2026年人工智能如何侵蚀人类能动性：形式模型研究报告（英文版）

ALVINMOONANDBENJAMINBOUDREAUX

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AboutThisReport

Inthisreport,wedevelopaformalframeworkformeasuringhowartificialintelligence(AI)affectscollec-tivehumanagencyindecisionmakingprocesses.Wedefinecollectiveagencyashumanity’scapacitytomakeconsequentialchoicesaboutsharedresources,institutions,andthesocialenvironment.

Drawingonsocialchoicetheory,wemodeldecisionmakingintermsofcoalitions:groupsthathavedeci-siveinfluenceoveroutcomes.WeproposequantitativemetricsfortrackinghowagencyconcentratesovertimeandidentifythreemechanismsthroughwhichAIsystemsreducehumanagency:humandisenfran-chisement,AIenfranchisement,andAIagendacontrol.

Thisreportisintendedforpolicymakers,AIresearchers,AIdeployers,andotherstakeholderswhoneedrigoroustoolsforanticipatingandrespondingtoAI’seffectsonhumandecisionmakingcapacity.

CenterfortheGeopoliticsofArtificialGeneralIntelligence

RANDGlobalandEmergingRisksisadivisionofRANDthatdeliversrigorousandobjectivepublicpolicyresearchonthemostconsequentialchallengestocivilizationandglobalsecurity.Thisworkwasundertakenbythedivision’sCenterfortheGeopoliticsofArtificialGeneralIntelligence(AGI),whichiscommittedtohelpingdecisionmakersunderstand,anticipate,andpreparetonavigatethenationalsecurityandgeopoliticalimplicationsofAGI.Thecenterconvenesleadingtechnologists,strategists,economists,politicalscientists,andoutsideexpertstoconsiderthefeasibilityandeffectivenessofprospectiveAGI-enabledcapabilities;thedomesticandinternationalimplicationsoftheiruse;andthestrategiesandpoliciesthatgovernments,busi-nesses,andcivilsocietycouldadopttorespondtonewrealities.Formoreinformation,visit

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Funding

ThisresearchwasindependentlyinitiatedandconductedwithintheCenterfortheGeopoliticsofArtifi-cialGeneralIntelligenceusingincomefromoperationsandgiftsfromRANDsupporters,includingphil-anthropicgiftsmadeorrecommendedbyDALHAPInvestmentsLtd.,ErgoImpact,FoundersPledge,Char-lottesochFredriksStiftelse,GoodVentures,Longview,andCoefficientGiving.RANDdonorsandgrantorshavenoinfluenceoverresearchfindingsorrecommendations.

Acknowledgments

WethankJoelPreddandtheGeopoliticsofAGIteamformanyhelpfulconversations.WeareespeciallythankfultoEdwardGeistfordiscussionsonmodelingandagency.ThisreportalsobenefitedgreatlyfromcommentsandhelpfulsuggestionsfromreviewersRobertLempert,ofRAND,andRaymondDouglas,ofACSResearch.Allerrorsareourown.

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Summary

Asartificialintelligence(AI)systemsassumemoredecisionmakingrolesingovernment,theeconomy,andsociety,aquestionemerges:Willhumansretainthecapacitytoshapecollectiveoutcomes?Severaltheo-riessuggestthat,oncehumandecisionmakingerodespastacertainthreshold,theskills,institutions,andpoliticalstandingneededtoreclaimthatdecisionmakingcapacitymaynolongerexist.However,nowidelyacceptedmetricsexistfortrackingthiserosion.Inthisreport,wedrawonsocialchoicetheorytodevelopaformalmodelofhowAIerodescollectivehumanagency;wealsomodeldecisionmakingintermsofcoali-tionsandproposequantitativemetricsfortrackingshiftsinthedistributionofdecisionmakingpowertoidentifythepointbeyondwhichthoseshiftscouldbecomeirreversible.

