
Vote inKonstanz, there are sixdierentvalidballotsavoter an ast under
the oial method, and there are
2 6 dierent ways to ast a ballot under
7
However, assuming an equal distribution of List Votes in Hesse and in Messel, the
orresponding
χ 2
goodness-of-ttestwith10degreesoffreedomyieldsap
-valueof0.369.We anonludethatthe ommunityisnot signiantlydierent fromthe stateforthe
ListVoteoutome.
8
AssuminganequaldistributionofListVotesinoursixpre-seletedpollingstationsand
in Konstanz,theorresponding
χ 2
goodness-of-ttest with 12degreesof freedomyields a p-value of 0.477. We an onlude that our six polling stations are not signiantlydierentfrom thewhole ofKonstanzfortheList Vote.
Approval Voting. A simpler way to represent the general voting behavior
of the partiipantsis togroup themaording to the numberof alternatives
theyapproved of. Figure1.1givesagraphialrepresentationoftheaggregate
data, andTable1.2presentsthedetaileddataforindividualpollingstations.
Figure 1.1: Perentage of voters who approved of a given number of alternatives,
both for Constitueny Vote (Candidates) and forList Vote (Parties).
(a) Messel
(b) Konstanz
The highest number of approvals for the andidates was eight in Messel
(that is, one voter just approved of all andidates) and ve in Konstanz,
respetively eight and seven for the List Vote. A large proportion of the
onstituents ast ballots with one, two or three approvals. Indeed, for all
four experimental eletionsthe mode of approvals perballot is two.
A signiant group of voters ast single vote ballots for the andidates,
traingthelineaftertherst andidateintheirpreferene proleasthey are
fored to do under plurality voting. Close examination of Table 1.2 for the
Konstanz experimentrevealsadisrepanyof168ballotsbetweenvoterswho
approved of asingle andidate and asingle party. Sine voters handed their
ballots forandidates andparties withinasingle envelope,wean ount the
voters who simultaneously approved of one andidate and one party only.
This amounts to 218 partiipants in Messel and 192 in Konstanz. In other
words, 77.31%of the valid votes inMessel and 86.56% of the validvotes for
the Constitueny Vote, respetively, 86.66% for the List Vote in Konstanz
ame from voters who atually deided to ast ballots whih they are not
allowed toast under pluralityvoting.
9
The meannumber ofapprovalsappears tobe anidiosynrati harater-
isti of eah eletion, most probably aruing to the politial limateof the
moment. Forinstane, voters inKonstanzapproved ofmoreandidatesthan
inMessel. Thisholdstruebothforthe ConstituenyVote(two-samplet-test
with unequal samplesize and variane, p-value 0.041), where atually there
were less available andidates in Konstanz than in Messel, and for the List
Vote, with equal number of available parties (p-value <0.001). The mean
number of approvals, however, does not dier signiantly among polling
stations for a xed experiment (Messel or Konstanz) and type of vote (an-
didate and party).
10
The only exeption is a partiular polling station in
Konstanz (Konstanz V), and only for the ase of ListVote.
11
9
Whethervoterswhoapprovedofonlyoneandidateandonepartyatuallyexpressed
a preferene for doing sois notentirelylear. Some voters might havebeen inuened
by theirpartiipation in theoial vote before taking partin the experiment. Further,
anedotal evidene, in the form of ommentswereeivedduring and after theeletions,
pointsoutthatthis behaviormightarueto simpleresistanetohange: Havingvoted
forsoand somanyyearsinthe pastbygivingonlyonepartymysupport,whyshould I
hangemyvotingbehavior?
10
An alternativeexplanation (suggested by M. Behtel) for the larger number of ap-
provalsin Konstanz is as follows. The Konstanz eletion was a Federal one, while the
Messel onewas astate eletion. Votersmight onsiderstateeletions, ompared to fed-
eralones,to beseondordereletions andhenebelessinformedaboutandidatesand
parties' programs,whihmightinturn resultin alowernumberofapprovals.
11
Weondutedpairwiset-teststo hekfordierenesinthemeansandorretedthe
overallalphafailure withtheHolm-Bonferronimethod. Thenullhypothesis anonlybe
Table 1.2: Number of ballots for the dierent eletions.
