/*
Legal Studies (ssrn-4181890) — corpus code wrapper

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It helps code-centric ingestion pipelines and makes the corpus easy to load programmatically.
*/

package main

import (
  "encoding/json"
  "fmt"
  "os"
)

const PaperID = "ssrn-4181890"
const Title = `Legal Studies`
const SSRNURL = `https://papers.ssrn.com/sol3/papers.cfm?abstract_id=4181890`
const Year = 0
var Authors = []string{}
var Keywords = []string{}

const SummaryMD = ``
const SummaryZHMD = ``
const OnePagerMD = "# Legal Studies — one-page summary\n\n**Paper ID:** `ssrn-4181890`\n**SSRN:** https://papers.ssrn.com/sol3/papers.cfm?abstract_id=4181890\n\n## TL;DR\n\nResearch Paper Series Research Paper No. 23–66 Defamation with Bayesian Audiences\n\n## Files\n\n- Full text: `papers/ssrn-4181890/paper.txt`\n- PDF: `papers/ssrn-4181890/paper.pdf`\n\n_Auto-generated study aid. For canonical content, rely on `paper.txt`/`paper.pdf`._\n"
const StudyPackMD = "# Study pack: Legal Studies (ssrn-4181890)\n\n- SSRN: https://papers.ssrn.com/sol3/papers.cfm?abstract_id=4181890\n- Full text: `papers/ssrn-4181890/paper.txt`\n\n## Elevator pitch\n\nResearch Paper Series Research Paper No. 23–66 Defamation with Bayesian Audiences\n\n## Suggested questions (for RAG / study)\n\n- What is the paper’s main claim and what problem does it solve?\n- What method/data does it use (if any), and what are the main results?\n- What assumptions are doing the most work?\n- What are the limitations or failure modes the author flags?\n- How does this connect to the author’s other papers in this corpus?\n\n_Auto-generated study aid. For canonical content, rely on `paper.txt`/`paper.pdf`._\n"
const ArticleText = "Legal Studies\nResearch Paper Series\nResearch Paper No. 23–66\nDefamation with Bayesian Audiences\nYonathan A. Arbel\nMurat C. Mungan\nThis paper can be downloaded without charge from the\nSocial Science Research Network Electronic Paper Collection\nElectronic copy available at: https://ssrn.com/abstract=4181890\n\n<<PAGE_BREAK>>\n\nJ,V0N0 1\nDefamation with Bayesian Audiences\nYonathanA.Arbel,* MuratC.Mungan†\nHowstrictlyshouldthelawregulatefalsedefamatorystatements? Wefirstshowthat\nthepresenceofjudicialerrorsoftenputsdefamationlawonaLaffercurve: regulation\nthatistoolaxortoostrictisinferiortomoderateregulation.Whilemoderateregulation\nis ideal, it is not always attainable, due to practical and legal constraints. With these\nconstraints,thepresenceofBayesianaudiencescancausetheoptimalregulationtobe\nlaxerthanisprescribedbystandardmodelswithna¨ıveaudiences.Thishighlightsthe\nimportanceofaccountingfortheimpactofdefamationlawsonbeliefformation.\nKeywords:Defamation,Bayesianaudience,informationregulation,disclosure.\nJELclassification:C72;D82;D83;K10;K13;K39.\n1. Introduction\nWhenstatementsaremadeinpublic,audiencesassesstheircredibilitybased\nonavarietyofcues.Oneofthesecuesishowstrictlythelawsanctionsfalse\nstatements, i.e., whether talk is cheap. Such audience effects complicate the\nstandardanalysisofdefamationlaw,whichtraditionallyonlyfocusesonhow\nthe law affects speakers and the subjects of their speech. We investigate here\ntheoptimalstrictnessofdefamationlawwhenaccountingforaudienceeffects.\nDefamation law imposes tort liability on speakers who publish false state-\nments that harm their target’s good name. A typical example comes from a\nrecentcasewhereahospitalstafferfalselyallegedthatadoctorwasworking\nundertheinfluenceofalcohol.Thedoctorwonalawsuitagainstthestafferand\nrecoveredmillionsofdollarsindamages(Denmanv.St.Vincent,2020).While\nthe basic structure of defamation law is well established, there is an ongoing\nsocialdebateondefamationlaw’sproperscope.WithcallsfromtheSupreme\nCourt, legal scholars, politicians, and various pundits, there is growing pres-\nsuretodaytoreformdefamationlaw(Arbel&Mungan,2019).Inthemidstof\nthesecalls,anewRestatementprojectwasrecentlyannounced.\nTheliteratureondefamationlawisvast,buttheeconomicanalysisofdefama-\ntion law is quite limited (Hemel, 2020). In deciding the level of strictness of\ndefamationlaw,standardlegalanalysesaredominatedbyatwo-sidedbalanc-\ning act. On the one hand, society considers the interests of the target of the\nspeech—her need for compensation and the need to protect her by deterring\ndefamatory speech against her. On the other hand, society also considers the\nspeaker,hisrighttofreespeech,andthesocialconcernwithchillingvaluable\nspeech(NYTimesv.Sullivan,1964).\n*UniversityofAlabamaSchoolofLaw.E-mail:yarbel@law.ua.edu\n†GeorgeMasonUniversity,AntoninScaliaLawSchool.E-mail:mmungan@gmu.edu.\nDraft,Vol.0,No.0,\ndoi:/ewmxxx\n©.\nAllrightsreserved.ForPermissions,pleaseemail:\nEElleeccttrroonniicc ccooppyy aavvaaiillaabbllee aatt:: hhttttppss::////ssssrrnn..ccoomm//aabbssttrraacctt==44118811889900\n\n<<PAGE_BREAK>>\n\n2 .V0N0\nInreality,wenoted,defamationlawalsoaffectspartiesbeyondthespeaker\nandhistarget.Inparticular, defamationlawalsoaffectsaudiencesofspeech.\nThisisnotjustduetothefamiliarideathatstrictdefamationlawwouldlimit\nthesupplyoffalsespeechthroughthedeterrenceofspeakers.Ifthatwerethe\ncase,theprotectionofaudienceswouldbeasimplematterofsettingsanctions\nasstrictaslegallypossible.Defamationlawalsoaffectsaudiencesbychanging\ntheirassessmentofthecredibilityofspeechand,thus,itaffectstheaudience’s\npropensitytoactuponstatements(Pennycooketal.2020, Arbel2022).Such\neffectsaddcomplexitythatthestandardanalysisneglects.Theneglectofau-\ndienceeffectsmaybebecauselawyersnaturallyfocusonthepartiesthattake\nanactivepartinthelegalprocess–thevictimastheplaintiffandthespeakeras\nthedefendant(Heymann,2012).Whateverthereason,tworecentinformalac-\ncounts(Hemel&Porat,2019&Arbel&Mungan,2019)suggestthatomission\nofaudienceeffectsisconsequentialtotheoptimalstrictnessofdefamationlaw.\nOur object here is to bridge this gap by offering a general framework that\nanalyzesbehaviorandevaluateswelfarebasedonthestrictnessofdefamation\nlaw. To do so, we construct a model that includes three key features: (i) a\nBayesian (rather than a na¨ıve) audience, (ii) errors in the court’s judgment\n(wrongfulliabilityaswellaswrongfulfailuretofindliability),and(iii)acap\nonrecoverabledamages.Weexplaintheroleeachofthesefeaturesplays,after\nbrieflyreviewingthestructureofourmodelanditsimplications.\nWeconsiderthebehaviorofthreeparties.Aspeaker,whohasprivateinfor-\nmation about a certain target – a business or an individual. The speaker may\nmake claims about the target to an audience member. The audience member\nthen decides whether to interact—trade, collaborate, socialize—with the tar-\nget. Targets can be a high- or low-type, and audiences would rather interact\nonly with the former kind. If the target loses an interaction, he may bring a\nlawsuitagainstthespeakerallegingdefamation.Westudybehaviorunderdif-\nferentlevelsofdamagesfordefamationandtheirsocialwelfareimplications.