KeyFindings

Thefollowingkeyfindingsarosefromourresearch:

•Agencyerosionismeasurableacrossdomains.Wedefinethreemetrics—distributionofdecisivecoalitions,minimalcoalitionsize,andcompositionofminimalcoalitions—thatareapplicabletoawidevarietyofdecisionmakingprocesses.Thesemetricsprovideaframeworkfortrackinghumanagencyimpactsacrossdomains,comparingchanges,anddetectingnonlinearaccelerationofagencyerosion.

•Distinctmechanismsdriveagencyerosion.WeidentifyandformallyvalidatethreepathwaysthroughwhichAIreduceshumanagency:humandisenfranchisement(fewerhumansindecisionmakingroles),AIenfranchisement(AIentitiesgainingdecisionmakingpowerandchangingthecompositionofdeci-sivegroups),andAIagendacontrol(AIsystemsshapingwhichalternativesreachhumandecisionmak-erstoconsolidatepowerinunintendedways).

•Aterminalstateexists.Themathematicalstructureofourmodelidentifiesaformalendstateofagencyerosion:asingleminimalcoalitionthatisdecisiveforallchoices.Thisprovidesatargetformonitoringhowfarthetrajectoryisfromthispointofirreversibility.

Recommendations

Wemakethefollowingrecommendations:

•Developagencyevaluations.ExistingAIevaluationsassesscapabilities,safety,andalignment,buttheydonotassessstructuraleffectsonhumandecisionmaking.ResearchersshoulddesignbenchmarksthatmeasurewhenAIsystemsreducethenumberofhumansindecisivecoalitions,influenceoutcomes,orshapewhichalternativesreachhumandecisionmakers.

•Establishhumanparticipationthresholds.Forhigh-stakesdomains(suchasdemocraticgovernance,militaryapplications,andcriticalinfrastructure),policymakersshouldconsiderminimumrequire-mentsforhumanpresenceindecisivecoalitions.Thesethresholdsshouldreflectdomain-specificrequirementsforlegitimacyandreversibility.Organizations,suchastheNationalInstituteofStandardsandTechnology,couldincorporatecoalitioncompositionasameasurabledimensionofAIriskalong-sideexistingmetricsforreliabilityandsecurity.

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•Monitorcoalitioncompositionlongitudinally.Thedangerofgradualdisempowermentisthatnosinglechangeappearscatastrophic.Organizationsandgovernmentsshouldtrackthehumancomposi-tionofdecisivecoalitionsacrossdomainsovertime.

•Benchmarkreversibilitycapacity.OrganizationsshouldassesswhethertheycouldrestorehumandecisionmakingifAI-drivenagencylossaccelerates.Doingsowouldrequiremaintainingthehumanexpertise,institutionalknowledge,anddeliberativeinfrastructureneededtoreversecourse.

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Contents

AboutThisReport iii

Summary v

Figures ix

AFormalModelofHowArtificialIntelligenceErodesHumanAgency 1

ResearchQuestionsandScope 1

ReportStructure 3

DynamicsofHumanAgencyLoss 3

IrreversibilityofAgencyLoss:DefinitionsandImplications 4

ACoalition-BasedModelofCollectiveAgency 5

CollectiveAgencyasaModelFeature 6

AnEndStateofAgencyLoss 9

ValidatingMechanismsThatReduceCollectiveHumanAgency 10

LimitationsoftheModel 13

Applications 14

FindingsandRecommendations 16

APPENDIXES

A.MathematicalDetails 19

B.CalculationsforEconomicDisenfranchisementScenario 21

C.AIAgendaControlThroughtheIntroductionofAlternatives 23

References 25

AbouttheAuthors 29

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Figures

1.DecisiveCoalitionsinaMajorityRuleSituation 8

2.DecayintheDistributionofDecisiveCoalitionsforMajorityRuleSystems 8

3.DecayinMinimalSizeofDecisiveCoalitionsforMajorityRuleSystems 9

4.DecisiveCoalitionsinanExampleVotingSystemwithThreeIndividuals 10

5.AnOrganizationwithSharedAgenticAIResources 13

6.PossibleChangestoDecisionmakersinGroupG 15

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AFormalModelofHowArtificialIntelligenceErodesHumanAgency

Theadoptionofpowerfulartificialintelligence(AI)systemswillchangewhomakesdecisionsandhowtheydoso.AsAIisdeployedinthegovernmentandtheeconomyinwaysthatautomatedecisions,ahardpolicyquestionemerges:Howcanchangestohumanity’scollectivecapacitytoshapethefuturebemeasured?

