Collective Decision Making: Views from Social Choice and Game Theory PDF
Preview Collective Decision Making: Views from Social Choice and Game Theory
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 Thisworkissubjecttocopyright.Allrightsarereserved,whetherthewholeorpartofthematerialis concerned,specificallytherightsoftranslation,reprinting,reuseofillustrations,recitation,broadcasting, reproductiononmicrofilmorinanyotherway,andstorageindatabanks.Duplicationofthispublication orpartsthereofispermittedonlyundertheprovisionsoftheGermanCopyrightLawofSeptember9, 1965,initscurrentversion,andpermissionforusemustalwaysbeobtainedfromSpringer.Violations areliabletoprosecutionundertheGermanCopyrightLaw. Theuseofgeneraldescriptivenames,registerednames,trademarks,etc.inthispublicationdoesnot imply,evenintheabsenceofaspecificstatement,thatsuchnamesareexemptfromtherelevantprotective lawsandregulationsandthereforefreeforgeneraluse. Coverdesign:IntegraSoftwareServicesPvt.Ltd.,Pondicherry Printedonacid-freepaper. SpringerispartofSpringerScience+BusinessMedia(www.springer.com) 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.
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