\nOur analysis reveals three central findings. First, we find that there is an\noptimallevelofdamagesthatsupportsseparatingequilibriainwhichwould-be\ndefamersaredeterredfromsharingfalseinformationandspeakersonlyshare\ninformationhonestlywiththeiraudience.Audiencemembersbelievespeakers\nand act upon this information. Naturally, social welfare is highest under this\nregime.\nSecond, we find that defamation laws often follow a ‘Laffer Curve.’ Lax\nregulationresultsinafloodofcheaptalk,whichleadstoaudiencesdiscount-\ning all statements—true or false—and simply acting on their priors. This re-\nsultsinequilibriawhereimportantinformationisleftuncommunicated.Sanc-\ntioningdefamationtoostrictlyisalsounwanted,becausehighsanctionsinvite\nfrivolous litigation, which in turn chills true negative statements. In between\nthesetwoextremes,theoptimallevelofdamagesfollowsaninverseUshape,\nwith a range of optimal damages. Thus, our unified framework shows that\nbothcheaptalkand‘overpriced’talkareundesirableastheydepriveaudiences\nofrelevantinformationthatcouldbemadeavailabletothemundermoderate\ndamages.\nEElleeccttrroonniicc ccooppyy aavvaaiillaabbllee aatt:: hhttttppss::////ssssrrnn..ccoomm//aabbssttrraacctt==44118811889900\n\n<<PAGE_BREAK>>\n\n-- 3\nOur third result emerges when the cap on damages is lower than the level\nnecessary to support equilibria in which the target’s type is fully revealed. In\nreality, it is difficult to calculate the exact level of damages, and even when\npossible,damagesareboundedbybothconstitutionalconsiderationsandlim-\nits on defendants’ wealth. In such cases, we find that a lax approach can be\nsuperiortoamorestringentone.Thereasonisthatstringentregulationinvites\naudience trust, but because some statements are false, this trust can be mis-\nplaced, leading to the deterrence of valuable interactions. Compounding the\nissueisthatstringentregulationincreaseslitigation.Laxregulation,however,\ninvitesaudiencestorelymoreontheirpriorsandreduceslitigation.Thus,per-\nhapscounter-intuitively,laxregulationbecomespreferabletostrictregulation\nwhenreputationalharmsarelarge,andtheoppositeconclusionmayholdwhen\nreputationalharmsaresmall.\nAll three features of our model (Bayesian audience, judgment errors, and\ndamagecaps)playimportantrolesintheproductionoftheseresults.\nFirst, when courts make no errors in judgment, people have no incentive\ntobringfrivolousclaimsagainstspeakers.Inthiscaseverylargedamages(if\nfeasible) are always preferable to smaller damages, because they only deter\nfalsespeechwithouthavinganyimpactontruenegativespeech.Thisisady-\nnamicthatemergesinmanyothercontextsaswell,andhighlightstheroleof\njudgment errors in explaining the inefficiency of very large damages in the\ndefamation context, and the emergence of the Laffer Curve to which we al-\nluded.\nSecond, the prior economics literature on defamation law assumes that a\npublisher(e.g.atabloid, journal,anindividualetc.)canalwaysharmanother\npersonbymakingnegativestatementsaboutthem,andtheextentofthisharm\nisindependentofthelawsinplace(e.g., Garoupa1999a,b, Bar-Gill&Ham-\ndani 2003).1 This is equivalent to the audience –whose beliefs and behavior\nisnotconsideredinthepriorliterature–naivelyformingitsbeliefsandacting\nuponthem.Thus,inthepriorliterature,themainfunctionofreformingthelaw\nis to alter the expected costs and benefits of making disparaging statements,\nbut not the harmful impact of defamatory statements. With a na¨ıve audience,\nincreasingdamagesleadstoareductionintheexpectedharmtothetarget,be-\ncauseitdetersnegativespeech.ThisisnotsowhentheaudienceisBayesian.\nBecauseverylowdamagesresultinfrequentfalseallegations,theydilutethe\ninformational content of speech, and therefore causes the audience to act ac-\ncordingtoitspriors.Thus,inadditiontoprovidingstraightforwardrationales\nfor some behavioral responses in the defamation context (e.g., disregarding\ncertainfalsespeech),theincorporationofBayesianaudiencesalsohasimpor-\ntantnormativeimplications, e.g., loweringdamagescanreducetheharmthat\nresultsfromdefamatorystatements.\n1. Themirrorimageofthisassumptionisalsoinvokedinthisliterature:thespeaker’sbenefit\nfrommakinganegativestatementisindependentoftheaudience’sbeliefs,becausetheaudienceis\nnotconsideredinthisliterature.Thisassumptionismade,forinstance,inDalviandRefalo(2008),\nwhichfocusesexclusivelyonthespeakers’incentivesandignoresnotonlytheaudience’sbeliefs\nandbehaviorbutalsothetarget’s.\nEElleeccttrroonniicc ccooppyy aavvaaiillaabbllee aatt:: hhttttppss::////ssssrrnn..ccoomm//aabbssttrraacctt==44118811889900\n\n<<PAGE_BREAK>>\n\n4 .V0N0\nThird, this normative distinction becomes quite significant with binding\ndamagecaps,2 inwhichcasefalsedisparagingremarkscannotbefullyelimi-\nnated.Thus,withBayesianaudiences,thechoiceisbetweenahighdegreeof\ninteractionsbetweentheaudienceandtargets(goodandbad)achievedthrough\nlowdamages,andthemaximumlevelofdamagesthatcausesbadinteractions\ntobedeterredalongwithsomegoodinteractions.Theformeroptionisprefer-\nablewhenthevalueofgoodinteractionsarelarge.Ontheotherhand, witha\nna¨ıveaudience,maximumdamagesarealwayspreferable,becauseevenwith\nlow damages the audience believes false disparaging remarks, which are in\nhighsupplyduetothelackofdeterrentdamages.\nIn short, the main impact of judicial errors in our analysis is to rule out\ntheoptimalityofverylargedamages.Thisbecomesanimportantissuewhen\nthe damage cap is very large (or non-existent), in which case the presence\nof judicial errors supplies an independent rationale for not having very large\ndamages.Ontheotherhand,whenthedamagecapisbinding,ana¨ıveaudience\nimpliesthatthemaximumdamageisoptimal,andthisresultisoverturnedwith\nBayesianaudiences.\nWhile our analysis focuses on defamation law, the basic question we pose\nhere is relevant for a broad range of legal contexts. The law regulates false\nspeechindomainsasdiverseascorporatedisclosures,falseadvertising,whistle-\nblowers, and law enforcement. Common to these domains is a basic tension\nbetweenthestrictnessofsanctionsformisreportingandtheinformativenessof\nspeech,andwecommentonpotentialimplications.\nThe next section offers some brief background and reviews the related lit-\nerature.Section3presentsthemodelanditsanalysis.Section4evaluatesthe\nwelfare implications of different damages regimes, and highlights the impor-\ntanceofaccountingforaudienceeffects.Section5containsseveralextensions\nand discussions of the basic model, such as the public enforcement case, the\ngeneralizationofthemodeltocaseswherespeakersmaybemotivatedtospeak\ntruthfullyortoexcessivelypraisethetarget,anddiscussionsofcontextsother\nthandefamationlaw.Section6providesconcludingremarks.\n2. LiteratureReview\nDefamationlawregulatesthedisseminationoffalsestatementsthatare‘defam-\natory.’ To be defamatory, a statement must not only be false but also made\npublicandbecapableofharmingone’sreputationandstandinginthecommu-\nnity.Defamationlawisconsideredtobeabranchoftorts,anditencompasses\nseveraldistincttorts,mostnotablylibelandslander.Today,however,thedis-\ntinctionhaslesspracticalsignificancethaninthepast,andinwhatfollows,we\nabstractfromit.