SeveralAIresearchersarguethatthetransitiontopowerfulAIsystemscouldpermanentlydiminishhumanagency.SomewarnofagradualdisempowermentinwhichAIsystemsslowlydisplacehumanpar-ticipationacrosseconomic,cultural,andpoliticaldomainswithouttherebeinganysinglecatastrophicevent(Kulveitetal.,2025).OthersarguethatsufficientlycapableAIsystemswillacquireresourcesandpowerasinstrumentalgoals,potentiallyculminatinginrapidhumandisplacement(Carlsmith,2023;Ngo,Chan,andMindermann,2024).Thesetheoriesdifferinmechanismandtimelines,buttheyshareatroublingpredictionthatonceagencyislost,recoverymaybeimpossible.

Despitethisconvergenceonirreversibility,existingframeworksdonotoffertheprecisionnecessaryforstrategicpolicyplanning.Withoutacommonmetric,policymakerscannotcomparescenarios,tracktrends,oridentifyinterventionpointsbeforechangesbecomepermanent.Meanwhile,novelandcapableAIsystemsmaybringsignificantbenefits,especiallytofirstmovers,whichcouldincentivizeAIdevelopersandotherstakeholderstoacceleratedevelopment(Abraham,Kavner,andMoon,2025)andunderscoretheurgencyofunderstandinghowagencymaybeaffected.

Inthiscontext,themotivationforrigorouslystudyingAI’seffectsonhumanagencyisclear.AformaltheoryofagencymayinformdecisionsabouthowtobestbenefitfromadoptingAItechnologieswhilehedg-ingagainstunintendedorundesirableoutcomes,suchasirreversiblelossofhumanagencyinkeydomains.

ResearchQuestionsandScope

Inthisreport,weconsidercollectiveagencytobethecapacityforhumanstomakedecisionsaboutsharedresources,institutions,andthephysicalandsocialenvironment.Agencydiminisheswhenhumanslosethecapacitytocollectivelyinfluenceoutcomesbasedontheirchosenandexistingdecisionmakingprocesses.Toexploreconditionsforirreversibleagencyloss,weaskthefollowingthreequestionsaboutcollectiveagency:

1.Howdochangestodecisionmakinggroups(suchaschangestotheirsizes,compositions,andavail-ablealternatives)translateintomeasurablelossesofcollectivehumanagency?

2.Whatindicatorsmightallowearlydetectionandinterventionbeforechangesbecomeirreversible?

3.Isthereaterminalstatetowardwhichthesedynamicstrend,andcanwecharacterizeitformally?

Answeringthesequestionsisurgent;somedeploymentdecisionsincriticalinfrastructure,governance,andeconomicinstitutionsmaybeeffectivelypermanent(wefurtherdiscussthisissueinthesectiontitled“Irre-versibilityofAgencyLoss:DefinitionsandImplications”).

Tobeginaddressingthesequestions,weproposeaformalframeworkformeasuringcollectivehumanagencyincertaindecisionmakingprocesses.Wedrewonsocialchoicetheorytodevelopacoalition-basedmodelthattranslatesintuitionsaboutagencylossintoquantifiablemetrics.Then,givenadecisionmakingprocessthatfallswithinthescopeofourframework,thismodelcanassesshowchangestoparticipants,theirrelativeinfluence,orthealternativesthattheyconsiderwillaffectcollectivehumanagency.