Approvals 0 1 2 3 4 5 6 7
≥
8 MeanMessel: Constitueny Vote (Options: 8)
Messel I 12 148 207 65 21 3 0 0 1 1.891 (0.939)
Messel II 2 151 173 73 5 1 0 0 0 1.830 (0.784)
Messel III 2 38 39 14 6 0 0 0 0 1.838 (0.907)
Overall 16 337 419 152 32 4 0 0 1 1.860 (0.874)
Messel: ListVote (Options: 17)
Messel I 5 106 190 92 40 14 9 0 1 2.306 (1.184)
Messel II 0 113 163 81 35 11 1 1 0 2.198 (1.063)
Messel III 0 31 34 27 3 1 0 3 0 2.202 (1.231)
Overall 5 250 387 200 78 26 10 4 1 2.250 (1.141)
Konstanz: Constitueny Vote (Options: 6)
Konstanz I 3 72 111 41 7 0 0 1.902 (0.803)
Konstanz II 0 43 89 28 5 0 0 1.970 (0.742)
Konstanz III 3 50 116 46 3 0 0 1.982 (0.740)
Konstanz IV 2 78 124 48 7 1 0 1.927 (0.816)
Konstanz V 2 95 148 48 7 0 0 1.877 (0.763)
Konstanz VI 2 62 125 55 8 0 0 2.020 (0.789)
Overall 12 400 713 266 37 1 0 1.943 (0.779)
Konstanz: List Vote (Options: 17)
Konstanz I 0 32 75 73 38 14 0 2 0 2.722 (1.153)
Konstanz II 1 23 69 42 20 6 3 1 0 2.558 (1.167)
Konstanz III 0 29 73 79 22 12 1 2 0 2.662 (1.121)
Konstanz IV 0 45 95 80 26 10 3 2 0 2.533 (1.146)
Konstanz V 0 68 133 61 29 5 4 0 0 2.273 (1.051)
Konstanz VI 0 35 91 75 30 14 6 1 0 2.679 (1.197)
Overall 1 232 536 410 165 61 17 8 0 2.557 (1.148)
Options= available options (8 andidates and 17parties in Messel, 6 andidates
and 17partiesin Konstanz). Mean olumn: Numbers in brakets are Std. errors.
In partiular, we annot support the onlusion of Laslier and Van der
Straeten (2008) that voters, ingeneral, onaverage approve of three alterna-
tives. Their partiipants on average approved of 3.15 out of 16 andidates
(where atotalof2587ballotswereast). Atually,themeansofapprovalsfor
theListVoteareofomparablemagnitudetotheoneinthe2007Frenhpres-
identialeletion experiment by Baujard and Igersheim (2009,2010) (Laslier
and Van der Straeten 2008 olleted data in the 2002 eletion). In this
experiment, 2813 partiipants on average approved of 2.23 out 12 feasible
andidates. Althoughthe dierenes invotingbehavior between Frenhand
German voters would be worth a study on its own, with the given data it
is impossible to identify the determiningfators without entering the realm
of speulation. Dierent numberof feasible alternatives, polarizingeletions
and the dierent methodsemployed learly play aruial role. On an even
oneive of some as yet not identied psyhologial or ultural fator that
mightalso inuene the dierenes inbehavior.
Sinewe an identify the numberofapprovalsfor andidatesand parties
for eah individual voter, we have data on two approval deisions for eah
voter and an ompute the orrelation between both variables. Pearson's
orrelation between number of approvals for andidates and for parties in
Messel was 0.598 (Spearman's
ρ = 0.652
). In the ase of Konstanz, the or-relation was 0.483 (Spearman's
ρ = 0.509
). Of ourse, voting deisions forandidates and for partiesin agiven eletionhave tobe expeted toexhibit
some orrelation. However, these orrelationsan alsoindiatethat individ-
ualvarianeinthenumberofapprovalsfollowspartlypersonalharateristis
of the voters.