\nMany defamation lawsuits are brought by individuals, but businesses and\nfirmscanalsobringsuit.Arecenthigh-profileexampleinvolvesalawsuitby\n‘Dominion,’ a firm that sells voting hardware and software, against various\n2. Asimilardynamicalsoemergeswhencourtsfrequentlymakejudgmenterrors,aswebriefly\nexplaininsection5.4.,below,andingreaterdetailinArbeland&Mungan2020.\nEElleeccttrroonniicc ccooppyy aavvaaiillaabbllee aatt:: hhttttppss::////ssssrrnn..ccoomm//aabbssttrraacctt==44118811889900\n\n<<PAGE_BREAK>>\n\n-- 5\npublicfiguresandmediaoutlets,whoallegeditwasinvolvedinthemanipula-\ntionofelectionvotes.3\nDefamation law evolved in the common and ecclesiastical courts of Eng-\nland. In the United States, the states took the doctrine and used it to develop\ntheirownvariants.Amajordevelopmenttookplacein1964,whentheSupreme\nCourt decided the seminal case of NYTimes v. Sullivan. There, the Court re-\nviewedtheexistingbodyofdoctrineinlightoftheFirstAmendmentprotec-\ntionoffreespeechandpress.TheCourtmadeitconsiderablyharderforpublic\nfigures to bring lawsuits on matters of public interest. In the years that fol-\nlowed,thedoctrinewasrefinedand,whilestillcarryingsignsofitsconvoluted\nhistory,reachedacertaindegreeofbalance.Inrecentyears,however,therehas\nbeengrowingpressuretoreformthelaw.CommentsfromtheSupremeCourt\n(McKee v. Cosby, 2019; Berrisha v. Lawson, 2021), the political sphere, le-\ngalcommentators, andpundits—allrevealdissatisfactionwiththelaw.Many\nofthesecommentssuggestthatdefamationlawshouldbemadestricter; e.g.,\nCassSunsteincalledtheNYTimesv.Sullivandecision‘anachronistic’andar-\nguedthatpublicfiguresshouldbeallowedtobringsuitmoreeasily(Sunstein,\n2021). Interestingly, the reason why the law should protect good name inter-\nestsisnotwellunderstood.Somegroundthelaw’sinterventioninaproperty\nlikeinterestingoodname,orgoodname’sbasisindignity,property,andhonor\n(Post, 1984) while others relate it to concepts of social status and reputation\n(Arbel,2021).\nThe legal literature on defamation law is rich and vast, and it explores a\nvarietyoftopics,involvingdeepquestionsofpoliticalphilosophyandconsti-\ntutionalcommitments.Itisthereforequitesurprisingthattheliteratureonthe\neconomicsofdefamationlaw‘haslagged’andissparse(Hemel,2020).Some\nnotablecontributionsinthisspaceincludesRichardPosner’spioneeringanal-\nysis (Posner, 1973, 1986), which highlighted the applicability of cost-benefit\nanalysis to defamation law. More recent work focuses on the law’s effect on\nmedia’sincentivestoinvestigateandreporttopicsofpublicinterest(Bar-Gill\n&Hamdani,2003,Dalvi&Refalo,2008,Acheson&Wohlschlegel,2018)and\non political dishonesty (Garoupa, 1999a,b). As noted, this paper differs from\ntheseanalysesbyconsideringaBayesianaudience,alongsidedamagecapsand\njudicialerrors.\nDespitethesecontributions,courtsandlegalcommentatorsarelimitedtoa\nfairlyrudimentaryunderstandingoftheincentivesfosteredbydifferentdefama-\ntion law regimes. Here we amplify on two informal contributions that recog-\nnizetherelevanceandimportanceofaudiencestotheanalysisofdefamation\nlaw (Hemel & Porat, 2019, Arbel & Mungan, 2019). Methodologically, our\narticle borrows tools from the rich literature on signaling (Spence 1973) and\ncheaptalk(Crawford&Sobel,1982).Ouranalysiscanalsobeinterpretedas\npart of emerging literature that looks at how laws can be used to create in-\nformalsanctionsthroughthebehaviorofthirdparties(e.g.,Deffains&Fluet,\n3. USDominion,Inc.v.FoxNewsNetwork,LLC,C.A.N21C-03-257EMD(Del.Super.Ct.\nDec.16,2021).\nEElleeccttrroonniicc ccooppyy aavvaaiillaabbllee aatt:: hhttttppss::////ssssrrnn..ccoomm//aabbssttrraacctt==44118811889900\n\n<<PAGE_BREAK>>\n\n6 .V0N0\n2019,Mungan2016,Be´nabou&Tirole,2006,2011,Rasmusen1996).\n3. Model\nWe model the interactions between three parties: the speaker (S, she), the\ntarget of the speech (T, he), and the audience, captured by a representative\nmember (A, it). A faces an informational problem: T is either a good or a\nbad type, and A’s value of interacting with T depends on T’s type, which\nis unknown to A. Before A decides whether to interact with the target, S,\nwho knows T’s type, communicates with A and may either disparage T or\nmakeanon-disparagingcomment.Becausewestudydefamation,weconsider\nthepossibilitythatS mayfalselydisparageT inordertodeteraninteraction\nbetweenAandT.Wedeferthediscussionofspeakersbeing(atleastpartly)\nmotivatedbyadesiretotruthfullyshareinformation,asthishaslimitedimpact\nonouranalysis.4 WemodeltheinteractionsasaBayesiangame,anduseitto\nidentifyPerfectBayesianEquilibria.5\n3.1 Preliminaries\nThetarget,T,obtainsabenefitofr fromtheinteraction,wheret∈{B,G}\nt\ndenotes his type and where the letters abbreviate bad and good, respectively.\nT’s type is privately known to himself and S, but not to A, who only knows\nthattheproportionofgoodtypesisγ ∈(0,1).6Apreferstointeractwithgood\ntypes,butnotbadtypes,becausethisresultsinautilityofg >0>−bwhere\nbisthedisutilityAbearsfrominteractingwithabadtype.Thus,absentfurther\ninformation,AwouldprefertointeractwithT ifγg−(1−γ)b > 0,andwe\nassumethisinequalityholds,sinceotherwisenointeractionswouldtakeplace\nbetween A and T even without (negative) input from S.7 Thus, the audience\npreferstointeractwiththetargetifitsupdatedbelief(basedonthestatementit\nreceivesfromS)ofT’slikelihoodofbeingagoodtypeexceedsthethreshold\nb\nx≡ <γ, (1)\n(cid:98) g+b\nwheretheinequalityfollowsfromtheassumptionthatAwouldprefertointer-\nactwithT absentinputfromS.\nThespeakerhasaninterestinwhetherAandT interact:Sobtainsagainofv\nwhenAavoidsinteraction(alternatively,vcanbeinterpretedasalossincurred\nwhenAchoosestointeractwithT).v isarandomvariablewiththecumula-\ntive distribution function F(v) with support (0,1] where the upper-bound of\nthe support is normalized to simplify notation. The specific v-draw is private\n4. Consistentlywiththelaw,truthfulnegativestatementsarenotconsidereddefamatory.How-\never,thecourtmaymakeerrorsinascertainingwhetheranegativestatementistruthful,andthis\npossibilityisincorporatedinourmodel,asweexplainbelow.\n5. Figure5intheAppendixdepictstheinteractionsbetweenthethreepartiesandishelpfulin\nfollowingthedetaileddescriptionsoftheinteractionsthatweprovide,next.\n6. Insection5wediscusstheconsequencesofendogenizingγ.\n7. Ananalysisofthiscasecanbefoundinanearlierversionofthisarticle, andyieldsno\nfurtherinsights(seeArbel&Mungan(2020)).\nEElleeccttrroonniicc ccooppyy aavvaaiillaabbllee aatt:: hhttttppss::////ssssrrnn..ccoomm//aabbssttrraacctt==44118811889900\n\n<<PAGE_BREAK>>\n\n-- 7\ninformationavailableonlytoS,andwecallv thespeaker’stype.Weassume\nthatinteractionsbetweenAandT aresociallyvaluableif,andonlyif,T isa\ngoodtype,i.e.r +g >1>0>r −b.\ng b\nAfter Nature determines the types of T and S, the target’s type becomes\ncommonknowledgeamongT andS(butnotA).Atthispoint,Schooseswhat\ntype of statement to send A regarding T’s type. The types of possible state-\nments follow defamation law’s distinction between disparaging statements,\nwhich are potentially actionable, and non-disparaging statements, which are\nnon-actionable(e.g.,positiveremarks,silence,opinion,etc.).