Collective Decision Making: Views from Social Choice and Game Theory

281 Pages·2010·1.67 MB·English

by  Adrian Van Deemen

THEORYANDDECISIONLIBRARY
GeneralEditors:W.Leinfellner(Vienna)andG.Eberlein(Munich)
SeriesA:PhilosophyandMethodologyoftheSocialSciences
SeriesB:MathematicalandStatisticalMethods
SeriesC:GameTheory,MathematicalProgrammingandOperationsResearch
SeriesD:SystemTheory,KnowledgeEngineeringandProblemSolving
SERIESC:GAMETHEORY,MATHEMATICALPROGRAMMING
ANDOPERATIONSRESEARCH
VOLUME43
Editor-in-Chief:H.Peters(MaastrichtUniversity,TheNetherlands);HonoraryEditor:S.H.
Tijs(TilburgUniversity,TheNetherlands)
Editorial Board: E.E.C van Damme (Tilburg University, The Netherlands); H. Keiding
(University of Copenhagen, Denmark); J.-F. Mertens (Université catholique de Louvain,
Belgium); H. Moulin (Rice University, Houston, USA); Shigeo Muto (Tokyo University,
Japan); T. Parthasarathy (Indian Statistical Institute, New Delhi, India); B. Peleg (Hebrew
University, Jerusalem, Israel); T.E.S. Raghavan (University of Illinois at Chicago, USA);
J. Rosenmüller (University of Bielefeld, Germany); A. Roth (Harvard University, USA);
D. Schmeidler (Tel-Aviv University, Israel); R. Selten (University of Bonn, Germany);
W.Thomson(UniversityofRochester,USA)
Scope:Particularattentionispaidinthisseriestogametheoryandoperationsresearch,their
formalaspectsandtheirapplicationstoeconomic,politicalandsocialsciencesaswellasto
sociobiology.Itwillencouragehighstandardsintheapplicationofgame-theoreticalmethods
toindividualandsocialdecisionmaking.
Forfurthervolumes:
http://www.springer.com/series/6618

·
Adrian Van Deemen Agnieszka Rusinowska
Editors
Collective Decision Making
Views from Social Choice and Game Theory
123
Editors
Dr.AdrianVanDeemen Dr.AgnieszkaRusinowska
RadboudUniversity GATEGrouped’Analyseetde
InstituteforManagementResearch ThéorieEconomique
ThomasvanAquinostraat3 CNRSUMR5824
6525GDNijmegen UniversitéLumièreLyon2
TheNetherlands 93,ChemindeMouilles,B.P.167
[email protected] 69131EcullyCedex
France
[email protected]
ISSN0924-6126
ISBN978-3-642-02864-9 e-ISBN978-3-642-02865-6
DOI10.1007/978-3-642-02865-6
SpringerHeidelbergDordrechtLondonNewYork
LibraryofCongressControlNumber:2010925110
(cid:2)c Springer-VerlagBerlinHeidelberg2010
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Preface and Introduction
HarriedeSwartisaDutchlogicianandmathematicianwithagreatandopeninter-
est in applications of logic. After being confronted with Arrow’s Theorem, Harrie
became very interested in social choice theory. In 1986 he took the initiative to
start up a group of Dutch scientists for the study of social choice theory. This
initiative grew out to a research group and a series of colloquia, which were held
approximately every month at the University of Tilburg in The Netherlands. The
organization of the colloquia was in the hands of Harrie and under his guidance
they became more and more internationally known. Many international scholars
likedvisitingthesocialchoicecolloquiainTilburgandenjoyedgivingoneormore
presentationsabouttheirwork.TheylikedHarrie’skindnessandhospitality,andthe
opennessofthegroupforanythingandeverythinginthefieldofsocialchoice.
The Social Choice Theory Group started up by Harrie consisted, and still con-
sists, of scholars from several disciplines; mostly economics, mathematics, and
(mathematical) psychology. It was set up for the study of and discussion about
anythingthathadtodowithsocialchoicetheoryincluding,andnotintheleast,the
supervisionofPhDstudentsinthetheory.Membersofthegroupwere,amongoth-
ers, Thom Bezembinder (psychologist), Hans Peters (mathematician), Pieter Ruys
(economist),StefTijs(mathematicianandgametheorist)and,ofcourse,Harriede
Swart (logician and mathematician). The group has always been very serious and
hashadaclearviewonsocialchoice.Logicandmathematicsareimportantforthe
theory;hencebothshouldformanimportantcomponentinthestudyofit.However,
socialchoicetheoryalsobelongstothesocialsciencesand,consequently,thesocial
scientific part is equally important. This two-component approach of the group to
social choice theory nicely converged in the first two PhD students trained by the
groupandsupervisedbyHarrie.Onestudent(TonStorcken)wasamathematician
andtheotherone(AdVanDeemen)wasasocialscientist.