The numberof approvalsinreases from Constitueny Vote to ListVote,
both in Messel and in Konstanz. The data set from the rst experiment
shows that 295 eletors approved of more parties than of andidates but
only 59voters did the opposite. ForKonstanz, the numbers are 630 and 90,
respetively. Although one ould formulate the hypothesis that the number
rejetedfortheaseofListVoteinKonstanz,andonlyforomparisonsinvolvingKonstanz
V, whihwasloatedin aresidenefortheelderlyandhadasigniantlyhigheraverage
voteragethanotherpollingstations.
of approvals is larger in the ase of List Vote simply beause the available
number of alternatives is larger, we annot test this hypothesis beause the
twodeisionsarenotomparable. Castingvotesfortheandidatesisnotthe
same as asting votes for the parties behind those andidates. Forexample,
95 partiipants in Konstanz approved of the SPD andidate, but did not
approve of the party itself.
12
1.3.2 Eletion Results
The atual hoies in the experiments are presented in Tables 1.3 to 1.6.
These tables are organized as follows. The olumn Votes lists the share
of partiipants who diretly approved of a party or andidate. Hene, the
perentages in this olumn do not add up to 100%. In the seond olumn,
Z-Share, we present the normalized share of approvals for eah party and
andidate,i.e.approvalsforapartyorandidatedividedbythetotalnumber
of approvals given by the voters. These results an be diretly ompared
with the oial outome. In order to easily see the hanges between the
outomes of the two methods, the olumnsZ-Rank and O-Rank indiate
the rankof eah alternative aording tothe ApprovalVotes reeived in the
experiment and aording to the share of total votes reeived in the oial
eletion, whih isitself presented in olumnO-Share. In ase of ties in the
(rounded) vote shares,the rankis determinedfollowingtheabsolutenumber
of approvals,whihislistedinTable 1.11inthe Appendix. Allresultsof the
oial eletion refer to personal eletors (i.e. without those who registered
to ast their vote per post) from the set of polling stations the experiment
took plae in, i.e. the whole of Messel for the rst experiment, and our six
seleted polling stationsin the ase of Konstanz.
Constitueny Vote, Messel (Table 1.3). There were 8 andidates in
the distrit eletions in Messel, eah representing one of the major parties:
12
Attheaggregatelevel,itisreasonabletoexpetalargeraveragenumberofapprovals
forparties thanforandidates,simplybeausenotallpartiesappointandidatesforthe
distrit eletion. If oneonsiders only parties whih did haveandidates in thedistrit
eletion, the average number of approvals was 1.937 in Messel (ompared to 1.860 for
andidates)and1.983inKonstanz(omparedto1.943forandidates).
Candidate Votes Z-Share Z-Rank O-Share O-Rank
△
Hofmann, SPD 58.0 31.2 1 45.9 1 -14.7
Milde, CDU 41.8 22.5 2 37.9 2 -15.4
Harth, Greens 31.4 16.9 3 4.5 4 +12.4
Dr. Krug, FDP 30.3 16.3 4 6.0 3 +10.3
Deistler, Left 10.4 5.6 5 3.4 5 +2.2
Herrmann, FV 7.4 4.0 6 0.8 7 +3.2
Bauer, REP 3.9 2.1 7 1.1 6 +1.0
Zeuner, NPD 2.8 1.5 8 0.3 8 +1.2
Total 186.0
The
△
olumnshowsthedierenebetweenZ-shareandO-Shareof theandidates.All data exept ranks are given in %.
the CDU (onservative), the SPD (soialdemorats), the Greens, the FDP
(liberal), the Republians (extreme right), the Left (extreme left), the Free
Voters(FV)andtheNPD(extremeright). TheandidatefortheSPDParty,
Miss Hofmann, wonthe diretseat.
Under approval voting, Miss Hofmann is still the top ranked andidate.
Although the shareof votes dereased from45.9%to 31.2%,we see that she
was able toreeive the assent of an absolutemajorityof 58% of the eletors
and that she was the only one who did so.
13
Unfortunately, this sort of
informationis lostunder the oial method.
