# Defamation with Bayesian Audiences Canonical page: https://works.battleoftheforms.com/papers/ssrn-4181890/ [p. 1] Legal Studies Research Paper Series Research Paper No. 23–66 Defamation with Bayesian Audiences Yonathan A. Arbel Murat C. Mungan This paper can be downloaded without charge from the Social Science Research Network Electronic Paper Collection [p. 2] J,V0N0 1 Defamation with Bayesian Audiences YonathanA.Arbel,* MuratC.Mungan† Howstrictlyshouldthelawregulatefalsedefamatorystatements? Wefirstshowthat thepresenceofjudicialerrorsoftenputsdefamationlawonaLaffercurve: regulation thatistoolaxortoostrictisinferiortomoderateregulation.Whilemoderateregulation is ideal, it is not always attainable, due to practical and legal constraints. With these constraints,thepresenceofBayesianaudiencescancausetheoptimalregulationtobe laxerthanisprescribedbystandardmodelswithna¨ıveaudiences.Thishighlightsthe importanceofaccountingfortheimpactofdefamationlawsonbeliefformation. Keywords:Defamation,Bayesianaudience,informationregulation,disclosure. JELclassification:C72;D82;D83;K10;K13;K39. 1. Introduction Whenstatementsaremadeinpublic,audiencesassesstheircredibilitybased onavarietyofcues.Oneofthesecuesishowstrictlythelawsanctionsfalse statements, i.e., whether talk is cheap. Such audience effects complicate the standardanalysisofdefamationlaw,whichtraditionallyonlyfocusesonhow the law affects speakers and the subjects of their speech. We investigate here theoptimalstrictnessofdefamationlawwhenaccountingforaudienceeffects. Defamation law imposes tort liability on speakers who publish false statements that harm their target’s good name. A typical example comes from a recentcasewhereahospitalstafferfalselyallegedthatadoctorwasworking undertheinfluenceofalcohol.Thedoctorwonalawsuitagainstthestafferand recoveredmillionsofdollarsindamages(Denmanv.St.Vincent,2020).While the basic structure of defamation law is well established, there is an ongoing socialdebateondefamationlaw’sproperscope.WithcallsfromtheSupreme Court, legal scholars, politicians, and various pundits, there is growing pressuretodaytoreformdefamationlaw(Arbel&Mungan,2019).Inthemidstof thesecalls,anewRestatementprojectwasrecentlyannounced. Theliteratureondefamationlawisvast,buttheeconomicanalysisofdefamation law is quite limited (Hemel, 2020). In deciding the level of strictness of defamationlaw,standardlegalanalysesaredominatedbyatwo-sidedbalancing act. On the one hand, society considers the interests of the target of the speech—her need for compensation and the need to protect her by deterring defamatory speech against her. On the other hand, society also considers the speaker,hisrighttofreespeech,andthesocialconcernwithchillingvaluable speech(NYTimesv.Sullivan,1964). *UniversityofAlabamaSchoolofLaw.E-mail:yarbel@law.ua.edu †GeorgeMasonUniversity,AntoninScaliaLawSchool.E-mail:mmungan@gmu.edu. Draft,Vol.0,No.0, doi:/ewmxxx ©. Allrightsreserved.ForPermissions,pleaseemail: EElleeccttrroonniicc ccooppyy aavvaaiillaabbllee aatt:: hhttttppss::////ssssrrnn..ccoomm//aabbssttrraacctt==44118811889900 [p. 3] 2 .V0N0 Inreality,wenoted,defamationlawalsoaffectspartiesbeyondthespeaker andhistarget.Inparticular, defamationlawalsoaffectsaudiencesofspeech. Thisisnotjustduetothefamiliarideathatstrictdefamationlawwouldlimit thesupplyoffalsespeechthroughthedeterrenceofspeakers.Ifthatwerethe case,theprotectionofaudienceswouldbeasimplematterofsettingsanctions asstrictaslegallypossible.Defamationlawalsoaffectsaudiencesbychanging theirassessmentofthecredibilityofspeechand,thus,itaffectstheaudience’s propensitytoactuponstatements(Pennycooketal.2020, Arbel2022).Such effectsaddcomplexitythatthestandardanalysisneglects.Theneglectofaudienceeffectsmaybebecauselawyersnaturallyfocusonthepartiesthattake anactivepartinthelegalprocess–thevictimastheplaintiffandthespeakeras thedefendant(Heymann,2012).Whateverthereason,tworecentinformalaccounts(Hemel&Porat,2019&Arbel&Mungan,2019)suggestthatomission ofaudienceeffectsisconsequentialtotheoptimalstrictnessofdefamationlaw. Our object here is to bridge this gap by offering a general framework that analyzesbehaviorandevaluateswelfarebasedonthestrictnessofdefamation law. To do so, we construct a model that includes three key features: (i) a Bayesian (rather than a na¨ıve) audience, (ii) errors in the court’s judgment (wrongfulliabilityaswellaswrongfulfailuretofindliability),and(iii)acap onrecoverabledamages.Weexplaintheroleeachofthesefeaturesplays,after brieflyreviewingthestructureofourmodelanditsimplications. Weconsiderthebehaviorofthreeparties.Aspeaker,whohasprivateinformation about a certain target – a business or an individual. The speaker may make claims about the target to an audience member. The audience member then decides whether to interact—trade, collaborate, socialize—with the target. Targets can be a high-or low-type, and audiences would rather interact only with the former kind. If the target loses an interaction, he may bring a lawsuitagainstthespeakerallegingdefamation.Westudybehaviorunderdifferentlevelsofdamagesfordefamationandtheirsocialwelfareimplications. Our analysis reveals three central findings. First, we find that there is an optimallevelofdamagesthatsupportsseparatingequilibriainwhichwould-be defamersaredeterredfromsharingfalseinformationandspeakersonlyshare informationhonestlywiththeiraudience.Audiencemembersbelievespeakers and act upon this information. Naturally, social welfare is highest under this regime. Second, we find that defamation laws often follow a ‘Laffer Curve.’ Lax regulationresultsinafloodofcheaptalk,whichleadstoaudiencesdiscounting all statements—true or false—and simply acting on their priors. This resultsinequilibriawhereimportantinformationisleftuncommunicated.Sanctioningdefamationtoostrictlyisalsounwanted,becausehighsanctionsinvite frivolous litigation, which in turn chills true negative statements. In between thesetwoextremes,theoptimallevelofdamagesfollowsaninverseUshape, with a range of optimal damages. Thus, our unified framework shows that bothcheaptalkand‘overpriced’talkareundesirableastheydepriveaudiences ofrelevantinformationthatcouldbemadeavailabletothemundermoderate damages. EElleeccttrroonniicc ccooppyy aavvaaiillaabbllee aatt:: hhttttppss::////ssssrrnn..ccoomm//aabbssttrraacctt==44118811889900 [p. 4] -- 3 Our third result emerges when the cap on damages is lower than the level necessary to support equilibria in which the target’s type is fully revealed. In reality, it is difficult to calculate the exact level of damages, and even when possible,damagesareboundedbybothconstitutionalconsiderationsandlimits on defendants’ wealth. In such cases, we find that a lax approach can be superiortoamorestringentone.Thereasonisthatstringentregulationinvites audience trust, but because some statements are false, this trust can be misplaced, leading to the deterrence of valuable interactions. Compounding the issueisthatstringentregulationincreaseslitigation.Laxregulation,however, invitesaudiencestorelymoreontheirpriorsandreduceslitigation.Thus,perhapscounter-intuitively,laxregulationbecomespreferabletostrictregulation whenreputationalharmsarelarge,andtheoppositeconclusionmayholdwhen reputationalharmsaresmall. All three features of our model (Bayesian audience, judgment errors, and damagecaps)playimportantrolesintheproductionoftheseresults. First, when courts make no errors in judgment, people have no incentive tobringfrivolousclaimsagainstspeakers.Inthiscaseverylargedamages(if feasible) are always preferable to smaller damages, because they only deter falsespeechwithouthavinganyimpactontruenegativespeech.Thisisadynamicthatemergesinmanyothercontextsaswell,andhighlightstheroleof judgment errors in explaining the inefficiency of very large damages in the defamation context, and the emergence of the Laffer Curve to which we alluded. Second, the prior economics literature on defamation law assumes that a publisher(e.g.atabloid, journal,anindividualetc.)canalwaysharmanother personbymakingnegativestatementsaboutthem,andtheextentofthisharm isindependentofthelawsinplace(e.g., Garoupa1999a,b, Bar-Gill&Hamdani 2003).1 This is equivalent to the audience –whose beliefs and behavior isnotconsideredinthepriorliterature–naivelyformingitsbeliefsandacting uponthem.Thus,inthepriorliterature,themainfunctionofreformingthelaw is to alter the expected costs and benefits of making disparaging statements, but not the harmful impact of defamatory statements. With a na¨ıve audience, increasingdamagesleadstoareductionintheexpectedharmtothetarget,becauseitdetersnegativespeech.ThisisnotsowhentheaudienceisBayesian. Becauseverylowdamagesresultinfrequentfalseallegations,theydilutethe informational content of speech, and therefore causes the audience to act accordingtoitspriors.Thus,inadditiontoprovidingstraightforwardrationales for some behavioral responses in the defamation context (e.g., disregarding certainfalsespeech),theincorporationofBayesianaudiencesalsohasimportantnormativeimplications, e.g., loweringdamagescanreducetheharmthat resultsfromdefamatorystatements. 1. Themirrorimageofthisassumptionisalsoinvokedinthisliterature:thespeaker’sbenefit frommakinganegativestatementisindependentoftheaudience’sbeliefs,becausetheaudienceis notconsideredinthisliterature.Thisassumptionismade,forinstance,inDalviandRefalo(2008), whichfocusesexclusivelyonthespeakers’incentivesandignoresnotonlytheaudience’sbeliefs andbehaviorbutalsothetarget’s. EElleeccttrroonniicc ccooppyy aavvaaiillaabbllee aatt:: hhttttppss::////ssssrrnn..ccoomm//aabbssttrraacctt==44118811889900 [p. 5] 4 .V0N0 Third, this normative distinction becomes quite significant with binding damagecaps,2 inwhichcasefalsedisparagingremarkscannotbefullyeliminated.Thus,withBayesianaudiences,thechoiceisbetweenahighdegreeof interactionsbetweentheaudienceandtargets(goodandbad)achievedthrough lowdamages,andthemaximumlevelofdamagesthatcausesbadinteractions tobedeterredalongwithsomegoodinteractions.Theformeroptionispreferablewhenthevalueofgoodinteractionsarelarge.Ontheotherhand, witha na¨ıveaudience,maximumdamagesarealwayspreferable,becauseevenwith low damages the audience believes false disparaging remarks, which are in highsupplyduetothelackofdeterrentdamages. In short, the main impact of judicial errors in our analysis is to rule out theoptimalityofverylargedamages.Thisbecomesanimportantissuewhen the damage cap is very large (or non-existent), in which case the presence of judicial errors supplies an independent rationale for not having very large damages.Ontheotherhand,whenthedamagecapisbinding,ana¨ıveaudience impliesthatthemaximumdamageisoptimal,andthisresultisoverturnedwith Bayesianaudiences. While our analysis focuses on defamation law, the basic question we pose here is relevant for a broad range of legal contexts. The law regulates false speechindomainsasdiverseascorporatedisclosures,falseadvertising,whistleblowers, and law enforcement. Common to these domains is a basic tension betweenthestrictnessofsanctionsformisreportingandtheinformativenessof speech,andwecommentonpotentialimplications. The next section offers some brief background and reviews the related literature.Section3presentsthemodelanditsanalysis.Section4evaluatesthe welfare implications of different damages regimes, and highlights the importanceofaccountingforaudienceeffects.Section5containsseveralextensions and discussions of the basic model, such as the public enforcement case, the generalizationofthemodeltocaseswherespeakersmaybemotivatedtospeak truthfullyortoexcessivelypraisethetarget,anddiscussionsofcontextsother thandefamationlaw.Section6providesconcludingremarks. 2. LiteratureReview Defamationlawregulatesthedisseminationoffalsestatementsthatare‘defamatory.’ To be defamatory, a statement must not only be false but also made publicandbecapableofharmingone’sreputationandstandinginthecommunity.Defamationlawisconsideredtobeabranchoftorts,anditencompasses severaldistincttorts,mostnotablylibelandslander.Today,however,thedistinctionhaslesspracticalsignificancethaninthepast,andinwhatfollows,we abstractfromit. Many defamation lawsuits are brought by individuals, but businesses and firmscanalsobringsuit.Arecenthigh-profileexampleinvolvesalawsuitby ‘Dominion,’ a firm that sells voting hardware and software, against various 2. Asimilardynamicalsoemergeswhencourtsfrequentlymakejudgmenterrors,aswebriefly explaininsection5.4.,below,andingreaterdetailinArbeland&Mungan2020. EElleeccttrroonniicc ccooppyy aavvaaiillaabbllee aatt:: hhttttppss::////ssssrrnn..ccoomm//aabbssttrraacctt==44118811889900 [p. 6] -- 5 publicfiguresandmediaoutlets,whoallegeditwasinvolvedinthemanipulationofelectionvotes.3 Defamation law evolved in the common and ecclesiastical courts of England. In the United States, the states took the doctrine and used it to develop theirownvariants.Amajordevelopmenttookplacein1964,whentheSupreme Court decided the seminal case of NYTimes v. Sullivan. There, the Court reviewedtheexistingbodyofdoctrineinlightoftheFirstAmendmentprotectionoffreespeechandpress.TheCourtmadeitconsiderablyharderforpublic figures to bring lawsuits on matters of public interest. In the years that followed,thedoctrinewasrefinedand,whilestillcarryingsignsofitsconvoluted history,reachedacertaindegreeofbalance.Inrecentyears,however,therehas beengrowingpressuretoreformthelaw.CommentsfromtheSupremeCourt (McKee v. Cosby, 2019; Berrisha v. Lawson, 2021), the political sphere, legalcommentators, andpundits—allrevealdissatisfactionwiththelaw.Many ofthesecommentssuggestthatdefamationlawshouldbemadestricter; e.g., CassSunsteincalledtheNYTimesv.Sullivandecision‘anachronistic’andarguedthatpublicfiguresshouldbeallowedtobringsuitmoreeasily(Sunstein, 2021). Interestingly, the reason why the law should protect good name interestsisnotwellunderstood.Somegroundthelaw’sinterventioninaproperty likeinterestingoodname,orgoodname’sbasisindignity,property,andhonor (Post, 1984) while others relate it to concepts of social status and reputation (Arbel,2021). The legal literature on defamation law is rich and vast, and it explores a varietyoftopics,involvingdeepquestionsofpoliticalphilosophyandconstitutionalcommitments.Itisthereforequitesurprisingthattheliteratureonthe economicsofdefamationlaw‘haslagged’andissparse(Hemel,2020).Some notablecontributionsinthisspaceincludesRichardPosner’spioneeringanalysis (Posner, 1973, 1986), which highlighted the applicability of cost-benefit analysis to defamation law. More recent work focuses on the law’s effect on media’sincentivestoinvestigateandreporttopicsofpublicinterest(Bar-Gill &Hamdani,2003,Dalvi&Refalo,2008,Acheson&Wohlschlegel,2018)and on political dishonesty (Garoupa, 1999a,b). As noted, this paper differs from theseanalysesbyconsideringaBayesianaudience,alongsidedamagecapsand judicialerrors. Despitethesecontributions,courtsandlegalcommentatorsarelimitedtoa fairlyrudimentaryunderstandingoftheincentivesfosteredbydifferentdefamation law regimes. Here we amplify on two informal contributions that recognizetherelevanceandimportanceofaudiencestotheanalysisofdefamation law (Hemel & Porat, 2019, Arbel & Mungan, 2019). Methodologically, our article borrows tools from the rich literature on signaling (Spence 1973) and cheaptalk(Crawford&Sobel,1982).Ouranalysiscanalsobeinterpretedas part of emerging literature that looks at how laws can be used to create informalsanctionsthroughthebehaviorofthirdparties(e.g.,Deffains&Fluet, 3. USDominion,Inc.v.FoxNewsNetwork,LLC,C.A.N21C-03-257EMD(Del.Super.Ct. Dec.16,2021). EElleeccttrroonniicc ccooppyy aavvaaiillaabbllee aatt:: hhttttppss::////ssssrrnn..ccoomm//aabbssttrraacctt==44118811889900 [p. 7] 6 .V0N0 2019,Mungan2016,Be´nabou&Tirole,2006,2011,Rasmusen1996). 3. Model We model the interactions between three parties: the speaker (S, she), the target of the speech (T, he), and the audience, captured by a representative member (A, it). A faces an informational problem: T is either a good or a bad type, and A’s value of interacting with T depends on T’s type, which is unknown to A. Before A decides whether to interact with the target, S, who knows T’s type, communicates with A and may either disparage T or makeanon-disparagingcomment.Becausewestudydefamation,weconsider thepossibilitythatS mayfalselydisparageT inordertodeteraninteraction betweenAandT.Wedeferthediscussionofspeakersbeing(atleastpartly) motivatedbyadesiretotruthfullyshareinformation,asthishaslimitedimpact onouranalysis.4 WemodeltheinteractionsasaBayesiangame,anduseitto identifyPerfectBayesianEquilibria.5 3.1 Preliminaries Thetarget,T,obtainsabenefitofr fromtheinteraction,wheret∈{B,G} t denotes his type and where the letters abbreviate bad and good, respectively. T’s type is privately known to himself and S, but not to A, who only knows thattheproportionofgoodtypesisγ ∈(0,1).6Apreferstointeractwithgood types,butnotbadtypes,becausethisresultsinautilityofg >0>−bwhere bisthedisutilityAbearsfrominteractingwithabadtype.Thus,absentfurther information,AwouldprefertointeractwithT ifγg−(1−γ)b > 0,andwe assumethisinequalityholds,sinceotherwisenointeractionswouldtakeplace between A and T even without (negative) input from S.7 Thus, the audience preferstointeractwiththetargetifitsupdatedbelief(basedonthestatementit receivesfromS)ofT’slikelihoodofbeingagoodtypeexceedsthethreshold b x≡ <γ, (1) (cid:98) g+b wheretheinequalityfollowsfromtheassumptionthatAwouldprefertointeractwithT absentinputfromS. ThespeakerhasaninterestinwhetherAandT interact:Sobtainsagainofv whenAavoidsinteraction(alternatively,vcanbeinterpretedasalossincurred whenAchoosestointeractwithT).v isarandomvariablewiththecumulative distribution function F(v) with support (0,1] where the upper-bound of the support is normalized to simplify notation. The specific v-draw is private 4. Consistentlywiththelaw,truthfulnegativestatementsarenotconsidereddefamatory.However,thecourtmaymakeerrorsinascertainingwhetheranegativestatementistruthful,andthis possibilityisincorporatedinourmodel,asweexplainbelow. 5. Figure5intheAppendixdepictstheinteractionsbetweenthethreepartiesandishelpfulin followingthedetaileddescriptionsoftheinteractionsthatweprovide,next. 6. Insection5wediscusstheconsequencesofendogenizingγ. 