\nSubsequently, A decides on whether to interact with T or to avoid him,\nand, finally, T, decides whether to bring a lawsuit against S if a disparaging\nremarkwasfollowedbyA’schoicetoavoidinteractingwithT.8 Wenotethat\nthis setting includes the possibility of T suing S, even if T is in fact a bad\ntype,i.e.,afrivolouslawsuitmaybebrought.Thisisanimportantpossibility\nbecausecourtsmayerrintheirjudgment.Tocapturetheparties’payoffsfrom\nlitigation,wedefinethefollowing:\nd: damagespaidbyS toT whenthecourtfindsforT\nl: totallitigationcosts.Weassumethatlitigationcostsarenotprohibitive(l<1)\nand,withoutlossofgenerality,thatthecostsareequallysharedbytheparties.\nq : probabilityofplaintiffvictorywhenT isoftypet∈{B,G}\nt\n(cid:16) (cid:17)\nWeassumetheprobabilityofwrongfulliabilityissmall: q <q l/2\nB G 1−l/2\nBecausecourtswieldbroadlatitudeinsettingthelevelofdamages,9wefol-\nlow the existing literature (see, e.g., Garoupa 1999a,b) and use d as a policy\nlever to operationalize different defamation regimes. The value of d can also\nbe interpreted as expected damages, i.e. d = E[d˜] where d˜is a random vari-\nablerepresentingactualdamagesawardedwhosedistributionisaffectedbythe\ncourt’sinterpretationofthelaw.Wealsonotethatdcanbechosenseparately\nfor each type of statement (represented by all variables described above, r ,\ng\nr ,g,b,etc.)beinganalyzed,whichwetakeasgiveninouranalysis.\nb\nIt is worth noting that we take the odds of winning at trial, q and q ,\nB G\nas exogenously given. This is a standard commitment assumption in the en-\nforcementliterature,andimpliesthatcourtsarecommittedtoreviewingcases\nonlyontheirmerit,i.e.,withoutbringingintheirinformedestimatesaboutthe\nproportion of frivolous cases. Our assumption relating q to q , above, cor-\nG B\nrespondstothecasewherejudicialerrorsarepossible,butoccurinfrequently.\nWenotethattheanalysisofthealternativecasewithlargejudicialerrorsleads\n8. Inpractice,courtsoftenrequiresomeproofofharmtoallowmonetaryrecovery,hencethe\nrequirementherethatthedefamatoryremarkpreventedaninteraction.\n9. Courtscan,withinlimitations,awardnominal,economic,non-economic,andpunitivedam-\nages, andhavedemonstratedconsiderablediscretioninpractice.SomeexamplesincludeLoth-\nschuetzv.Carpenter,898F.2d1200,1205(6thCir.1990)($1innominaldamages);WasteMgmt.\nofTexas,Inc.v.TexasDisposalSys.Landfill,Inc.,434S.W.3d142,162(Tex.2014)($450,000\nineconomicharms); Cantuv.Flanigan,705F.Supp.2d220(E.D.N.Y.2010)($150millionin\nnon-economicdamages);Armstrongv.Shirvell,596F.App’x433,448(6thCir.2015)($500,000\ninpunitivedamages).\nEElleeccttrroonniicc ccooppyy aavvaaiillaabbllee aatt:: hhttttppss::////ssssrrnn..ccoomm//aabbssttrraacctt==44118811889900\n\n<<PAGE_BREAK>>\n\n8 .V0N0\ntosimilarresults,andacompleteanalysisofthiscasecanbefoundinArbel&\nMungan(2020).\n3.2 Players’Actions,Beliefs,Strategies,andPayoffs\nNext,wedescribetheplayersstrategies,beliefs,andactions.Forsimplicity,\neachplayer’sactionislabelledaseither0or1,asfollows:\nTable1: Players’PotentialActions\nPlayer Action\n0 1\nS Don’tDisparage Disparage\nA Interact Avoid\nT Don’tLitigate Litigate\nWe note that labeling A’s action of interacting as 0 may appear counter-\nintuitive.However,thebenefitofthisnotationisthatasuitisfiledonlyincases\nwhere all players’ actions are 1. This makes it simpler to express the pay-off\nofthespeaker(asinTable3,below),sinceshefacesexpectedlitigationcosts\nonlywhenallactionsequal1.\nUsingthisnotation,wecandescribethestrategiesofeachplayerasfollows:\nTable2: Players’Strategies\nPlayer Strategy\nS s(t,v):{B,G}×(0,1]→{0,1}\nA a(z):{0,1}→{0,1}\nT p(t):{B,G}→{0,1}\nHere,inspecifyingA’sstrategy,zdenotesthestatementreceivedbyA.\nBecauseoursolutionconceptisaPerfectBayesianEquilibrium(henceforth\nPBE),wealsospecifyA’sbeliefsregardingT’stype,as:10\nx : BeliefthatT isagoodtypegivenz =i\ni\nWiththisnotation,weexpresstheexpectedpay-offsofeachplayer,giventheir\nbeliefsandinformation,asfollows:\nTable3: Players’Payoffs\nPlayer Payoff\nS a(s(t,v))(v−p(t)s(t,v)(q d+ l))\nt 2\nA a(z)(x g−(1−x )b)\nz z\nT (1−a(s(t,v)))p(t)(q d− l)+a(s(t,v))r\nt 2 t\n10. BecauseA’svaluationofhisinteractionwithT dependsonlyonT’stype,weneednot\nspecifyA’sbeliefsregardingS’stypeforpurposesofidentifyingthePBE.\nEElleeccttrroonniicc ccooppyy aavvaaiillaabbllee aatt:: hhttttppss::////ssssrrnn..ccoomm//aabbssttrraacctt==44118811889900\n\n<<PAGE_BREAK>>\n\n-- 9\n3.3 EffectiveandIneffectiveCommunicationEquilibria\nPerfect Bayesian Equilibria consist of assessments (i.e. a profile of beliefs\nand strategies) that satisfy sequential rationality and consistency of beliefs.\nSincetherequirementsforPBEarewellknown,werelegatetheirformaldef-\ninitions to Appendix A, below. As in many other contexts, communications\ncanbedisregardedbytheaudienceinsomeequilibria.Wedistinguishbetween\ntheseandothertypesofequilibriabyusingthefollowingdefinition.\nDefinition1APBEisaneffectivecommunicationequilibriumif,andonly\nif,theaudiencechoosesnottointeractwiththetargetwithsomepositiveprob-\nabilitybasedontheinformationitreceivesfromthespeaker.\nWe start by noting that defamation law cannot eliminate ineffective com-\nmunication equilibria. This is because when the audience’s beliefs regarding\nthe target’s types are unconditional on the speaker’s statement and equal to\nits prior (i.e. x = x = γ), it chooses to interact with the target regardless\n0 1\nof what it hears from the target (i.e. a∗(z) = 0). This results in payoffs of 0\nandrtothespeakerandtarget,respectively.Thesepayoffsareindependentof\nthe actions of the speaker and target, which makes them indifferent between\nplaying any of the strategies available to them. Thus, any assessment where\nthe speaker plays a strategy that supports the audience’s beliefs constitutes a\nPBE.Thesimplestexampleisonewherethespeakerneverchoosestodispar-\nagethetarget(i.e.s(t,v)=0foralltandv).Weformalizethisobservationas\nfollows.\nProposition 1. Under all defamation regimes, there exist ineffective com-\nmunicationequilibria.\nProof. The assessment consisting of x∗ = x∗ = γ, a∗(z) = 0, s∗(t,v) =\n(cid:26) 0 if q d⩽l/2 1 fort 0 ∈{B,G}\n0, and p∗(t) = t satisfies sequential\n1 if q d⩾l/2 fort∈{B,G}\nt\nrationality and consistency of beliefs (i.e. requirements 1-4 in Appendix A),\nandthusisaPBE.\nProposition 1 notes that ineffective communication equilibria are always\npresent, regardless of the defamation regime in place. If these were the only\nequilbria, defamation law would be irrelevant. Thus, we proceed by showing\nthatsomelevelsofdamagesinfactgenerateeffectivecommunicationequilib-\nria.\nProposition 2. (i) Extremely low damages (i.e. d < l ) and extremely\n2qG\nhighdamages(i.e.d> 2−l)onlygenerateineffectivecommunicationequilib-\n2qB\n(cid:16) (cid:17)\nria. (ii) There exist a range of moderate damages, D ⊂ l , 2−l , which\n2qG 2qB\ngenerate effective communication equilibria. (iii) The audience acts consis-\ntentlywiththespeaker’sstatement,i.e.a∗(z)=z,inalleffectivecommunica-\ntionequilibria.\nProof. SeeAppendix.