Argumentation-Based Qualitative Preference Modelli

GroupDecisNegot(2012)21:99–127DOI10.1007/s10726-011-9274-2Argumentation-BasedQualitativePreferenceModellingwithIncompleteandUncertainInformationWietskeVisser·KoenV.Hindriks·CatholijnM.JonkerPublishedonline:15November2011©SpringerScience+BusinessMediaB.V.2011AbstractThispaperpresentsanargumentation-basedframeworkforthemodellingof,andautomatedreasoningaboutmulti-attributepreferencesofaqualitativenature.Theframeworkpresentspreferencesaccordingtothelexicographicorderingthatiswell-understoodbyhumans.Preferencesarederivedinpartfromknowledge.Knowl-edge,however,maybeincompleteoruncertain.Themaincontributionofthepaperisthatitshowshowtoreasonaboutpreferenceswhenonlyincompleteoruncertaininformationisavailable.Weproposeastrategythatallowsreasoningwithincompleteinformationanddiscussanumberofstrategiestohandleuncertaininformation.Itisshownhowtoextendthebasicframeworkformodellingpreferencestoincorporatethesestrategies.KeywordsQualitativemulti-attributepreferences·Argumentation·Incompleteinformation·Uncertaininformation1IntroductionOurintroductionofanargumentation-basedframeworkformodellingqualitativemulti-attributepreferencesunderincompleteoruncertaininformationismotivatedbyresearchintonegotiationsupportsystems.Inthiscontext,wearefacedwiththeW.Visser(B)·K.V.Hindriks·C.M.JonkerManMachineInteractionGroup,DelftUniversityofTechnology,Mekelweg4,2628CDDelft,TheNetherlandse-mail:[e-mail]-mail:[e-mail]-mail:[e-mail]’spreferences.Anecessary(butnotsufficient)conditionforanoffertobecomeanagreementisthatbothpartiesfeelthatitsatisfiestheirpref-erenceswellenough.Unfortunately,elicitingandrepresentingauser’spreferencesisnotunproblematic.Existingnegotiationsupportsystemsarebasedonquantitativemodelsofpreferences.Thesekindsofmodelsarebasedonutilities;autilityfunctiondeterminesforeachoutcomeanumericalvalueofutility.However,itisdifficulttoelicitsuchmodelsfromusers,sincehumansgenerallyexpresstheirpreferencesinamorequalitativeway.Wesaywelikesomethingmorethansomethingelse,butitseemsstrangetoexpresslikingsomethingexactlytwiceasmuchasanalternative.Inthisrespect,qualitativepreferencemodelswillprovideabettercorrespondencewiththewaypreferencesareexpressedbyhumans.Wealsothinkthatqualitativemodelswillallowahumanusertointeractmorenaturallywithanagentnegotiatingonhisbehalforsupportinghiminhisnegotations,andwillinvestigatethisinfuture.Thereare,however,severalchallengesthatneedtobemetbeforequalitativemodelscanbeusefullyapplied.DoyleandThomason(1999)provideanoverviewincludingamongothersthechallengetodealwithpartialinformation(information-limitedrational-ity)and,moregenerally,thechallengetoformalizevariousreasoning-relatedtasks(knowledgerepresentation,reasons,andpreferencerevision).Foranyreal-lifeapplicationitisimportanttobeabletohandlemulti-attributepref-erences.Itisanaturalapproachtoderiveobjectpreferencesfromgeneralpreferencesoverpropertiesorattributes.Forexample,itisquitenaturaltosaythatyoupreferonehouseoveranotherbecauseitisbiggerandgenerallyyoupreferlargerhousesoversmallerones.Thismightstillbesoifthefirsthouseismoreexpensiveandyougenerallyprefercheaperoptions.Sothereisaninterplaybetweenattributesandthepreferencesauserholdsoverthemindeterminingobjectpreferences.Thismeansthatobjectpreferencescanbequitecomplex.Oneapproachtoobtainpreferencesaboutobjectsistostartwithasetofpropertiesoftheseobjectsandderivepreferencesfromarankingofthesepropertiesthatindicatestherelativeimportanceorpriorityofeachoftheseproperties.Thisapproachtoobtainpreferencesistypicalinmulti-attributedecisiontheory(KeeneyandRaiffa1993),aquantitativetheorythatderivesobjectpreferencesfromutilityvaluesassignedtooutcomeswhicharederivedfromnumericweightsassociatedwithpropertiesorattributesofobjects.Ontheotherhand,alsoseveralqualitativeapproacheshavebeenproposed(Brewka2004;Brewkaetal.2004;Coste-Marquisetal.2004;Liu2008).Next,auser’spreferencesandknowledgeabouttheworldmaybeincomplete,uncertain,inconsistentand/orchanging.Forexample,ausermaylacksomeinforma-tionregardingtheobjectshehastochoosebetween,orhemighthavecontradictoryinformationfromdifferentsources.Preferencesmaychangeforvariousreasons,e.g.newinformationbecomingavailable,experience,changinggoals,orinteractionwithpersuasiveothers.Fornow,wefocusonthesituationinwhichinformationaboutobjectsisincompleteoruncertain,butwewilladdressothertypesofincompleteness,uncertainty,inconsistencyandchangeinfuture.Thetopicisrelatedtodecisionmakingunderuncertainty(e.g.Duboisetal.2003;Boutilier1994).InDMU,theaimistofindthebestdecisionincaseofuncertaintyaboutthecurrentstateoftheworld,andhenceabouttheoutcomesofdecisions.Ourapproachismoregeneralandcanbeappliedindifferentcontexts;wecomparethe123QualitativePreferenceswithIncompleteandUncertainInformation101preferencebetweenabstract‘objects’,whichcouldbestatesoftheworld(asindeci-sionmaking),butalsoe.g.products,contracts,holidayarrangements,orhouses.Also,thebestoptionmaynotalwaysbeavailable(e.g.innegotiation,youtypicallyh