7. Ananalysisofthiscasecanbefoundinanearlierversionofthisarticle, andyieldsno furtherinsights(seeArbel&Mungan(2020)). EElleeccttrroonniicc ccooppyy aavvaaiillaabbllee aatt:: hhttttppss::////ssssrrnn..ccoomm//aabbssttrraacctt==44118811889900 [p. 8] -- 7 informationavailableonlytoS,andwecallv thespeaker’stype.Weassume thatinteractionsbetweenAandT aresociallyvaluableif,andonlyif,T isa goodtype,i.e.r +g >1>0>r −b. g b After Nature determines the types of T and S, the target’s type becomes commonknowledgeamongT andS(butnotA).Atthispoint,Schooseswhat type of statement to send A regarding T’s type. The types of possible statements follow defamation law’s distinction between disparaging statements, which are potentially actionable, and non-disparaging statements, which are non-actionable(e.g.,positiveremarks,silence,opinion,etc.). Subsequently, A decides on whether to interact with T or to avoid him, and, finally, T, decides whether to bring a lawsuit against S if a disparaging remarkwasfollowedbyA’schoicetoavoidinteractingwithT.8 Wenotethat this setting includes the possibility of T suing S, even if T is in fact a bad type,i.e.,afrivolouslawsuitmaybebrought.Thisisanimportantpossibility becausecourtsmayerrintheirjudgment.Tocapturetheparties’payoffsfrom litigation,wedefinethefollowing: d: damagespaidbyS toT whenthecourtfindsforT l: totallitigationcosts.Weassumethatlitigationcostsarenotprohibitive(l<1) and,withoutlossofgenerality,thatthecostsareequallysharedbytheparties. q : probabilityofplaintiffvictorywhenT isoftypet∈{B,G} t (cid:16) (cid:17) Weassumetheprobabilityofwrongfulliabilityissmall: q 2−l)onlygenerateineffectivecommunicationequilib2qB (cid:16) (cid:17) ria. (ii) There exist a range of moderate damages, D ⊂ l , 2−l , which 2qG 2qB generate effective communication equilibria. (iii) The audience acts consistentlywiththespeaker’sstatement,i.e.a∗(z)=z,inalleffectivecommunicationequilibria. Proof. SeeAppendix. EElleeccttrroonniicc ccooppyy aavvaaiillaabbllee aatt:: hhttttppss::////ssssrrnn..ccoomm//aabbssttrraacctt==44118811889900 [p. 11] 10 .V0N0 The intuition behind the first part of proposition 2 is relatively straightforward.Whendamagesareextremelylow,thetargetisdeterredfromsuingthe speaker, even when he has a meritorious case, since expected damages (i.e. q d)arelowerthanlitigationcosts.Thiscausesthespeaker’sstatementstobe G perceived as cheap-talk by the audience, since the speaker faces no negative consequence from making disparaging statements. Thus, the audience disregards the speaker’s statements and acts according to its priors. On the other hand,whendamagesareextremelyhigh,alltargetsareincentivizedtolitigate, andexpecteddamagesarehighenoughtodeterallspeakertypesfrommaking disparaging statements. Thus, the audience is once again left without any informativestatements,thistimeduetotheover-pricingofspeechasopposedto thepresenceofcheap-talk. Itisonlymoderatedamagesthatsupporteffectivecommunicationsbetween speakers and audience members, and this is formalized in proposition 2-(ii). Part (iii) of proposition 2 simply rules out the possibility of counter-intuitive equilibria,forinstance,inwhichtheaudienceinfersfromadisparagingremark thatthetargetmustbeagoodtypeandvice-versa(i.e.wherea∗(z)=1−z). These preliminary findings indicate that if defamation laws are to have any impact, theymustdosothrougheffectivecommunicationequilibriaobtained under moderate damages. Thus, we analyze these equilibria in further detail, next. 3.4 ModerateDamagesandEffectiveCommunicationEquilibria The damages in place affect the target’s incentive to sue when disparaged, aswellasthespeaker’sincentivestodisparagethetargetinthefirstplace.We notetwopairsofcriticaldamagesthatpertaintoeachparty’sincentives.First, l l d ≡ andd ≡ (2) 1 2q 3 2q G B are the smallest damages that causes a type G and B target, respectively, to bring suit whenever the speaker disparages him.11 On the other hand, when damagesaregreaterthan 2−l 2−l d ≡ andd ≡ (3) 2 2q 4 2q G B typeGandBtargets,respectively,areexpectedtobringsuit,andthisdetersthe speakerfromdefamingthetarget.Ourassumptionofnon-prohibitivelitigation costsandsmalljudicialerrorsimpliesthatthesefourcriticaldamagelevelsare orderedasfollows: d l > q d.Thus,inaneffectivecommunicationequilibrium,the G 2 B speaker faces no threat of litigation from disparaging a bad type, and thus a type B target is disparaged with certainty. On the other hand, if the speaker encountersatypeGtarget,sheexpectsthatdisparaginghimwillleadtoacost of l v (d)≡q d+ . (5) G G 2 Thus,thespeakerchoosestodisparageatypeGtargetifhertypeexceedsthis value.Therefore,atypeGtargetisdisparagedwithaprobabilityof 1−F(v (d)) (6) G Ouranalysisthusfaridentifiesthebehaviorofthespeakerandtargetinan effectivecommunicationequilibrium,assumingthatitexists.But,forthistype ofequilibriumtobesupportable,theaudience’sbeliefsmustbeconsistentwith theequilibriumbehavioroftheotherparties.Thus,theaudiencemustholdthe belief that a target who is not disparaged must be a good type, since all bad typesaredisparaged,i.e. x∗ =P(t=G|z =0)=1 Ontheotherhand,whentheaudiencereceivesadisparagingstatement,itmust believethatthetargetisneverthelessagoodtypewithaprobabilityof γ[1−F(v (d))] x∗(d)=P(t=G|z =1)= G <γ (7) 1 γ[1−F(v (d))]+(1−γ) G This is because a type G target is disparaged with probability 1−F(v (d)) G whereas a type B individual is disparaged with certainty, and the likelihood withwhichthetargetisagoodtypeisγ. Aswenotedvia(1)theaudiencefindsitinitsbestinteresttointeractwith thetargetifitbelievesheisagoodtypewithaprobabilityexceedingxˆ.Thus, aneffectivecommunicationequilibriumissupportableinthisrangeif x∗(d)γ and 0 γ+(1−γ)F(v (d)) B x∗=P(t=G|z =1)=0 EElleeccttrroonniicc ccooppyy aavvaaiillaabbllee aatt:: hhttttppss::////ssssrrnn..ccoomm//aabbssttrraacctt==44118811889900 [p. 14] -- 13 Figure1 Sincexˆ<γ,itfollowsthatx∗ >xˆ>x∗,andthereforeeffectivecommunica0 1 tionequilibriaaresupportablebyallhighdamages. As the above discussion indicates, increasing damages in this range only reduces the frequency with which speakers disparage a type B target. Thus, increasing damages in this range has countervailing effects: it increases the frequencyofinteractionswithbadtypesbutreducesthefrequencyoflitigation. Wesummarizeourfindingsinthissubsectionthroughfigure1,below,which depictsthequalitativerelationshipbetweendamagesandthebeliefsofA;the likelihood with which a type t ∈ {B,G} target is disparaged; and the likelihood of litigation in effective communication equilibria. Next, we conduct a welfareanalysiswhichbuildsonthesekeyfindings. EElleeccttrroonniicc ccooppyy aavvaaiillaabbllee aatt:: hhttttppss::////ssssrrnn..ccoomm//aabbssttrraacctt==44118811889900 [p. 15] 14 .V0N0 4. WelfareAnalysis Inanalyzingthesocialdesirabilityofdifferentdefamationregimes,weuse a simple social welfare function which consists of the sum of each player’s expectedpay-off.Weconductthiswelfareanalysistohighlightthethreemain pointsthatweemphasizedintheintroduction.First,welfareisnon-monotonic in damages for defamation. More