\nEElleeccttrroonniicc ccooppyy aavvaaiillaabbllee aatt:: hhttttppss::////ssssrrnn..ccoomm//aabbssttrraacctt==44118811889900\n\n<<PAGE_BREAK>>\n\n10 .V0N0\nThe intuition behind the first part of proposition 2 is relatively straightfor-\nward.Whendamagesareextremelylow,thetargetisdeterredfromsuingthe\nspeaker, even when he has a meritorious case, since expected damages (i.e.\nq d)arelowerthanlitigationcosts.Thiscausesthespeaker’sstatementstobe\nG\nperceived as cheap-talk by the audience, since the speaker faces no negative\nconsequence from making disparaging statements. Thus, the audience disre-\ngards the speaker’s statements and acts according to its priors. On the other\nhand,whendamagesareextremelyhigh,alltargetsareincentivizedtolitigate,\nandexpecteddamagesarehighenoughtodeterallspeakertypesfrommaking\ndisparaging statements. Thus, the audience is once again left without any in-\nformativestatements,thistimeduetotheover-pricingofspeechasopposedto\nthepresenceofcheap-talk.\nItisonlymoderatedamagesthatsupporteffectivecommunicationsbetween\nspeakers and audience members, and this is formalized in proposition 2-(ii).\nPart (iii) of proposition 2 simply rules out the possibility of counter-intuitive\nequilibria,forinstance,inwhichtheaudienceinfersfromadisparagingremark\nthatthetargetmustbeagoodtypeandvice-versa(i.e.wherea∗(z)=1−z).\nThese preliminary findings indicate that if defamation laws are to have any\nimpact, theymustdosothrougheffectivecommunicationequilibriaobtained\nunder moderate damages. Thus, we analyze these equilibria in further detail,\nnext.\n3.4 ModerateDamagesandEffectiveCommunicationEquilibria\nThe damages in place affect the target’s incentive to sue when disparaged,\naswellasthespeaker’sincentivestodisparagethetargetinthefirstplace.We\nnotetwopairsofcriticaldamagesthatpertaintoeachparty’sincentives.First,\nl l\nd ≡ andd ≡ (2)\n1 2q 3 2q\nG B\nare the smallest damages that causes a type G and B target, respectively, to\nbring suit whenever the speaker disparages him.11 On the other hand, when\ndamagesaregreaterthan\n2−l 2−l\nd ≡ andd ≡ (3)\n2 2q 4 2q\nG B\ntypeGandBtargets,respectively,areexpectedtobringsuit,andthisdetersthe\nspeakerfromdefamingthetarget.Ourassumptionofnon-prohibitivelitigation\ncostsandsmalljudicialerrorsimpliesthatthesefourcriticaldamagelevelsare\norderedasfollows:\nd <d <d <d (4)\n1 2 3 4\nThus,therearethreecategoriesofmoderatedamages,whichwecalllow,inter-\nmediate,andhighdamages.Weexplaintheincentivesthateachplayerfacesin\n11. Weassume,onlytosimplifyexposition,thatanindifferenttargetchoosesnottolitigate.\nEElleeccttrroonniicc ccooppyy aavvaaiillaabbllee aatt:: hhttttppss::////ssssrrnn..ccoomm//aabbssttrraacctt==44118811889900\n\n<<PAGE_BREAK>>\n\n-- 11\neachofthesedamagecategoriesunderaneffectivecommunicationequilibrium\n(whenoneexists).\nLowDamages(d∈(d ,d ))\n1 2\nIn this range, the target has the incentive to litigate only if he is type G,\nsinceq d > l > q d.Thus,inaneffectivecommunicationequilibrium,the\nG 2 B\nspeaker faces no threat of litigation from disparaging a bad type, and thus a\ntype B target is disparaged with certainty. On the other hand, if the speaker\nencountersatypeGtarget,sheexpectsthatdisparaginghimwillleadtoacost\nof\nl\nv (d)≡q d+ . (5)\nG G 2\nThus,thespeakerchoosestodisparageatypeGtargetifhertypeexceedsthis\nvalue.Therefore,atypeGtargetisdisparagedwithaprobabilityof\n1−F(v (d)) (6)\nG\nOuranalysisthusfaridentifiesthebehaviorofthespeakerandtargetinan\neffectivecommunicationequilibrium,assumingthatitexists.But,forthistype\nofequilibriumtobesupportable,theaudience’sbeliefsmustbeconsistentwith\ntheequilibriumbehavioroftheotherparties.Thus,theaudiencemustholdthe\nbelief that a target who is not disparaged must be a good type, since all bad\ntypesaredisparaged,i.e.\nx∗ =P(t=G|z =0)=1\n0\nOntheotherhand,whentheaudiencereceivesadisparagingstatement,itmust\nbelievethatthetargetisneverthelessagoodtypewithaprobabilityof\nγ[1−F(v (d))]\nx∗(d)=P(t=G|z =1)= G <γ (7)\n1 γ[1−F(v (d))]+(1−γ)\nG\nThis is because a type G target is disparaged with probability 1−F(v (d))\nG\nwhereas a type B individual is disparaged with certainty, and the likelihood\nwithwhichthetargetisagoodtypeisγ.\nAswenotedvia(1)theaudiencefindsitinitsbestinteresttointeractwith\nthetargetifitbelievesheisagoodtypewithaprobabilityexceedingxˆ.Thus,\naneffectivecommunicationequilibriumissupportableinthisrangeif\nx∗(d)<xˆ<x∗ =1 (8)\n1 0\nIn the upper portion of this range, this condition certainly holds, since 1 −\nF(v (d ))=0,i.e.thespeakerisalwaysdeterredfromdisparagingatypeG\nG 2\ntarget.Moreover,x∗(d)isclearlydecreasinginthisdamagerange,whichcan\n1\neasily be verified by inspecting (7). Therefore, within low damages, there is\nsome critical damage dˆ, above which effective communication equilibria are\nobtained.Whetherdˆ=d ,i.e.whethereffectivecommunicationequilibriaare\n1\nsupportable with all lower moderate damages, depends on parametric values\nandhasnoimportantimplications.\nEElleeccttrroonniicc ccooppyy aavvaaiillaabbllee aatt:: hhttttppss::////ssssrrnn..ccoomm//aabbssttrraacctt==44118811889900\n\n<<PAGE_BREAK>>\n\n12 .V0N0\nBased on these observations, we can summarize the impacts of increasing\ndamagesintherange(dˆ,d )onthebehaviorofallplayersineffectivecommu-\n2\nnication equilibria. As damages are increased, the speaker disparages type G\nindividualslessfrequently,sincethethresholdspeechbenefitthatsherequires\nisincreasingindamagesper(5).Thisleadstolessfrequentlitigationaswell\nas less frequent blocking of beneficial interactions between the audience and\nthetypeGtarget.Thelevelofdamagesleadstonofurthereffects, becausea\ntypeBtargetisdisparagedwithcertaintyinthisrange.\nIntermediateDamages(d∈[d ,d ])\n2 3\nWhen damages are increased into the intermediate range the speaker is al-\nwaysdeterredfromdisparagingatypeGtarget.Thisisbecausetheexpected\ndamages and litigation costs associated with doing so exceed the benefit that\nshe obtains from blocking the target’s interaction with the audience. More-\nover,becaused<d ,atypeBtargetlackstheincentivestolitigate.Thus,the\n3\nspeakeralwaysdisparagesatypeB target.Basedonthisbehavior, itfollows\nthatinaneffectivecommunicationequilibriumtheaudience’sbeliefsaregiven\nby\nx∗=P(t=G|z =0)=1and\n0\nx∗=P(t=G|z =1)=0\n1\nThis trivially implies that effective communication equilibria are supportable\nbyalldamagesinthisrange,since0=x∗ <xˆ<x∗ =1.\n1 0\nQuite importantly, in this range all effective communication equilibria are\nseparatingequilibriawhereinthespeakerchoosesto[not]disparagewhenever\nsheknowsthatthetargetistypeB [G].Welaternotethesuperiorityofthese\nequilibriawhenweconductawelfareanalysis.