Thereare twoswithes inrankings,onebetweentheFDPandtheGreens
andidates and one between those ofthe REPand the Free Voters. Further,
thegapbetweenthetwoandidatesofSPDandCDUandtheothersbeomes
smaller. Theshare of votes inreases from 4.5%forthe Greens and from6%
13
Under Approval Voting, it is theoretially possible that more than one andidate
reeivesan absolute majority of approvals. However, in eah of the three experimental
pollingstations,MissHofmannwastheonlyandidateapprovedofbyanabsolutemajority
ofpartiipants.
for the FDP andidate to 16.9% and 16.3% respetively, while the share of
the CDU's and SPD's andidates dereases. Essentially, the dierenes in
vote shares for andidates in the enter of the politial spetrum derease.
The andidates ranked on the last positions (7 and 8) are those from the
far-right parties.
Constitueny Vote, Konstanz (Table 1.4). For the distrit vote in
Konstanz, sixandidateswereavailable,eahrepresentingamajorparty: the
CDU, the SPD,the FDP,the Greens,the Left andthe NPD. The andidate
of the CDU (Mr. Jung) reeived the most votes and won the diret seat for
his party.
Under Approval Voting, however, the results are radially dierent. A
major swith in rankings ours between the Greens' andidate, Mr. Seiler,
and the CDU andidate, Mr. Jung. While ranked on third position in
the oial eletion, Mr. Seiler is approved of by an absolute majority and
learlyistheAV-winner. Mr. Jungdropsfromrstpositionundertheoial
to third position in the AV-ranking. Not only did AV alter the andidate
ranking, a dierent andidate than the one suggested by the oialmethod
would have won the diret seat for hisparty under AV.
Table 1.4: Konstanz: Approval vs. Plurality Voting, Constitueny Vote.
Candidate Votes Z-Share Z-Rank O-Share O-Rank
△
Seiler, Greens 50.6 26.0 1 19.0 3 +7.0
Friedrih, SPD 46.5 23.9 2 25.6 2 -1.7
Jung, CDU 45.1 23.2 3 37.8 1 -14.6
Homburger,FDP 33.7 17.4 4 10.7 4 +6.7
Stier, Left 17.4 9.0 5 6.5 5 +2.5
Louis, NPD 1.0 0.5 6 0.4 6 +0.1
Total 194.3
The
△
olumnshowsthedierenebetweenZ-shareandO-Shareof theandidates.All data exept ranks are given in %.
Similarly to our observations from the rst experiment in Messel, the
andidatesofthetwomajorparties,CDUandSPD,aretheonlyalternatives
losing in terms of share when the method is swithed from PV to AV. The
share of the SPD andidate dereases from25.6%to 23.9%,the share of the
CDU andidate from 37.8% to 23.2%. There is no dierene in the rank of
the remainingandidates between the oial eletion and the experiment's
results.
List Vote, Messel (Table 1.5). In the state eletion in Messel, there
were 17 dierent parties from whih to hoose: the CDU, the SPD, the
Greens, the FDP, the Republians, the Animal Protetion Party, the Civil
Liberties Party, the PSG (ommunist), the Popular Vote Party, the Grey
Party(orientedtowards seniorissues), theLeft,the VioletParty,the Family
Party, the Free Voters, the NPD, the `Hessian Pirates' (an organization of
omputer hakers), and the UB Party.
14
Fortheomparison between plurality voting and approvalvotingresults,
weroughlyobservethesamepatternasfortheConstituenyVote. TheSPD
remainsthe strongest partysupportedbyanabsolutemajorityof approvals,
followed by the seond-ranked CDU. Additionally,those arethe onlyparties
whih lose in terms of share under approval voting. Again there is a swith
in ranks between the FDP and the Greens. The parties from both ends of
the politialspetrumlose in termof ranks. The NPD drops fromrank7 to
11, the REPfrom 6 to9 and the far-left party PSG from15 to16.
A simple onsideration shows whih parties gain the most. On average,
eletorsinMesselast2.25partyapprovalsperballot. Toobtaintheapproval
votesoftheaverageparty,weansimplymultiplyitsperentageofvotesfrom
the oial eletionby a fator of 2.25. We an also ompute the individual
fator of a party by dividing the number of approvals per partiipant it
14
Usually, it is less likely to observe ties in the party ranking the larger the mass of
onstituents. If wekeepin mind therelativelysmall numberof experimentpartiipants
and urnvoters,itisnotsurprisingthatseveraltiesourintheexperimentaswellasin
theoialMesselvote. E.g.,theAnimalProtetionPartyandtheFamilyPartyreeived
anequaltotalnumberofapprovalsintheexperiment. ThesameistruefortheNPDand
the`HessianPirates',rankedon11thposition,andCivilLibertiesPartyandPSG,ranked
onplae16in theexperiment'spartyrankingin Messel.