The group met regularly, approximately once a month, not only to prepare the
students to go to any length, but also to discuss a wide range of topics in social
choicetheory;fromvariationsofArrow’stheoremtocoalitionformationinsimple
games. The first two PhD students graduated in 1990 and 1991 respectively; both
withhonors.However,thiswasnotthatmuchofasurpriseconsideringthescientific
strength,theinvolvementandthecommitmentofthegroup.
v
vi PrefaceandIntroduction
In fact, the group did not have a clear name; it was simply called: the Social
ChoiceTheoryGroupor:theSocialChoiceGroup.Inthebeginningofthenineties,
thegroupexpandedandmoreDutchuniversitiesbecameinvolved.Asaresult,more
PhDstudentsfollowed.However,thegroupkeptitseasy-accessandopenstatus.The
organization of the meetings remained in Harrie’s hands and with that its inviting
andinformalcharactercontinued.
Only in 1999, the group became something of an administrative unit. The par-
ticipating universities represented in the group were asked to do their bit and to
contributeanannualamounttomeetthecostsforthecolloquia.Consequently,from
then on an annual meeting had to be held to discuss and approve the invitation
policy and a financial report. These annual meetings were chaired by Harrie and,
typically,nevertookmorethanhalfanhour.Theadministrationandpolicieswere
alwaysfoundtobeinorder.Itwasasmalldetail,ifnotasmalldistraction,which
unfortunatelyhadtobedealtwith.Themainobjectivewas,andstillis,socialchoice
theory.Curiosity,openness,andhospitalityremainedthekeywords.
In2009,theSocialChoiceTheoryGroupofficiallyandformallyexisted10years.
ItwascelebratedwithaninternationalsocialchoiceconferenceattheendofMay
2009. Moreover, something completely different but nevertheless very important
occurred in that year: in September Harrie de Swart reached the pension age and,
asisobligedinTheNetherlands,hadtoretire.Fortunately,thecontinuationofthe
SocialChoiceGroupwillnotbeinjeopardy.Theorganizationofthecolloquiawill
be gradually transferred to other hands, accompanied and supported by Harrie’s
experienceandinsights.ItisclearthatHarrieleavesbehindapreciousandimportant
institution, operating in an informal way and directed primarily at studying social
choice.
ThisbookisdedicatedtoHarriedeSwart.Itistohonorhisinitiativesandactivi-
tiesfortheSocialChoiceTheoryGroupandthemonthlySocialChoiceColloquia.It
istothankhimforallhiseffortsandenergyhespentonthisgroupanditscolloquia.
Wethinkthathefulfilledanenormoustask.Thesocialchoicecolloquiaareinterna-
tionally well-known by now. Moreover, social choice theory became an important
andstrongscientificfieldintheNetherlandsbecauseofthis.
Inthecolloquia,almostanytopicwithinthefieldofcollectivedecisionmaking
has been discussed; from voting and power distribution in the European Council
tocabinetformationintheNetherlands;frompluralityvotingandtheBordacount
to restricted domains for Arrovian social welfare functions; from freedom, rights
and networks to stability of network formation; from committee decision making
to coalition formation games. We wanted a book that represents the open view on
collective decision making and also reflects the richness and diversity of the col-
loquia. We approached a number of authors who have all presented one or more
lectures in the social choice colloquia. They all responded very enthusiastically.
Withoutexception,theywantedtocontributetoHarrie’sbookasitiscalledonthe
fly. Clearly, not all topics discussed in the course of all those years are covered.
However,wethinkthattheresultisadiversandrichreflectionindeed.
In chapter “From Black’s Advice and Arrow’s Theorem to the Gibbard–
SatterthewaiteResult”,DonaldSaarigives,asever,achallenginginterpretationof
PrefaceandIntroduction vii
Arrow’sTheoremandrelatesittoproblemsofpairedcomparisonandstrategicvot-
ing.Inhisview,thecauseofArrow’sresultliesmainlyintheinter-profilecondition
of IIA. This condition requires a rule to ignore important information about the
voters’ transitivity of preference. Since IIA forces a rule to compare the alterna-
tives pairwise, better partwise, and independently, the connecting information for
thepartstocreateawholeismissing.Inotherwords,themacro-resultofanaggre-
gation process satisfying IIA – the social choice or the social preference – is not
basedonallthepreferenceinformationavailableonmicro-level.Itisinterestingto
notethatalsoAmartyaSenapproachedtheordinalnon-comparabilityframeworkof
Arrowfromaninformationalpointofview(seeSen’sCollectiveChoiceandSocial
Welfare, 1970, San Francisco, Holden-Day, Inc ). However, there is an important
difference between Saari and Sen. According to Sen, the cause of Arrow’s result
liesinthefactthatonlyordinalpreference(utility)informationisused.Thecause
isintheexclusionofnon-preferenceinformation.IntheviewofSaari,however,the
cause lies in the fact that not all available ordinal preference information is used.