\nHighDamages(d∈(d ,d ))\n3 4\nWith high damages, a type B target is given the incentive to frivolously\nlitigate. This, in turn, causes the speaker to be deterred from disparaging a\ntypeB targetwhenherbenefitfromblockinginteractionsislow.Specifically,\nshechoosestodisparageatypeBindividualonlyifherbenefitexceeds\nl\nv (d)≡q d+ (9)\nB B 2\nThus,abadtypeisdisparagedwithaprobabilityof\n1−F(v (d))<1 (10)\nB\nOn the other hand, when the speaker encounters a type G target, she never\ndisparages him given the high damages. Based on this behavioral profile, in\nequilibriumtheaudience’sbeliefsaregivenby\nγ\nx∗(d)=P(t=G|z =0)= >γ and\n0 γ+(1−γ)F(v (d))\nB\nx∗=P(t=G|z =1)=0\n1\nEElleeccttrroonniicc ccooppyy aavvaaiillaabbllee aatt:: hhttttppss::////ssssrrnn..ccoomm//aabbssttrraacctt==44118811889900\n\n<<PAGE_BREAK>>\n\n-- 13\nFigure1\nSincexˆ<γ,itfollowsthatx∗ >xˆ>x∗,andthereforeeffectivecommunica-\n0 1\ntionequilibriaaresupportablebyallhighdamages.\nAs the above discussion indicates, increasing damages in this range only\nreduces the frequency with which speakers disparage a type B target. Thus,\nincreasing damages in this range has countervailing effects: it increases the\nfrequencyofinteractionswithbadtypesbutreducesthefrequencyoflitigation.\nWesummarizeourfindingsinthissubsectionthroughfigure1,below,which\ndepictsthequalitativerelationshipbetweendamagesandthebeliefsofA;the\nlikelihood with which a type t ∈ {B,G} target is disparaged; and the likeli-\nhood of litigation in effective communication equilibria. Next, we conduct a\nwelfareanalysiswhichbuildsonthesekeyfindings.\nEElleeccttrroonniicc ccooppyy aavvaaiillaabbllee aatt:: hhttttppss::////ssssrrnn..ccoomm//aabbssttrraacctt==44118811889900\n\n<<PAGE_BREAK>>\n\n14 .V0N0\n4. WelfareAnalysis\nInanalyzingthesocialdesirabilityofdifferentdefamationregimes,weuse\na simple social welfare function which consists of the sum of each player’s\nexpectedpay-off.Weconductthiswelfareanalysistohighlightthethreemain\npointsthatweemphasizedintheintroduction.First,welfareisnon-monotonic\nin damages for defamation. More precisely, we show that the shape of wel-\nfare obtained through effective communication equilibria vis- a`-vis damages\nresemblesaLafferCurve:welfareisincreasinginthelowerrangeofmoderate\ndamages (i.e. for d ∈ (dˆ,d )), is maximized in the intermediate range (i.e.\n2\nwhen d ∈ [d ,d ]), and is decreasing in the upper range of moderate dam-\n2 3\nages (i.e. when d ∈ (d ,d )). Second, when there is a cap on damages (e.g.\n3 4\nreflecting the wealth of the defendant or a legal bound on permissible dam-\nages), then all effective defamation remedies may reduce welfare. Third, we\ncontrasttheimplicationsofamodelwithaBayesianversusana¨ıveaudience.\nWhentheaudienceisna¨ıveandeasilymisledbyfalsestatements,typeGtar-\ngets always prefer stricter defamation laws. The same is not true when the\naudienceisBayesian,becauseabsentsizeabledamagestheaudienceperceives\nthe speaker’s disparaging statements as cheap-talk and disregards them. This\ninsight leads to a divergence between the normative implications of the two\nmodels:withbindingcapsondamages,itmaybeoptimaltohavenodefama-\ntionlawsatallwithaBayesianaudiencebutoptimaltohavemaximaldamages\nwithana¨ıveaudience.Next,weconsiderandformalizeeachofthesepoints.\n4.1 TheLafferCurveofDefamationLaw\nUnderineffectivecommunicationequilibria,theaudienceactsaccordingto\nits priors. Thus, it chooses to interact with the target regardless of the state-\nments by the speaker. There is no litigation since interaction always takes\nplace.Thus,expectedwelfareisindependentofdamages,andisgivenby\nW ≡(1−γ)[r −b]+γ[r +g] (1)\nI B G\nOn the other hand, under effective communication equilibria, the specific\nfunctionalformofwelfarediffersdependingonwhichofthethreerangesdam-\nagesarein,asexplainedtheprevioussection.Next,weconsiderwelfareunder\neachrange.\nWithlowdamagesthatsupporteffectivecommunicationequilibria(i.e.d∈\n(dˆ,d )), when the target is type B, the speaker disparages him, the audience\n2\nrefuses to interact, and the target chooses not to litigate. Thus, with a proba-\nbilityof(1−γ)expectedwelfareequalsthespeaker’sexpectedbenefitE[v].\nWhenthetargetistypeG,thespeakerdisparageshimonlywhenv > v (d).\nG\nIn those cases, the audience avoids an interaction with T, and the target liti-\ngates.Thus,withaprobabilityofγ,expectedwelfareisF(v (d))[r +g]+\nG G\n(cid:82)1\n(v−l)f(v)dv.Therefore,expectedwelfareisgivenby:\nvG(d)\n(cid:32) (cid:33)\n(cid:90) 1\nW (d)≡(1−γ)E[v]+γ F(v (d))[r +g]+ (v−l)f(v)dv (2)\nL G G\nvG(d)\nEElleeccttrroonniicc ccooppyy aavvaaiillaabbllee aatt:: hhttttppss::////ssssrrnn..ccoomm//aabbssttrraacctt==44118811889900\n\n<<PAGE_BREAK>>\n\n-- 15\nWhendamagesareintermediate(i.e.d∈[d ,d ]),effectivecommunication\n2 3\nleadstoseparatingequilibriawhereininteractionstakeplaceif,andonlyif,the\ntargetisagoodtype.Moreover,thereisnolitigationsincetypeB targetslack\ntheincentivestolitigate.Thus,welfareinthisrangeisgivenby\nW ≡(1−γ)E[v]+γ[r +g] (3)\nS G\nFinally,whendamagesareintheuppermoderaterange(i.e.d ∈ (d ,d )),\n3 4\nthespeakerchoosesnottodisparageatypeGtarget.Thus,withaprobability\nof γ, welfare is r + g. When the target is type B, the speaker chooses to\nG\ndisparagehimonlywhenv > v (d),andthisleadstolitigation.Thus,witha\nB\n(cid:82)1\nprobabilityof1−γ,expectedwelfareisF(v )[r −b]+ (v−l)f(v)dv.\nB B vB(d)\nThus,expectedwelfareis\n(cid:32) (cid:33)\n(cid:90) 1\nW (d)≡(1−γ) F(v (d))[r −b]+ (v−l)f(v)dv +γ[r +g](4)\nH B B G\nvB(d)\nA very simple yet important observation is that W is increasing whereas\nL\nW isdecreasingindamages.Thisisbecause,whendamagesareinthelower\nH\nmoderaterange, theimpactofincreasingdamagesistoreducethelikelihood\nofdefamatorystatementsagainstatypeGtarget.Thisisbeneficial,becauseit\nreducesthelikelihoodofblockedbeneficialinteractionsbetweenAandT as\nwell as wasteful litigation between T and S. Similarly, when damages are in\ntheuppermoderaterange,loweringdamagesleadstoanincreaseinthelikeli-\nhoodwithwhichatypeBtargetisdisparaged.Thisincreasesthelikelihoodof\nharmfulinteractionsbeingblocked,butattheexpenseofincreasedlitigation.\nThe former (beneficial) effect dominates the latter (detrimental) effect, since\nthespeakerdisparagesatypeB targetonlyifherbenefitsfromdoingsomore\nthan off-set total litigation costs. This last point can be formalized by noting\nthat\nW′ =(1−γ)f(v )v′ {(r −b)−(v −l)}⩽0 (5)\nH B B B B\nsincer <bandv (d)⩾v (d )=l.\nB B B 3\nTo summarize these observations, we depict welfare as a function of dam-\nagesinfigure2,below,whichisaccompaniedbyclarifyingnotes.12\nThe most striking feature of figure 2 is that welfare obtained under effec-\ntivecommunicationequilibriamimicsaninverseUshape,notwithstandingthe\nfactsthatitcontainsadiscretedrop13 aroundd = d andthatwelfareiscon-\n3\nstant in the [d ,d ] range. This is what we interpret as the Laffer curve of\n2 3\ndefamationlaw.Welfareisnotmonotonicallyincreasingindamages,because\n12. Wenotethateffectivecommunicationequilibriamayormaynotbesupportableforalllow\ndamages,asexplainedintheprevioussection.Figure2depicts,onlyforexpositionalpurposes,a\ncasewherealllowdamagessupporteffectivecommunicationequilibria.\n13. Once damages pass over to the upper moderate range, damages are sufficient to invite\nfirivilouslitigationbytypeBtargets.Thisleadstoadiscretereductioninwelfare,sinceitcauses\nthelikelihoodofdisparagingstatementsagainsttypeBindividualstodiscretelydropfrom1to\n1−F(vB(d))anditalsocausesadiscretejumpinthelikelihoodoflitigation(seefigure1).