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Whatprocessesaremodeledbyourframework?Decision-theoreticanalysestypicallydividedecisionproblemsintotwodistinctsetsoftasks(Gongetal.,2017).Decisionstructuringtasksdefinetheproblem,identifyobjectives,andassembleamenuofoptionsforachievingthoseobjectives.1Choicetaskstheninvolveselectingthebestoptionfromthatmenu,givenestimatesofconsequences.Humanagencyencompassesbothtasks:theabilitytoassesswhatmattersandtheabilitytochooseamongalternatives.

AIsystemsmightchangeagencythroughbothchannels.AnAIthatcontrolsdecisionstructuring(e.g.,byshapinghowproblemsaredefined,whichobjectivesareprioritized,orwhichoptionsareconsidered)candetermineoutcomesbeforeanychoicetaskbegins.AnAIthatcontrolsthechoicetask(e.g.,byreplacinghumanparticipantsintheprocessthatselectsamongoptions)erodesagencyevenwhentheframingisdonebyhumans.

Theformalmodelwedevelopinthisreportprimarilyaddressesthechoicetasksideofthisdistinction.Specifically,wemodeldecisionmakingprocesseswiththefollowingtwofeatures:

•Decision-structuringtasksarelimitedtochangingwhichoptionsareconsidered,suchasbyeliminatingoraddingoptions.Wedonotconsidertasksthatidentifyproblemsandobjectivesorotherwiseinflu-encehowproblemsandobjectivesareset.

•Choicetaskscanbemodeledasaggregatingprocessesthatusemultipleindividualpreferencesandinputs.

Thisscopeisdeliberatelynarrow.Theagendacontrolmechanism(discussedinlatersectionsandAppen-dixC)partiallybridgesthegapbymodelinghowAIcanmanipulatewhichalternativesreachhumandeci-sionmakers,butitdoesnotcapturethedeeperdynamicthroughwhichAImightreshapehowhumanscon-ceptualizeproblemsinthefirstplace.Extendingformalagencymeasurestodecisionstructuringremainsanimportantdirectionforfuturework.

Withinourscope,theclearestexampleofamodeledprocessisavotingsystem,althoughwediscusshowtheframeworkgeneralizestosystemsoutsideavotingsetting,suchashuman-in-the-loopsystems(i.e.,semi-automatedorfullyautomatedsystemsinwhichhumandecisionmakersinteractwithautomatedprocesses).Anexampleofanout-of-scopeprocessisahumanusinganAIsystem(suchasalargelanguagemodelchat-bot)toinformindividualdecisions:Itschoicetasksdonotinvolveaggregationacrossmanyindividualprefer-ences,andsuchaprocessisthereforeoutofscope.AlthoughAI-humanchatbotinteractioncouldinfluenceaggregatedecisions,theimpactsonindividualsaredistinct(Treyger,Matveyenko,andAyer,2025)andlikelyrequireadifferentcharacterization(Sharmaetal.,2026).

Withinthescopeofourframework,wefindthefollowingthreepreliminaryanswerstoourquestions:

1.Inseveralimportantexamplescenarios,ourquantifiablemetrics(whichmeasuresize,composition,anddistributionofdecisivegroupswithinthemodel)decreasewithchangestothesystemthatshouldheuristicallydecreasecollectiveagency.

2.Quantitativeorqualitativethresholds,suchasratesofchangeinourmetricsinresponsetochangestodecisionmakingprocesses,mayindicatetippingpointsatwhichcollectiveagencylossisirreversible.

3.Ourframeworkfeaturesaterminalstateofhumanagencyloss—specifically,theexistenceofasingleminimallysizeddecisivegroup.

Becausethescopeofourframeworkisnarrowerthanthefullgeneralityrequiredtodiscussallaspectsofdecisionmaking,weleaveseveralinterestingandopenquestionsforfutureresearch.Anobviousbutimpor-

1Incomparison,ethicists,suchasNussbaum(2000;2011),recognizethesetasksaspracticalreasonorthecapacitytocriti-callyreflectandformaconceptionofthegood.