Connectinginformationatthemicrolevel(transitivityofpreferences)isneglected.
So,Arrow’sTheoremisnotcausedbyashortageofinformationasstatedbySen,
butbyaneglectofavailableinformation.Clearly,thisisfascinating.
In chapter “The Impact of Forcing Preference Rankings When Indifference
Exists”, William Gehrlein brings in an important contribution to the probability
approach to the Condorcet paradox. Instead of the traditional Impartial Culture
Condition, he uses the (much more difficult to handle) Impartial Weak Ordered
CultureConditionandshowsthatpartiallyindifferentvoterpreferenceshaveaseri-
ousimpactontheprobabilityofaCondorcetwinner.Subsequently,hestudieswhat
willhappenwiththeprobabilitiesofaCondorcetwinnerwhenindifferentvotersare
forcedtochangetheirindifferencepartintoaranking.Heingeniouslycalculatesthe
probabilitiesfordifferentproportionsofvoterswhoareforcedtoproducecomplete
rankings.HeshowsthattheprobabilitiesofaCondorcetwinnerforpartiallyindif-
ferentvotersareremarkablydifferentfromtheprobabilitiesunderforcedcomplete
rankings.
Inchapter“ConnectionsandImplicationsoftheOstrogorskiParadoxforSpatial
VotingModels”,HannuNurmiandDonaldSaaridealwiththedifficultOstrogorski
paradoxandrevealsomeofitssecrets.Theyestablishaclearandbeautifulconnec-
tionwithMcKelvey’sChaosTheorem:iftheOstrogorskiparadox(andtherelated
Anscombeparadox)occurs,thecoreofaspatialvotinggamewillbeempty.Hence,
accordingtoMcKelvey’sTheorem,aglobalcyclewillthenexist.Furthermore,they
resolve Kelly’s conjecture about the relationship between the absence of a Con-
dorcetwinnerandtheOstrogorskiparadox.Itisabeautifulpaperthatmightinduce
astreamofnewresearchontheOstrogorskiparadox.
Chapter“MaximalDomainsforMaskinMonotoneParetoOptimalandAnony-
mousChoiceRules”writtenbyOlivierBochetandTonStorckentypicallybelongs
tothehardcoreofsocialchoice.Inthiscontribution,domainrestrictionsarestud-
ied, not only as is traditional for the specific majority rule, but more general for a
class of social choice rules satisfying Pareto optimality, Maskin monotonicity and
anonymity. They employ a positive approach, that is, they construct and proof the
viii PrefaceandIntroduction
existenceofamaximal,strategy-proofandnon-dictatorialpossibilitydomainboth
for the three- or- more agent case as for the special case of two agents. It is an
accurate and technically excellent elaborated study. We have met this professional
skillfulnessquitefrequently inthesocial choice colloquia. Itiswhat makes social
choicetheorysuchanattractiveandbeautifulfieldofscience.
Chapter“ExtremalRestriction,Condorcetsets,andMajorityDecisionMaking”
by Adrian Van Deemen and Elena Saiz re-examines a specific domain restriction
called Extremal Restriction (ER). This restriction is supposed to be necessary and
sufficientfortheexistenceofaCondorcetwinner.Somecounter-examplesforthis
resultaregiveninthecasethatzero-assignments,thatisassignmentsofpreferences
tonovoteratall,arenotallowed.Moreover,allmaximalsetsofpreferencessatisfy-
ingERareenumeratedforthethreealternativecase.Finally,astudyofCondorcet
sets, or as Saari calls them Condorcet profiles (see chapter “From Black’s Advice
and Arrow’s Theorem to the Gibbard–Satterthewaite Result”), and of their exten-
sionsoverweakorderingsisgiven.
Chapter “Rights Revisited, and Limited” written by Maurice Salles and Feng
Zhangisinthestyleofthefamousnon-starredchaptersofSen’sCollectiveChoice
andSocialWelfare.Itisaneasyaccessibleandintuitiveaccountofsomeimportant
resultsonlimitedrights.(Limited)rights,libertyandSen’sfamousliberalismtheo-
remarestudiedbothintheaggregationframeworkandthechoiceframeworkandare
comparedtoeachother.Itisarguedthatinneithercaselimitedrightsareanescape
routefortheSen-typeimpossibilityresults.Animportantandchallengingpointin
theirchapteristhatliberalismcanbestudiedintermsofobligation(necessity)and
possibility. They therefore propose to use modal and related logics in the formal
analysisofrightsandlibertyinthefuture.Theybelievethattheuseoftheselogics
maythrownewlightontheproblemswithrespecttorightsandliberty.