\nEElleeccttrroonniicc ccooppyy aavvaaiillaabbllee aatt:: hhttttppss::////ssssrrnn..ccoomm//aabbssttrraacctt==44118811889900\n\n<<PAGE_BREAK>>\n\n16 .V0N0\nFigure2\nlarge damages (i.e. d > d ) reduce welfare by deterring accurate negative\n3\nspeech against a type B target. On the other hand, reducing damages to low\nlevels (i.e. d < d ) is also detrimental because it leads to defamatory state-\n2\nmentsagainstatypeGindividual,whicharetakenseriouslybytheaudience.\nAnotherfeatureofthewelfarecurvedepictedinfigure3isthattheseparat-\ning equilibria obtained through intermediate damages lead to greater welfare\nthanineffectivecommunicationequilibria.Wenotethatthisisnocoincidence,\nandoccursduetothefactthatwhiletheaudienceinteractswitheithertypein\nineffectiveequilibria,itinteractswithatargetif,andonlyif,itisagoodtype\nwhen damages are in the intermediate moderate range. Thus, when there are\nnocapsondamagesitfollowsthatsettingdamagesintheintermediatemoder-\naterangeissociallydesirable.Weformalizethisresultthroughthefollowing\nproposition,whoseprooffollowsfromourcomments,above.\nProposition3. SeparatingequilibriawhereSchoosestodisparageT if,and\nonlyif,heistypeB leadtogreaterexpectedwelfarethananyotherequilibria\nandareobtainableonlythroughintermediatedamages.\nAnimplicationofproposition3isthatmaximizingwelfarethroughdefama-\ntion law requires the implementation of separating equilibria through the use\nof intermediate damages. We note that this implication is obtained under the\nassumption that these damages are feasible. However, when these damages\nare too large for the defendant to pay (i.e. when the defendant is judgement-\nproof)orwhentherearelegalrestrictions(e.g.constitutional)onthedamages\nEElleeccttrroonniicc ccooppyy aavvaaiillaabbllee aatt:: hhttttppss::////ssssrrnn..ccoomm//aabbssttrraacctt==44118811889900\n\n<<PAGE_BREAK>>\n\n-- 17\nthatcanbechosen,damageslargeenoughtosupportequilibriainwhichtarget\ntypesarefullyrevealedmaynotbeavailable.Wediscussthiscase,next.\n4.2 BoundedDamages\nWeused¯todenotetheupperboundondamages.Animmediateimplication\nofproposition3isthatwhend¯⩾d ,theupperboundisnon-binding.Thus,we\n2\nfocusonthecasewhered¯< d .Withthisrestrictioninplace, thereareonly\n2\ntworelevantrangesofdamagesthatonecanselectfrom;(i)verylowdamages\nwhich only support ineffective communication equilibria (d ⩽ d ), and (ii)\n1\ndamagesinthelowerrange(d∈(d ,d¯)).\n1\nIn the latter range, if d¯is close to d it is possible for effective communi-\n1\ncationequilibriatobeunsupportable,14 andtheanalysisofthiscaseistrivial:\nthereisnofeasiblelevelofdamagesthatcanresultineffectivecommunication\nequilibria, and hence the choice of damages is irrelevant. Thus, we focus on\nthe more interesting case where maximum damages are sufficient to support\nsomeeffectivecommunicationequilibria,i.e.x∗(d¯)<xˆ.\n1\nInthiscase,wecancomparethewelfarebenefitsandcostsassociatedwith\nineffective and effective communication equilibria. The former equilibria, as\nreflectedby(1), alwaysleadtointeractionsbetweenT andA.Theseinterac-\ntionsarewelfarereducingwhenthetargetistypeB.Hence, whenthetarget\nistypeB,effectivecommunicationequilibriaperformbetter,sincetheydeter\ninteractionsbetweenT andA.However,thiscomesatthecostofdeterringso-\nciallybeneficialinteractionsbetweenatypeGtargetandAwhenthespeaker\nhas a sufficiently high type (i.e. v > v ). This implies that a switch from an\nG\nineffective communication equilibrium to an effective communication equi-\nlibrium trades-off deterrence of good interactions against deterrence of bad\ninteractions. Therefore, when the harm to the target from defamatory state-\nmentsislargerelativetootherconsiderations,arathercounter-intuitiveresult\nis obtained. Even when it is possible to implement effective communication\nthroughdefamationlaws,itissociallymoredesirablenottodoso.Thishap-\npensbecauseputtingapriceonspeechlendsmorecredibilitytothespeaker’s\nstatements,whichshecanthenusetoinefficientlyblockagoodinteraction.In\nsuch cases, the superior option is to not make speech credible and cause the\naudiencetorelyonitspriors,whichcausesittointeractwiththetarget.\nWeformalizethisresultviaproposition4below,andweprovideanexample\nanditsgraphicaldepictionviafigure4toillustrateit.\nProposition4. Supposetherearebindingmaximumdamages(i.e.d¯<d ).\n2\nThen, given all other parameters, there exists a threshold harm from effec-\ntive defamation, r¯ , such that ineffective communication equilibria lead to\nG\n(weakly) higher welfare than all effective communication equilibria if, and\nonlyif,r ⩾r¯ .\nG G\n14. Thisoccurswhenmaximumdamagesarenotenoughtodeterspeechagainstgoodtypes\nfrequentlyenoughinaneffectivecommunicationequilibrium,asnotedvia(7)-(8)andtheaccom-\npanyingdiscussion.\nEElleeccttrroonniicc ccooppyy aavvaaiillaabbllee aatt:: hhttttppss::////ssssrrnn..ccoomm//aabbssttrraacctt==44118811889900\n\n<<PAGE_BREAK>>\n\n18 .V0N0\nProof. Using(1)and(2),wecanexpressthedifferenceinbetweenineffective\nandeffectivecommunicationequilibriaas:\n(cid:90) 1\nW −W =(1−γ)[r −b−E[v]]+γ [r +g−v+l]f(v)dv\nI L B G\nvG(d)\nThisexpressionisincreasingandunboundedinr .Thus,thereexistsr¯ such\nG G\nthatW ⩾W iffr ⩾r¯ .\nI L G G\nIn figure 3, below, we depict multiple cases which illustrate the rationale\nbehindproposition4.Inthisexample,visdistributeduniformlyandr¯ =1.7\nG\nisusedtoillustrateallthreepossibilities.15\nAsthefigureillustrates,thegapbetweenwelfareobtainedthroughlowdam-\nages under the two types of equilibria is decreasing in damages but increas-\ningtheharmthatthetargetsuffersfromeffectivedefamation.Thus,forsmall\ndefamation harms to the target, effective communication equilibria obtained\nthrough maximum damages are superior, and the opposite conclusion holds\nforlargedefamationharms.Theexceptionalcasewherethetwotypesofequi-\nlibrialeadtothesameamountofwelfarewhenmaximumdamagesareusedis\nalsodepictedasanintermediatecase(i.e.thecasewherer =r¯ ).\nG G\nTheseobservationsimplythatwhendamagesinducingcompleterevelation\nof target types are not feasible, it is socially desirable to strive for effective\ncommunication equilibria only when the harms from defamation are small.\nThisresultappearscounter-intuitive,becauseitsuggeststhattheoptimalityof\neffective defamation remedies ought to be inversely related to the size of the\nalleged harm to the plaintiff. The rationale behind this result is that making\nspeechcredibleinanenvironmentwheredefamatoryspeechcannotbelargely\neliminated has the function of making some false speech credible, and thus\nharmful to type G targets. When the size of the harm to these individuals is\nlarge,itnaturallybecomesmoredesirabletotakeawaythecredibilityofneg-\nativespeechaltogether.\n4.3 WelfarewithBayesianversusNa¨ıveAudiences\nInouranalysisthusfar,wehaveconsideredaBayesianaudiencewhosebe-\nliefsareconsistentwithequilibriumbehavior.Analternativeassumptionoften\ninvokedintheliteratureisthattheharmfromdefamatorystatementsisinde-\npendentofthefrequencyoffalsestatements.Wecalltheaudienceunderthis\nalternative assumption na¨ıve, and we consider the differences in the implica-\ntionsofamodelwithana¨ıveversusBayesianaudience.Whentheaudienceis\nna¨ıve, itavoidsaninteractionwiththetargetif, andonlyif, itreceivesadis-\nparagingstatementfromthespeaker,anditdoessoregardlessofthefrequency\noffalsestatements.