Party Votes Z-Share Z-Rank O-Share O-Rank
△
SPD 53.8 23.9 1 38.9 1 -15.0
CDU 44.6 19.8 2 36.0 2 -16.2
Greens 36.1 16.0 3 7.0 4 +9.0
FDP 32.6 14.5 4 9.0 3 +5.5
Left 12.3 5.5 5 4.9 5 +0.6
AnimalProt. Party 9.6 4.3 6 0.8 7 +3.5
The FamilyParty 9.6 4.3 6 0.2 12 +4.1
The Free Voters 7.1 3.1 8 0.5 9 +2.6
Republian Party 3.3 1.5 9 1.0 6 +0.5
The Popular Vote 2.9 1.3 10 0.2 13 +1.1
NPD 2.8 1.2 11 0.8 7 +0.4
The Hessian Pirates 2.8 1.2 11 0.3 10 +0.9
The GreyParty 2.5 1.1 13 0.2 13 +0.9
UB 2.1 0.9 14 0.1 15 +0.8
The VioletParty 1.0 0.5 15 0.3 11 +0.2
PSG 0.9 0.4 16 0.1 15 +0.3
CivilLiberties Party 0.9 0.4 16 0.1 15 +0.3
Total 225.0
The
△
olumn shows the dierene between Z-share and O-Share of the parties.All data exept ranks are given in %.
reeived inthe experiment by the perentage of votes reeived inthe oial
eletion.
15
Hene, a party fator above 2.25 in Messel indiates that the
partyatuallybenetedfromthehange toApprovalVoting,andvieversa.
Whilethe fators of the CDU andSPD with 1.24 and 1.38are learly below
the 2.25 average, the fators for the Greens and FDP are 5.18 and 3.62.
Aboveaverage aswellare the fators of the NPD and the RepublianParty
with 3.74 and 3.45. Outstanding, however, with 44.64, 12.75 and 14.66 are
15
Toavoidrounding errors,weomputepartyfatorsusing theexatnumberofvotes
providedinTable1.11intheAppendix.
the fators of the Family Party, the Animal Protetion Party and the Free
Voters. All threeparties are moderate and issue-foused.
List Vote, Konstanz (Table 1.6). Voters ould hoose one of 17 dier-
ent parties: the CDU, the SPD, the Greens, the FDP, the Left, the NPD,
the Republians, the PBC(struggles for upholdingChristian valuesin mod-
ern soiety), the MLPD (the Marxist-Leninist party of Germany), the Civil
Liberties Party, the Popular Vote Party, the ADM (onservative), the DVU
(extremeright),theVioletParty,the AnimalProtetionParty, theödp (ori-
ented towards environmental issues),and the Pirate Party.
Table 1.6: Konstanz: Approval vs. Plurality Voting, List Vote.
Party Votes Z-Share Z-Rank O-Share O-Rank
△
Greens 58.1 22.7 1 20.1 3 +2.6
SPD 47.3 18.5 2 21.9 2 -3.4
CDU 41.5 16.2 3 28.6 1 -12.4
FDP 36.3 14.2 4 16.9 4 -2.7
The Pirate Party 20.8 8.1 5 3.7 6 +4.4
Left 18.4 7.2 6 6.2 5 +1.0
AnimalProt. Party 12.2 4.8 7 0.9 7 +3.9
ödp 7.4 2.9 8 0.3 9 +2.6
The Popular Vote 4.9 1.9 9 0.2 10 +1.7
The VioletParty 3.1 1.2 10 0.2 10 +1.0
Republian Party 1.3 0.5 11 0.2 12 +0.3
NPD 1.0 0.4 12 0.4 8 +0.0
MLPD 1.0 0.4 13 0.1 14 +0.3
PBC 1.0 0.4 13 0.2 13 +0.2
CivilLiberties Party 0.7 0.3 15 0.0 16 +0.3
ADM 0.3 0.1 16 0.0 15 +0.1
DVU 0.3 0.1 17 0.0 16 +0.1
Total 255.7
The
△
olumn shows the dierene between Z-share and O-Share of the parties.All data exept ranks are given in %.