precisely, we show that the shape of welfare obtained through effective communication equilibria vis-a`-vis damages resemblesaLafferCurve:welfareisincreasinginthelowerrangeofmoderate damages (i.e. for d ∈ (dˆ,d )), is maximized in the intermediate range (i.e. when d ∈ [d ,d ]), and is decreasing in the upper range of moderate dam2 3 ages (i.e. when d ∈ (d ,d )). Second, when there is a cap on damages (e.g. 3 4 reflecting the wealth of the defendant or a legal bound on permissible damages), then all effective defamation remedies may reduce welfare. Third, we contrasttheimplicationsofamodelwithaBayesianversusana¨ıveaudience. Whentheaudienceisna¨ıveandeasilymisledbyfalsestatements,typeGtargets always prefer stricter defamation laws. The same is not true when the audienceisBayesian,becauseabsentsizeabledamagestheaudienceperceives the speaker’s disparaging statements as cheap-talk and disregards them. This insight leads to a divergence between the normative implications of the two models:withbindingcapsondamages,itmaybeoptimaltohavenodefamationlawsatallwithaBayesianaudiencebutoptimaltohavemaximaldamages withana¨ıveaudience.Next,weconsiderandformalizeeachofthesepoints. 4.1 TheLafferCurveofDefamationLaw Underineffectivecommunicationequilibria,theaudienceactsaccordingto its priors. Thus, it chooses to interact with the target regardless of the statements by the speaker. There is no litigation since interaction always takes place.Thus,expectedwelfareisindependentofdamages,andisgivenby W ≡(1−γ)[r −b]+γ[r +g] (1) I B G On the other hand, under effective communication equilibria, the specific functionalformofwelfarediffersdependingonwhichofthethreerangesdamagesarein,asexplainedtheprevioussection.Next,weconsiderwelfareunder eachrange. Withlowdamagesthatsupporteffectivecommunicationequilibria(i.e.d∈ (dˆ,d )), when the target is type B, the speaker disparages him, the audience refuses to interact, and the target chooses not to litigate. Thus, with a probabilityof(1−γ)expectedwelfareequalsthespeaker’sexpectedbenefitE[v]. WhenthetargetistypeG,thespeakerdisparageshimonlywhenv > v (d). G In those cases, the audience avoids an interaction with T, and the target litigates.Thus,withaprobabilityofγ,expectedwelfareisF(v (d))[r +g]+ G G (cid:82)1 (v−l)f(v)dv.Therefore,expectedwelfareisgivenby: vG(d) (cid:32) (cid:33) (cid:90) 1 W (d)≡(1−γ)E[v]+γ F(v (d))[r +g]+ (v−l)f(v)dv (2) L G G vG(d) EElleeccttrroonniicc ccooppyy aavvaaiillaabbllee aatt:: hhttttppss::////ssssrrnn..ccoomm//aabbssttrraacctt==44118811889900 [p. 16] -- 15 Whendamagesareintermediate(i.e.d∈[d ,d ]),effectivecommunication 2 3 leadstoseparatingequilibriawhereininteractionstakeplaceif,andonlyif,the targetisagoodtype.Moreover,thereisnolitigationsincetypeB targetslack theincentivestolitigate.Thus,welfareinthisrangeisgivenby W ≡(1−γ)E[v]+γ[r +g] (3) S G Finally,whendamagesareintheuppermoderaterange(i.e.d ∈ (d ,d )), 3 4 thespeakerchoosesnottodisparageatypeGtarget.Thus,withaprobability of γ, welfare is r + g. When the target is type B, the speaker chooses to G disparagehimonlywhenv > v (d),andthisleadstolitigation.Thus,witha B (cid:82)1 probabilityof1−γ,expectedwelfareisF(v )[r −b]+ (v−l)f(v)dv. B B vB(d) Thus,expectedwelfareis (cid:32) (cid:33) (cid:90) 1 W (d)≡(1−γ) F(v (d))[r −b]+ (v−l)f(v)dv +γ[r +g](4) H B B G vB(d) A very simple yet important observation is that W is increasing whereas L W isdecreasingindamages.Thisisbecause,whendamagesareinthelower H moderaterange, theimpactofincreasingdamagesistoreducethelikelihood ofdefamatorystatementsagainstatypeGtarget.Thisisbeneficial,becauseit reducesthelikelihoodofblockedbeneficialinteractionsbetweenAandT as well as wasteful litigation between T and S. Similarly, when damages are in theuppermoderaterange,loweringdamagesleadstoanincreaseinthelikelihoodwithwhichatypeBtargetisdisparaged.Thisincreasesthelikelihoodof harmfulinteractionsbeingblocked,butattheexpenseofincreasedlitigation. The former (beneficial) effect dominates the latter (detrimental) effect, since thespeakerdisparagesatypeB targetonlyifherbenefitsfromdoingsomore than off-set total litigation costs. This last point can be formalized by noting that W′ =(1−γ)f(v )v′ {(r −b)−(v −l)}⩽0 (5) H B B B B sincer d ) reduce welfare by deterring accurate negative speech against a type B target. On the other hand, reducing damages to low levels (i.e. d < d ) is also detrimental because it leads to defamatory state2 mentsagainstatypeGindividual,whicharetakenseriouslybytheaudience. Anotherfeatureofthewelfarecurvedepictedinfigure3isthattheseparating equilibria obtained through intermediate damages lead to greater welfare thanineffectivecommunicationequilibria.Wenotethatthisisnocoincidence, andoccursduetothefactthatwhiletheaudienceinteractswitheithertypein ineffectiveequilibria,itinteractswithatargetif,andonlyif,itisagoodtype when damages are in the intermediate moderate range. Thus, when there are nocapsondamagesitfollowsthatsettingdamagesintheintermediatemoderaterangeissociallydesirable.Weformalizethisresultthroughthefollowing proposition,whoseprooffollowsfromourcomments,above. Proposition3. SeparatingequilibriawhereSchoosestodisparageT if,and onlyif,heistypeB leadtogreaterexpectedwelfarethananyotherequilibria andareobtainableonlythroughintermediatedamages. Animplicationofproposition3isthatmaximizingwelfarethroughdefamation law requires the implementation of separating equilibria through the use of intermediate damages. We note that this implication is obtained under the assumption that these damages are feasible. However, when these damages are too large for the defendant to pay (i.e. when the defendant is judgementproof)orwhentherearelegalrestrictions(e.g.constitutional)onthedamages EElleeccttrroonniicc ccooppyy aavvaaiillaabbllee aatt:: hhttttppss::////ssssrrnn..ccoomm//aabbssttrraacctt==44118811889900 [p. 18] -- 17 thatcanbechosen,damageslargeenoughtosupportequilibriainwhichtarget typesarefullyrevealedmaynotbeavailable.Wediscussthiscase,next. 4.2 BoundedDamages Weused¯todenotetheupperboundondamages.Animmediateimplication ofproposition3isthatwhend¯⩾d ,theupperboundisnon-binding.Thus,we focusonthecasewhered¯< d .Withthisrestrictioninplace, thereareonly tworelevantrangesofdamagesthatonecanselectfrom;(i)verylowdamages which only support ineffective communication equilibria (d ⩽ d ), and (ii) damagesinthelowerrange(d∈(d ,d¯)). In the latter range, if d¯is close to d it is possible for effective communi1 cationequilibriatobeunsupportable,14 andtheanalysisofthiscaseistrivial: thereisnofeasiblelevelofdamagesthatcanresultineffectivecommunication equilibria, and hence the choice of damages is irrelevant. Thus, we focus on the more interesting case where maximum damages are sufficient to support someeffectivecommunicationequilibria,i.e.x∗(d¯) v ). This implies that a switch from an G ineffective communication equilibrium to an effective communication equilibrium trades-off deterrence of good interactions against deterrence of bad interactions. Therefore, when the harm to the target from defamatory statementsislargerelativetootherconsiderations,arathercounter-intuitiveresult is obtained. Even when it is possible to implement effective communication throughdefamationlaws,itissociallymoredesirablenottodoso.Thishappensbecauseputtingapriceonspeechlendsmorecredibilitytothespeaker’s statements,whichshecanthenusetoinefficientlyblockagoodinteraction.In such cases, the superior option is to not make speech credible and cause the audiencetorelyonitspriors,whichcausesittointeractwiththetarget. Weformalizethisresultviaproposition4below,andweprovideanexample anditsgraphicaldepictionviafigure4toillustrateit. Proposition4. Supposetherearebindingmaximumdamages(i.e.d¯d ),thespeakerisdeterredagainst makingdisparagingstatementsagainstbothtypes,andthena¨ıveaudienceinteracts with both types. Thus, in this range welfare with a na¨ıve audience is equaltowelfarewithaBayesianaudience. Inshort,themoststrikingdifferencearisingfromaswitchfromaBayesian audience to a na¨ıve audience occurs when damages are too low to cause the target to litigate (i.e. d ⩽ d ). The most prevalent normative impact of this difference is observed when there is an upper bound on maximum damages, since otherwise optimal equilibria are trivially obtained in the intermediate moderate range (i.e. d ∈ [d ,d ]) under both models. Thus, we focus on the 2 3 case where d¯ < d to highlight the greatest difference between the models withaBayesianandana¨ıveaudience. Aswepreviouslynoted,withaBayesianaudience,typeGtargetsaremade worseoffwhendamagesinthelowermoderaterangelendcredibilitytospeaker’s statements. Thus, as we noted via proposition 4, when defamatory harms are large,welfareisactuallyreducedwhendefamationlawsareeffectivecompared towhentheyarenot.Theoppositeconclusionholdswithana¨ıveaudience.In this case, increasing damages always leads to less frequent defamatory statements,andtypeGtargetsalwayspreferstricterdefamationlaws.Thus,when defamatoryharmsarelarge,contrarytothecasewithaBayesianaudience,it isoptimaltousemaximaldamages. We illustrate this result through figure 4, which depicts welfare obtained in the example used to generate the high r case in figure 3,16 but this time G italso includeswelfareobtainedwith ana¨ıveaudience. Thefigureillustrates thatwhileitisoptimaltoincreasedamagestotheirmaximallevelwithana¨ıve audience,itisoptimaltousedamageslowenoughtoguaranteetheemergence ofineffectivecommunicationequilibriawithaBayesianaudience.Thus,when harms from defamatory statements are large, assuming that the audience is na¨ıveisnotmerelyasimplifyingassumption,itisonethatcangeneratemisleadingnormativeimplications. 16. Asareminder,thiscorrespondstothecasewherevisuniformlydistributed;rG = 9 ; γ=rB =l= 3 ;g=b=1;andqG= . EElleeccttrroonniicc ccooppyy aavvaaiillaabbllee aatt:: hhttttppss::////ssssrrnn..ccoomm//aabbssttrraacctt==44118811889900 [p. 22] -- 21 Figure4 EElleeccttrroonniicc ccooppyy aavvaaiillaabbllee aatt:: hhttttppss::////ssssrrnn..ccoomm//aabbssttrraacctt==44118811889900 [p. 23] 22 .V0N0 5. ExtensionsandDiscussion InSections3and4, wepresentedamodelthatallowedustoclearlyfocus ondefamationlaws’impactontheaudience’sequilibriumbeliefsandactions. In doing so, we abstracted from many issues that bear on the regulation of information in more general settings, particularly, the possibility of there being a committed public enforcer, quality being endogenously chosen by the target, the existence of honest and other types of speakers, and courts being lessaccuratethanwepreviouslyassumed.Hereweturnourattentiontothese issues. 5.1 EndogenousTypesandDynamicEfficiencies In our analysis thus far, we assumed that the target’s type is exogenously determined by nature to be either G or B with probabilities γ and 1−γ, respectively. One might question the reality of this assumption, as people can makeinvestmentsthatwouldmakethembetterorworsetradingpartners,e.g., create higher quality products, maintain safety standards, or keep higher hygienestandards.Garoupa1999a,b,forinstance,takesasimilarapproach,and assumesthatthetarget’sbehaviorisimpactedbywhatlawsareinplace.Here, we explain how the types in our setting can be endogenized, and how doing so yields results similar to those in prior work where the target’s behavior is endogenous. One option of incorporating quality investments into our analysis is to replace Nature’s choice of types with a preliminary stage where the target, T, makes a costly investment (c) that can increase her likelihood of becoming a good type. Formally, we may assume that γ = γ(c) with γ′ > 0 > γ′′, limγ′(c)=∞,γ(0)=γ and limγ(c)=γ where1>γ >γ >xˆ>0. c→0 c→∞ Thequalityinvestmentdecisionisnowpartofalargergame.Givenanysubgameequilibrium,thebestresponseofT istomakeaninvestmenttomaximize hisexpectedpay-off,whichcanbedenotedasγ(c)m +(1−γ(c))m −c G B wherem andm refertothepayoffsheobtainsinthesub-gameequilibria. G B Thisobservationrevealsaveryclearresult: Whenthelawsareextreme,i.e. d ̸∈ [d ,d ], the target has no reason to invest in quality. This follows from 1 4 Proposition 2, which shows that with extreme laws, the audience acts based on its priors and interacts with the target. Thus, investments have no private returnsforthetarget. Itisonlywhenthelawsaremoderatethattargetsmayhaveanincentiveto investinquality.Thiscanbedemonstratedbyfocusingonthelowerboundof intermediatedamages,i.e.d .Inthiscase,ineffectivecommunicationequilib1 ria,itfollowsthatm =0(becauseallbadtypesaredisparaged)whilem = B G F(v (d))r(becausegoodtypesaredisparagedwithprobability1−F(v (d)), G G inwhichcasethereisalawsuitwhichpaysthetargetexpecteddamagesequal