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tantquestioniswhatotherframeworkscanextendourformalunderstandingofcollectiveagencytoencom-passbroadergroupsofdecisionmakingprocesses.Anotherimportantquestion,whichwediscussinourrecommendationstopolicymakers,isdetermininghowmuchhumanagencyshouldberequiredindifferentdecisionmakingdomains.

Ultimately,ourmodelcontributesafirststeptowardformallyunderstandingtheeffectsofAIdeploy-mentsonhumanagency.

ReportStructure

Thisreportisorganizedasfollows.WereviewliteratureonAI-drivendisempowerment,AIpower-seekingbehavior,humancognitiveatrophy,anddecisionmakinglegitimacy.Weestablishirreversibilityasakeyfea-tureofourframework.Then,wederiveourcoalition-basedmodelofcollectiveagencyfromsocialchoicetheory.Wecarefullycircumventknownproblemswiththemodelstemmingfromafeatureofpreferencescalledtransitivityandthecontextofvotingsystems,whichwediscussinthesectiononlimitations.

Next,weapplyourmodeltovalidatethreedynamicsthroughwhichAIreducescollectivehumanagency:humandisenfranchisement(fewerhumansindecisionmakingroles),AIenfranchisement(AIentitiesgain-ingdecisionmakingpower),andAIagendacontrol(AIsystemsshapingwhichalternativesreachhumandecisionmakers).WeconcludewithabriefdiscussionofapplicationstoAIevaluationsandpublicpolicy,followedbyrecommendationsanddirectionsforfuturework.Wealsoaddressfurthermathematicaldetailsintheappendixes.

DynamicsofHumanAgencyLoss

SeveraldynamicssuggestthatAIdevelopmentmaydriveirreversiblelossesofhumanagency.Inthissec-tion,wereviewtherelevantliteraturebeforeestablishingirreversibilityasakeydesignprincipleforourformalmodel.

ThewidespreaddeploymentofAIscoulddrivechangestosocialsystems.Thispossibilityisobviousinscenariosinwhichamisalignedartificialsuperintelligencerapidlyseizespowerandseekstocontroloreradi-catehumanity(seeYudkowskyandSoares[2025],Bostrom[2016],Yampolskiy[2015],andmanyothers).ButwidespreadAIadoptionmayalternativelydecouplesocietalsystemsfromhumanintereststhroughmore-gradualreplacementofhumanparticipationacrosseconomic,cultural,andpoliticaldomains.Kulveitetal.

(2025)arguethatthesesystemssupporthumanprioritiesonlysofarashumanscontributetothem,and,onceAIsystemsoffermore-competitivemachinealternatives,decisionmakerswillfacepressuretominimizehumaninvolvement.Thisdynamicmayunfoldthroughlaborsubstitution,algorithmiccontentgeneration,orautomationofpoliticaljudgment.Similarly,thedegreeofautonomyofAIsystems(i.e.,thescopeandsig-nificanceofdecisionsmadewithouthumanintervention)determineswhetherAIsystemsfunctionaspar-ticipantsormerelyastools.Theoriesofinstrumentalconvergence(Omohundro,2008;Bostrom,2016;Rus-sell,2020;Dung,2025;Carlsmith,2023)furthershowhowgoal-drivenautonomycouldleadtowardresourceorpoweracquisition.Theriskofsuchdisplacementisalsocompoundedbycognitiveatrophy.Automation’s“irony,”asdescribedbyBainbridge(1983)andconfirmedbyLeeetal.(2025),suggeststhatrelianceonAIdullscriticalthinkingandexceptionhandling;Koeszegi(2023)foundthat,withcertaindesigns,algorithmicmanagementcandisempowerworkers.Overtime,lostcompetencemakesmeaningfuloversightmoredif-ficult,andaffectedpartiesmayloseopportunitiesforcontestationandreason-giving.