UnderApproval Voting, the pitureissimilartothe one skethed for the
Constitueny Vote. The lear winner is the Green Party, with an absolute
majority of approvals(58.1%). Thewinner ofthe oialeletion,the CDU,
drops to the 3rd position. The marginal Pirate Party, whih reeived only
3.7% of the votes inthe oialeletion,is approved of by astunning 20.8%
of the eletorate and is ranked even beforethe Left. The AnimalProtetion
Party and the green-oriented ödp alsoexperienelarge inreases, from0.9%
resp. 0.3%shares inthe oialeletionto12.2% and7.4% approvalrates in
the experiment.
1.3.3 General Disussion
Several desirableproperties of the Approval Voting methodan befound in
the literature whih are highlighted in our data or beame lear during the
experiments. It has been argued (e.g. Brams and Fishburn, 2005) that the
methodredues strategionsiderationsasthewastedvote eet,bywhih
voters do not reveal the parties they favor most and bet on popular alter-
natives instead. Under Approval Voting, individualsan ast votes for their
preferredminorityalternativesandthemostpopularones. Thus,themethod
enourages sinerevoting(see alsoBramsand Fishburn,1978and Wolitzky,
2009) and provides voters with more options to represent their preferenes.
Minority andidates reeive their true level of support, so that the outome
under Approval Voting should be a better reetion of the aeptability of
all andidates amongthe eletorate.
It is alsooften laimed (e.g. Brams and Fishburn, 1978), that ompared
tomoreompliatedrankingmethods, itiseasyforvoterstounderstandthe
Approval Voting method. It provides a simple way for voters to express a
larger part of the informationontained intheir preferenes withoutforing
them todevelop full andidate/party rankings. Hene,it isaognitiveom-
promisebetween deidingonlyabest andidateand generatingaomplete
ranking.
Finally, the method is supposed to redue inentives for negative am-
paigning, sine lose andidates need no longer ompete against eah other
for the vote of the eletor. They an share a ommon base. As a onse-
quene, by a simple politial proximity argument, we an expet a larger
inrease in the base shared by entrist andidates than in that shared by
extremist andidates. Hene, Approval Voting strengthens the position of
moderate, entrist andidates, withoutatthe same timedenyingvoters the
opportunity toexpress their support for moreextremist andidates (Brams
and Fishburn, 1978, p. 831).
Qualitative Lessons from the Data
Letusbrieydisusshowtheseinsightstranslateintoour experimentaldata.
The typial image of the German party system at the time we ran our ex-
periments was haraterized by two big enter, ath-all-parties, the CDU
and the SPD who, with a broad support inthe population, struggleagainst
eah other for the rst position in the party ranking. Parties like the FDP,
the Greens and the Left were only of interest when partners for forming a
rulingoalitionwereneeded. In theontextoftheexperiments'outome,we
dare speulatethatthis viewmightatually beanadho artifatreated by
the prevailing voting method, rather than an aurate image of the voters'
preferenes.
The Approval Voting system used in our experiments fundamentally al-
tered the pereption of the party landsape,showing instead fourmain par-
ties, eah of them with a signiant proportion of the vote (see Tables 1.5
and1.6). TheallegedlysmallerGreenPartyandtheliberalFDP,whihuntil
the date of writing are universally viewed as oalition partners but not as
andidatesforwinninganeletion,anbeseen tohavealevelofsupportnot
far behind that of the two main parties. That is, the omparison between
our experimentaldataand thedata ofthe oialeletionsisonsistentwith
the view that, when voters are asked to hoose only one of the available
alternatives, the wasted vote argument plays a more than signiant role.
It beomes less attrative to vote for smaller parties whih are pereived as
not having the option for winning the eletion or entering the parliament,
althoughthey mightatbest represent the voter's opinion. Eletorstrade-o