tolitigationcosts).Thus,thetarget’spay-offisγ(c)F(v (d))r−c,and,thereG fore,thetargetprofits(inexpectation)frominvesting.Whetherthisissocially good or bad, depends, of course, on whether there are net social gains from such investments. In our context, this is socially valuable as long as the exEElleeccttrroonniicc ccooppyy aavvaaiillaabbllee aatt:: hhttttppss::////ssssrrnn..ccoomm//aabbssttrraacctt==44118811889900 [p. 24] -- 23 pectedbenefitsfromgoodinteractions(F(v (d))g)—whicharenotinternalG izedbyT—aregreaterthantheexpectedlitigationcostslandthelossofbenefit to S from blocking an interaction, i.e. F(v (d))E[v|v > l]. In fact, if G 2 investments in quality are socially valuable, as is implicitly assumed in the literature (e.g., Garoupa 1999a,b), then increasing damages within the intermediate range up to d will be desirable. This is because these higher dam2 ages lead to a lower probability of disparaging remarks made against good types (as illustrated in Figure 2) and, thus, increase m , while still keeping G expectedpayoffsfrombeingabadtypeatm = 0.Therefore,theextension B of our model with endogenous types resonates with Garoupa’s (1999a,b) insightsthatmoderatedamagescanincentivizeinvestmentsinbecomingagood type.Moreover,ithighlightsthepotentialsocialcostsandbenefitsassociated withsuchinvestmentmorespecifically. Thediscussionherehighlightstheimportanceofinformationregulationfor broadermarketdynamics.Theintuitionunderlyingourresultsarestraightforward.Extremelawsleadtoineffectivecommunicationequilibria.Incontrast, moderatelawscreateanenvironmentwithmorereliableinformationregarding types, thus generating a greater gap between the payoffs obtainable by good typesversusbadtypes.17Inrealisticsettings,providingsuchadditionalincentivesissociallydesirablewhenthepotentialinvestorisunderincentivizeddue to problems like information asymmetries. The gains from such investments inqualityshouldbeaddedtotheotherbenefitsofmoderatelawsthatwehave identified. 5.2 HonestSpeakersandEulogists Existinganalysesofdefamationlawtypicallyassumethatthespeaker’snegative statement always harms the target, which is equivalent to the audience being na¨ıve. Moreover, these analyses (e.g. Garoupa 1999a,b and Bar-Gill & Hamdani2003)considerstrategicspeakerswhobenefitfromdefamingthetarget,andwhosebenefitsfromdoingsoareindependentoftheveracityoftheir statements.Inreality,however,manyspeakersmaynothavesuchmotivations. Quite importantly, many people, when asked their opinion, provide an honest assessment of others. Moreover, there are also people who are motivated by doing the exact opposite of what the speakers in our model are motivated by; namely, promoting the relationship between the target and the audience. Inwhatfollowswedistinguishbetweenthefirsttype,truthspeakers,thelatter type,eulogists,andtheonesweformerlydiscussedinsection3asdisparagers. Here,webrieflyexplainwhatoccurswhenthesekindsofspeakersareincorporatedintoouranalysis. Inourdiscussion,weconceiveofthesetypesasfollows.Disparagers,aswe noted,receiveapositivevaluefromblockinganinteraction;truth-speakersare 17. Thisresultisreminiscientofthedeterrencereducingimpactsofjudicialerrorsobtained inthelawenforcementliterature(see,e.g.,Png(1986),RizzolliandGraoupa(2012),Mungan (2017), and Lando and Mungan (2018)) wherein judicial errors dilute the deterrence effect of punishmentbycreatingadisconnectbetweenpunishmentandbehavior. EElleeccttrroonniicc ccooppyy aavvaaiillaabbllee aatt:: hhttttppss::////ssssrrnn..ccoomm//aabbssttrraacctt==44118811889900 [p. 25] 24 .V0N0 indifferent with respect to whether the parties will interact but receive some valuefromspeakingtheirmind; and,eulogistsreceiveavaluefromtherebeinganinteraction.Therefore,solongascostsofsodoingarenothigh,disparagers will badmouth the target and truth-speakers will reveal their true type. Eulogists, in contrast, would always want to praise the target, as there is no recourse under defamation law for false positive statements (the question of whythisasymmetryexistsgoesbeyondthescopeofourarticle). Theincorporationofthesetypesofspeakershasnoimpactontheobservationthatextremelystrongdefamationlawsleavetheaudiencetoactupontheir priors. This follows, because once a critical threshold of damages is passed, disparagers as well as truth speakers are deterred from making negative remarks.Thus,extremelystrongdefamationlawscausedisparagers,truthspeakers, and eulogists alike to abstain from making negative statements, and the audiencehasnooptionbuttoactaccordingtoitspriors. The same cannot be said, however, for extremely weak defamation laws. When damages are very low, targets lack an incentive to bring suit, making talk cheap. Despite that, disparaging statements are still somewhat informative:Giventheexistenceofsometruth-speakers,thereissomeprobabilitythat anynegativestatementistrue.Consequently,anaudiencethathearsanegative statementevaluatesitscredibilitybasedontheratiooftruth-speakerstodisparagers.Thus,inanassessmentwitha∗(z)=z,wecanformulatetheaudience’s consistentbeliefthatthetargetisagoodtype,conditionalonanegativestatement as x∗ = γ ∆ where τ denotes the proportion of truth speakers, 1 ∆+(1−γ)τ and ∆ is the proportion of disparagers. On the other hand, non-disparaging remarksdonotnecessarilymeanthatT isagoodtype.Bysimilarlogic,there is some probability that any given praise is false given the existence of eulogists.Anaudiencewhichhearsapositivestatementevaluatesitsveracityasa function of the ratio of eulogists to truth-speakers. Thus, we can express the audience’sbeliefasx∗ =γ τ+ε ,whereεistheproportionofeulogists. 0 γτ+ε Using these observations it is easy to verify that, under lax laws, both disparaging and non-disparaging statements are somewhat informative of types. Inotherwords,non-disparagingstatementsaremoreindicativeofgoodtypes than no information at all (x∗ > γ), and disparaging statements are more indicativeofbadtypesthannoinformationatall,i.e.x∗ <γ.Thus,iftheau1 dience’snecessarylevelofconfidenceforinteraction,(x),iscloseenoughtoγ (cid:98) suchthatx∗ ⩾ x ⩾ x∗,onecanachieveanequilibriumwhereintheaudience 0 (cid:98) 1 meaningfullyusestheinformationprovidedbyspeakers,evenwhenthereare nosanctionsforfalsestatements.If,however,x∈/ [x∗,x∗],thenlaxlawscause (cid:98) 1 0 theaudience toignore thestatement andact accordingto its priors, as inour analysisinsection3.Thus,wefocusourremainingdiscussiontocaseswhere x∗ ⩾x⩾x∗. 