ThesedynamicssuggestthatAIsystemsmaybecomeeffectiveparticipantsincertaindecisiondomains.Critically,thesedynamicsdonotrequireAIsystemstoactcontrarytohumaninterests.Evenaperfectly

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alignedAIthatreliablyproducesdecisionsthathumanswouldendorsecanerodecollectiveagencybydis-placinghumanparticipation.Thiserosioncanoccurbecausebroadhumanparticipationinconsequentialdecisionsnotonlyisinstrumentallyvaluablebutalsopreservestheskillsandinstitutionalknowledgeneededtogoverneffectively,sustaindiscursivelegitimacy(Habermas,1996;Cohen,1997;GutmannandThompson,2004),andmaintainoptionality,thecapacitytochangecourseifcircumstancesorvaluesshift.AnAIthatconsistentlymakesgooddecisionswhileremovinghumansfromthedecisionmakingprocessmayoptimizeforpresentoutcomeswhileforeclosingfutureones.Tocapturethesepossibilities,ourmodelisagnosticaboutwhetherAIsystemsshareordivergefromhumaninterests;itmeasuresthestructuralcapacityofhumanstoinfluenceoutcomes.

IrreversibilityofAgencyLoss:DefinitionsandImplications

Pressureonsocietalsystemstodecouplefromhumaninterests,power-seekingbehaviorofautonomousAIsystems,andhumancognitiveatrophymayallcontributetofuturedynamicsthatdecreasecollectivehumanagency.Thetheoryofirreversibledecisionsiswell-troddengroundineconomics,startingwithkeystudiesbyHenry(1974)(andbyArrowandFisher[1974])thatestablishedthateconomicdecisionsareoftenirreversible.Henrydefinesanirreversibledecisionasonethat“significantlyreducesforalongtimethevarietyofchoicesthatwouldbepossibleinthefuture”(1974,p.1006).AlthoughHenryoriginallydefinedthistermforeco-nomicanalysis,wefinditsufficientlygeneraltoapplytootherdomains,suchascultureandpolitics,andsoitisdirectlyrelevanttodecisionsthatchangecollectiveagency.Giventhisdefinitionofanirreversibledeci-sion,acriticalquestionarises:Whenarelossestocollectivehumanagencylikelytobeirreversible?TheAIagencyliteraturesuggeststhatthiswillbethecaseforsomescenariosofsignificantagencyloss,sowebuildouragencyevaluationframeworktofocusonwhatdrivesdecisionmakingpowertoconcentrateinsmallergroupsasdeploymentofAIsystemsincreases.Inthissetting,wecanexploretheirreversibilityquestionbyprovidinginsightintowhichconditionsdriveandacceleratetheconcentrationofdecisionmakingpower.

Ourfocusonirreversibilityisbasedonacoupleofobservations.Thefirstobservationisthatmanyofthesechangeswillbeeconomicinnature.Forexample,automationthroughAImaybringdramaticchangestoeconomicsectorsacrossawiderangeofscales,fromindividualworkerstotheglobaleconomy.Bytheprinciplethatsignificanteconomicdecisionsaregenerallyirreversible(Henry,1974;ArrowandFisher,1974),automationthroughAIatthisscalewillbeirreversibletoo.Arecentexamplethatsupportsthistrendisinautomatedstockmarkettrading:Automatedtradingmachineshavesteadilyreplacedhumantradersandarebeingdesignedwithgreaterautonomyintheirroles(BorchandMin,2022).Giventheeconomicadvan-tagesofautomatedtradersandthefactthattradingcompanieshaveinvestedsignificantlyinsoftwareandhardware,aswellasinfindingandexploitingoptimalphysicallocationsfortrading(Wissner-GrossandFreer,2010),wefinditunlikelythattradingcompanieswouldbeabletoeasilyreverttohuman-basedornon-algorithmictrading.Effectively,thischangeisirreversibleaccordingtoHenry’sdefinition.