Inchapter“SomeGeneralResultsonResponsibilityforOutcomes”,MartinVan
Heesinvestigatestheproblemofresponsibilityforoutcomesincommitteedecision
making.Hisaccountofresponsibilityconsistsoftwocomponents.Amemberofa
committee can be held responsible first if she is causally effective for the realiza-
tionofanoutcomeandsecondlyifshehashadthe“opportunitytodootherwise”.
Clearly,aformalapproachtothiskindofresponsibilitywillbenotoriouslydifficult.
However,VanHeesgivesaveryelegantandbeautifulformalanalysis,whichleads
toaclearinsightintherelationbetweendifferentformsoftransparencyincollective
decision making and responsibility. We find this a path-breaking chapter that may
leadtoastreamofnewresearch.
Inchapter“ExistenceofaDictatorialSubgroupinSocialChoicewithIndepen-
dent Subgroup Utility Scales, an Alternative Proof”, Anna Khmelnitskaya works
within a research program of social choice theory that tries to extend the ordi-
nal non-comparable framework of Arrow. She constructs new proof for an exist-
ing theorem (see Khmelnitskaya & Weymark, 2000, Social Choice & Welfare,
17, 739–748) about the existence of a dictatorial group for different extended
measurability-comparability frameworks (see Sen’s Collective Choice and Social
Welfare,Chap.8).Theproofprovidesinsightintothe“structureofpossibleinterre-
lationsbetweenutilitiesofdifferentindividuals”.
PrefaceandIntroduction ix
Chapter “Making (Non-standard) Choices” written by Wulf Gaertner is about
making non-standard choices. Using the axiomatic method, he describes choice
functions that violate contraction and expansion consistency conditions. He finds
that non-standard choices do not have a uniform structure. However, choice func-
tions that violate the standard rationality conditions do not imply that individuals
arebehavingirrationally.
In the next interesting chapter “Puzzles and Paradoxes Involving Averages: An
Intuitive Approach”, Feld and Grofman study seemingly paradoxical aggregation
results. They present the insight that sometimes these paradoxical puzzles can be
solvedbyreconstructingthemfromtheirconstituentpartsbyappropriatelyweight-
ingthesepartsandsequentiallybyusingthenotionofweightedaverage.Inthisway,
theyareabletoanswercuriousquestionslike“howcanitbethatmosthouseholds
intheUnitedStatesareheadedbyunmarriedadults,yetmostadultsaremarried?”
or“Howcanfamilyincomebegoingdowneventhoughpercapitaincomeisgoing
up?”
Inchapter“VotingWeights,ThresholdsandPopulationSize:MemberStateRep-
resentation in the Council of the European Union”, Madeleine Hosli analyzes the
empiricaldistributionofvotesintheCounciloftheEuropeanUnioninasolidand
thorough way. Her empirical investigations clearly show that voting rules in this
committeeindeedembodyanimportanttrade-offbetweenthenumberofindividuals
requiredformakingacollectivedecisionontheonehand,andtheexpectedcostsof
decisionmakingontheother.Withthisniceempiricalresult,shestronglyconfirms
the well-known trade-off model of Buchanan and Tullock from The Calculus of
Consent(1962,AnnArbor,TheUniversityofMichiganPress),
Chapter “Stabilizing Power Sharing” is a challenging chapter about stability of
power sharing written by Steven Brams and D. Marc Kilgour. They model power
sharingbothasaduelinwhichtheplayersfiresequentiallyandasaduelinwhich
theyinteractsimultaneously.Inbothmodelingapproaches,theplayersareallowed
to choose to share prizes. Moreover, they study which prize ratio renders power
sharing stable. They find and explain that the incentives to share power in the
simultaneous interaction case are greater than in the sequential interaction case. It
isinterestingtoseethedifferencesbetweensequentialinteractivedecisionmaking
andsimultaneousinteractivedecisionmakingsoclearly.
Chapter“DifferentApproachestoInfluenceBasedonSocialNetworksandSim-
ple Games”, written by Michel Grabisch and Agnieszka Rusinowska, is a concise
andin-depthoverviewofdifferentapproachestoinfluenceprocessesamongagents
in collective decision making situations. The inclination of an individual to make
a decision may clearly differ from his or her actual decision making behavior.
Many kinds of influences may transform the inclination into a different decision.
GrabischandRusinowskadescribeanddiscussdifferentapproachestotheseinflu-
ence processes in collective decision making processes. The models presented are
thoroughly discussed and reviewed both formally and informally. The result is a
distinctive and amiable work that presents the state-of-the-art in this exciting field
ofresearchinaclearway.Inaddition,itpresentsanagendaofopenproblemsfor
futureresearch.