0 (cid:98) 1 Incaseswheredamagesaremoderate, someoftheclaimsmadeinsection 3 need to be qualified, whereas others remain intact. In particular, it is still the case that moderate damages improve the reliability of information over extremedamages.Toseethis,consider,forinstance,theimplicationsofraisEElleeccttrroonniicc ccooppyy aavvaaiillaabbllee aatt:: hhttttppss::////ssssrrnn..ccoomm//aabbssttrraacctt==44118811889900 [p. 26] -- 25 ingdamagesfromlowlevelsto l .Amongspeakers,thischangeonlyalters 2qG the incentives of disparagers, because these are the only speakers who have aninterestinmakingfalsestatementsaboutgoodtypes,who,giventhislevel ofdamages,bringalawsuitagainstthem.Thus,theproportionofdisparagers who make false statements is reduced, which causes x∗ to fall and x∗ to in1 0 crease,i.e.itcausesinformationsuppliedbyspeakerstobemoreinformative. Thisobservationrevealsanotherofourresultsthatcarriesoverinamodified way:onecanusedamagesequaltod d˜ 2pq th G espeake 4 rdoe 2 s p n q o B tmakedis2 paragingstatementsagainstgoodtypes,andrefrainsfrommakingdisparaging statementsagainstbadtypeswhend > d˜.Itcanbeeasilyverifiedthateach ofthesevaluesislargerthantheircorrespondinganalogintheprivateenforcementcontext,i.e.d˜ >d andd˜ >d . 2 2 4 4 The commitment to bringing a lawsuit also changes the speaker’s behavior, as a lawsuit is possible even when expected damages are low. We next explainthebehaviorofthespeakerineffectivecommunicationequilibria,under three different damages ranges, and subsequently compare them with the correspondingbehaviorunderprivateenforcement. Asunderprivateenforcement,itfollowsthatwhendamagesareveryhigh, i.e.,d>d˜,alldisparagingremarksaredeterred.However,whend∈(d˜,d˜), 4 2 4 the speaker refrains from disparaging good types, but disparages bad types wheneverhervaluefromblockinginteractionsissufficientlyhigh(i.e.v˜ (d)≡ B p(q d− l) < v)whichhappenswithprobability1−F(v˜ (d)) > 0.Thus, B 2 B in this range, a disparaging remark conclusively reveals to the audience that thetargetisabadtype;andanon-disparagingcommentisaninformative,but inconclusive,signalthatthetargetisagoodtype,i.e.x∗ =0<γ 0,badtypesbeingdisparagedwithaprobabilityof G 1−F(v˜ (d))<1,orboth.Thisimmediatelyimpliesthatprivateenforcement B dominatespubicenforcementintermsofitswelfareconsequences.Thedifference in the welfare obtainable under the two regimes is enhanced further by thefactthatunderpublicenforcement,theenforcementagency’scommitment resultsinlitigation. Thelastpointhighlightsamoregeneralandimportantadvantageofprivate enforcementoverpublicenforcement.Specifically, privateenforcementdelegates the decision to litigate to the party with the best information about the meritsofthecase.Moderatedamagescanbecraftedtoseparategoodandbad types based on their willingness to sue, and this enables the speaker’s statementstobemoreinformativeofthetarget’stype. Insum,thiscomparisonilluminatetherelativevalueofpublicversuspublic enforcement.However,asourfocushereisoncommitment,weabstractfrom otherrelevantconsiderations, suchastherelativecostsoflearningaboutdisparagingremarksorproducingevidence.Inasmuchaspublicagenciesemploy discretion, they are also susceptible to capture and other public choice problems.Theseconsiderationsshouldalsobetakenintoaccountincomparingthe relative social desirability of pubic versus private enforcement in regulating speech. 5.4 InaccurateCourts To keep our analysis focused, we presented results obtained in the case wherethecourtisrelatively‘accurate’inrenderingdecisions,inthesensethat itcommitserrorswithlowfrequency(i.e.q x forz ∈{0,1} z (cid:98) (4) a∗(z)=1 if x l/2 fort∈{B,G} t R2statesthatthePBEstrategyofT mustbesuchthatinsubgameswhereS disparageshim,T litigateswheneverthecostsofdoingso(l/2)arelowerthan theexpecteddamagerewardsthathecanobtainfromlitigation.Conversely,T choosesnottolitigatewhenthecostsarehigherthanexpecteddamages.Inthe exceptionalcasewhereq d=l/2,T isindifferentbetweenlitigatingandnot. t Requirement3(R3):Shasnoprofitabledeviations:Forallt,vpairs,s∗(t,v) maximizesplayerS’spayoff,whichcanbeexpressedas l U ≡a∗(s(t,v))(v−p∗(t)s(t,v){q d+ }) (6) S t 2 The requirement with respect to S appears more complex than the requirementsthatpertaintoT andA’sstrategies,becauseS choosesheractions in anticipation of the other players’ actions. Still, the requirement is simply that,givenherowntype,T’stype,andtheanticipatedbehaviorofAandT,S mustchoosethecourseofactionthatwouldmaximizeherpayoff. Requirement4(R4):A’sbeliefsareconsistent: x∗ =Γ(t=G|z,s∗)wheneverΓ(t=G|z,s∗)̸=Υforbothz ∈{0,1} (7) z R4 simply states that A’s beliefs must be consistent with the implied conditionalprobabilityofT beingaparticulartypebasedontheequilibriumstrategy EElleeccttrroonniicc ccooppyy aavvaaiillaabbllee aatt:: hhttttppss::////ssssrrnn..ccoomm//aabbssttrraacctt==44118811889900 [p. 32] REFERENCES 31 of S. This requirement is applicable only to strategies which have a positive probabilityofbeingplayedbyS. Proof of Proposition 2: The proof begins with part (iii), which is used in provingpart(i). (iii) We show that the audience ends up always interacting with T, in all equilibria where the actions of the audience are not described by a∗(z) = z forz ∈{0,1}. SupposethereisaPBEwherea∗(z) = 0forallz.Bydefinition,theaudiencealwaysinteractsinsuchassessments. Suppose there is a PBE where a∗(z) = 1 − z for all z, then per R3, s∗(t,v) = 0 for all v and t, and, therefore, µ(s∗) = 0, which implies that Γ(t = G|0,s∗) = γ.ThisimpliesviaR4thatx∗ = γ,which,inturnimplies viaR1that a∗(0)=0,whichcontradictstheassumptionthata∗(0)=1. Suppose there is a PBE where a∗(z) = 1for all z. If µ(s∗) = i ∈ {0,1}, then Γ(t = G|i,s∗) = γ, which implies via R4 that x∗ = γ. This implies i viaR1thata∗(i)=0,whichisacontradictionwiththeinitialsupposition.If, on the other hand, µ(s∗) ∈ (0,1), observe that, per R4, x∗ ⩽ γ implies that x∗ ⩾ γ, because x∗(1−µ(s∗))+x∗µ(s∗) = γ. Thus, x∗ ⩽ γ implies that 1 0 1 0 x∗ ⩾γ >x,whichisacontradictionwiththeimplicationofR1thatx∗ ⩽x. 1 (cid:98) 1 (cid:98) (i) Consider damages d < d , and suppose a∗(z) = z for all z. It follows viaR2thatp∗(t)=0forallt.Thus,R3impliesthats∗(t,v)=1forallvand t, and, therefore, x∗ = γ due to R4 . 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