AsecondobservationisthatAIimplementationinorganizationsandgovernmentswilllikelyeliminatehumanrolesindecisionmakingprocesses.AcorevaluepropositionforAIautomationisthatAIsystemswillbeabletoaccomplishtasksandfillavarietyofroles.Alikelyconsequenceofthisautomationisthatsomehumanpositionswillbeeliminated,2workflowswillchange,andprocesseswillrelymoreheavilyonAIsys-tems.ReversingAIautomationwouldrequirethereconstructionofdismantledcapacityforhumaninvolve-ment,whichwefindisunlikelytobereversible.Forexample,consideringthepreviousdiscussiononhuman

2Thedegreetowhichhumanpositionswillbeeliminatedbecauseofautomationisanactiveareaofresearch.SeeworkbySytsma(2025)thatanalyzedpossibleeffectsofautomationpolicyunderuncertainty.

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cognitiveatrophyandagencyloss,wehypothesizethatthehumancapitalrequiredformeaningfuloversightofAI-drivenprocesseswilldegradewithdisuse.Oncethatknowledgebaseislost,buildingupaworkforcethatiscapableofreversingchangestokeysocietalsystemswillbeacostlyactivity.

ACoalition-BasedModelofCollectiveAgency

Intheprevioussection,webrieflyreviewedtheliteraturesurroundingAIandhumanagencytoidentifycriticalconceptsaboutagencyloss.Inthissection,weborrowfromthesocialchoiceliteraturetoproposeamodel-theoreticdefinitionofcollectiveagencythatisexpressiveenoughtorepresenttheseconcepts.Thesocialchoiceliteratureisvastandinterdisciplinary,so,tomatchthescopeofthisshortreport,wepresentonlyalimitedexpositionofthefieldasitintersectswithvotingsystems(seeSen’s[1977;1999]reviewsonsocialchoiceforamorecomprehensiveoverviewofsocialchoicetheory).

Weconsideragroupofindividualswhoareparticipatinginadecisionmakingprocess.Thisprocess,iden-tifiedasavotingsystem,ischaracterizedbythefollowingthreeadditionalconcepts:

•alternatives,whichlistpossibleoutcomesofthedecision

•preferences,whichindicateindividualandgrouppreferencesbetweenalternatives

•constraints,whichdescribeconventionsandrulesthatpreferencesshouldfollow.

Followingstandardconventions(CampbellandKelly,2000),werepresentthesefourelementsofavotingsystemusingthefollowingmathematicalobjects,withtheintentionofextendingtheformalismtonon–voting-basedprocessesaswell(seeAppendixAforamoreaxiomatictreatment):

•Individualsarelabeledfrom1toN.Whenwerefertotheseindividualsasagroup,especiallyinrefer-encetoadecisionmakingprocess,weusetheshorthandG.

•Alternativesarelabeledasuppercaseletters(X,Y,Z,etc.).

•Preferencesarerepresentedbythesymbol≤.X<YmeansthatYisstrictlypreferredtoX,andX~YmeansthatYandXareequivalentlypreferredasoutcomes.

•Constraintsarerulesonhowpreferencesshouldbehaveandrepresentthefactthatindividualsarepar-ticipatinginaprocesswithwell-definedproceduresandintendedfeatures.

Muchofthesocialchoiceliteratureisconcernedwiththerelationshipbetweenpreferencesandcon-straints.Wesupposeeachindividualhasapreference,labeled≤iforIndividuali.Letpdenoteanarbitrarylistofallindividualpreferences.Anaggregatepreferenceisamethodofusingtheinputpofindividualprefer-encestoproduceanaggregatedpreference≤p.3Implicitly,adecisionbetweenalternativesshouldfollowtheaggregatedpreference.Wealsoadoptthefollowingdefinitionfromthesocialchoiceliterature,whichidenti-fiesindividualswhohavedecisiveinfluenceoverhowaggregatedpreferencesaredetermined(Hansson,1976,asreferencedinCampbellandKelly,2000):

AsubgroupofindividualsHisadecisivecoalitionif,foralllistspofindividualpreferencesinscopeofthe

decisionmakingprocess,wheneverX<jYforallindividualsjinH,X≤pY.

Inotherwords,adecisivecoalition’spreferencesarealwaysrepresentedintheaggregatepreference.Someresultsintheliteraturerequireanarrowerdefinitionofdecisivecoalitionsthatforcesstrictpreferenceinthe

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