\nThus,withana¨ıveaudience,thespeakerisabletosuccessfullyblockinter-\nactionswithbothtargettypeswhendamagesareverylow(i.e.d ⩽ d ).This\n1\n15. Weusethefollowingvaluestoproducecurvesthatdonotoverlapwitheachotherfor\nexpositionalpurposes:γ=rB =l= 3\n4\n;g=b=1;andqG=\n1\n7\n0\n.\nEElleeccttrroonniicc ccooppyy aavvaaiillaabbllee aatt:: hhttttppss::////ssssrrnn..ccoomm//aabbssttrraacctt==44118811889900\n\n<<PAGE_BREAK>>\n\n-- 19\nFigure3\nEElleeccttrroonniicc ccooppyy aavvaaiillaabbllee aatt:: hhttttppss::////ssssrrnn..ccoomm//aabbssttrraacctt==44118811889900\n\n<<PAGE_BREAK>>\n\n20 .V0N0\nisbecausethesedamagesaretoolowtogenerateanylitigationthreatfromthe\ntarget, and thus the speaker disparages the target independently of his type.\nThena¨ıveaudience, unliketheBayesianaudience, reliesonthestatementby\nthespeakerinsteadofitsprior,andthereforealwaysavoidsaninteractionwith\nthetarget.\nWhendamagespassontothemoderaterange,theequilibriumbehaviorand\nwelfareinthena¨ıveaudiencecaseisidenticaltothosethatareobservedunder\naneffectivecommunicationequilibriumoftheBayesianaudiencecase.Thisis\nbecausetheBayesianaudience,likethena¨ıveaudience,actsinamannercon-\nsistentwiththespeaker’sstatementsineffectivecommunicationequilibria.Fi-\nnally,whendamagesareveryhigh(i.e.d>d ),thespeakerisdeterredagainst\n4\nmakingdisparagingstatementsagainstbothtypes,andthena¨ıveaudiencein-\nteracts with both types. Thus, in this range welfare with a na¨ıve audience is\nequaltowelfarewithaBayesianaudience.\nInshort,themoststrikingdifferencearisingfromaswitchfromaBayesian\naudience to a na¨ıve audience occurs when damages are too low to cause the\ntarget to litigate (i.e. d ⩽ d ). The most prevalent normative impact of this\n1\ndifference is observed when there is an upper bound on maximum damages,\nsince otherwise optimal equilibria are trivially obtained in the intermediate\nmoderate range (i.e. d ∈ [d ,d ]) under both models. Thus, we focus on the\n2 3\ncase where d¯ < d to highlight the greatest difference between the models\n2\nwithaBayesianandana¨ıveaudience.\nAswepreviouslynoted,withaBayesianaudience,typeGtargetsaremade\nworseoffwhendamagesinthelowermoderaterangelendcredibilitytospeaker’s\nstatements. Thus, as we noted via proposition 4, when defamatory harms are\nlarge,welfareisactuallyreducedwhendefamationlawsareeffectivecompared\ntowhentheyarenot.Theoppositeconclusionholdswithana¨ıveaudience.In\nthis case, increasing damages always leads to less frequent defamatory state-\nments,andtypeGtargetsalwayspreferstricterdefamationlaws.Thus,when\ndefamatoryharmsarelarge,contrarytothecasewithaBayesianaudience,it\nisoptimaltousemaximaldamages.\nWe illustrate this result through figure 4, which depicts welfare obtained\nin the example used to generate the high r case in figure 3,16 but this time\nG\nitalso includeswelfareobtainedwith ana¨ıveaudience. Thefigureillustrates\nthatwhileitisoptimaltoincreasedamagestotheirmaximallevelwithana¨ıve\naudience,itisoptimaltousedamageslowenoughtoguaranteetheemergence\nofineffectivecommunicationequilibriawithaBayesianaudience.Thus,when\nharms from defamatory statements are large, assuming that the audience is\nna¨ıveisnotmerelyasimplifyingassumption,itisonethatcangeneratemis-\nleadingnormativeimplications.\n16. Asareminder,thiscorrespondstothecasewherevisuniformlydistributed;rG = 9\n4\n;\nγ=rB =l= 3\n4\n;g=b=1;andqG=\n1\n7\n0\n.\nEElleeccttrroonniicc ccooppyy aavvaaiillaabbllee aatt:: hhttttppss::////ssssrrnn..ccoomm//aabbssttrraacctt==44118811889900\n\n<<PAGE_BREAK>>\n\n-- 21\nFigure4\nEElleeccttrroonniicc ccooppyy aavvaaiillaabbllee aatt:: hhttttppss::////ssssrrnn..ccoomm//aabbssttrraacctt==44118811889900\n\n<<PAGE_BREAK>>\n\n22 .V0N0\n5. ExtensionsandDiscussion\nInSections3and4, wepresentedamodelthatallowedustoclearlyfocus\nondefamationlaws’impactontheaudience’sequilibriumbeliefsandactions.\nIn doing so, we abstracted from many issues that bear on the regulation of\ninformation in more general settings, particularly, the possibility of there be-\ning a committed public enforcer, quality being endogenously chosen by the\ntarget, the existence of honest and other types of speakers, and courts being\nlessaccuratethanwepreviouslyassumed.Hereweturnourattentiontothese\nissues.\n5.1 EndogenousTypesandDynamicEfficiencies\nIn our analysis thus far, we assumed that the target’s type is exogenously\ndetermined by nature to be either G or B with probabilities γ and 1−γ, re-\nspectively. One might question the reality of this assumption, as people can\nmakeinvestmentsthatwouldmakethembetterorworsetradingpartners,e.g.,\ncreate higher quality products, maintain safety standards, or keep higher hy-\ngienestandards.Garoupa1999a,b,forinstance,takesasimilarapproach,and\nassumesthatthetarget’sbehaviorisimpactedbywhatlawsareinplace.Here,\nwe explain how the types in our setting can be endogenized, and how doing\nso yields results similar to those in prior work where the target’s behavior is\nendogenous.\nOne option of incorporating quality investments into our analysis is to re-\nplace Nature’s choice of types with a preliminary stage where the target, T,\nmakes a costly investment (c) that can increase her likelihood of becoming\na good type. Formally, we may assume that γ = γ(c) with γ′ > 0 > γ′′,\nlimγ′(c)=∞,γ(0)=γ and limγ(c)=γ where1>γ >γ >xˆ>0.\nc→0 c→∞\nThequalityinvestmentdecisionisnowpartofalargergame.Givenanysub-\ngameequilibrium,thebestresponseofT istomakeaninvestmenttomaximize\nhisexpectedpay-off,whichcanbedenotedasγ(c)m +(1−γ(c))m −c\nG B\nwherem andm refertothepayoffsheobtainsinthesub-gameequilibria.\nG B\nThisobservationrevealsaveryclearresult: Whenthelawsareextreme,i.e.\nd ̸∈ [d ,d ], the target has no reason to invest in quality. This follows from\n1 4\nProposition 2, which shows that with extreme laws, the audience acts based\non its priors and interacts with the target. Thus, investments have no private\nreturnsforthetarget.\nItisonlywhenthelawsaremoderatethattargetsmayhaveanincentiveto\ninvestinquality.Thiscanbedemonstratedbyfocusingonthelowerboundof\nintermediatedamages,i.e.d .Inthiscase,ineffectivecommunicationequilib-\n1\nria,itfollowsthatm =0(becauseallbadtypesaredisparaged)whilem =\nB G\nF(v (d))r(becausegoodtypesaredisparagedwithprobability1−F(v (d)),\nG G\ninwhichcasethereisalawsuitwhichpaysthetargetexpecteddamagesequal\ntolitigationcosts).Thus,thetarget’spay-offisγ(c)F(v (d))r−c,and,there-\nG\nfore,thetargetprofits(inexpectation)frominvesting.Whetherthisissocially\ngood or bad, depends, of course, on whether there are net social gains from\nsuch investments. In our context, this is socially valuable as long as the ex-\nEElleeccttrroonniicc ccooppyy aavvaaiillaabbllee aatt:: hhttttppss::////ssssrrnn..ccoomm//aabbssttrraacctt==44118811889900\n\n<<PAGE_BREAK>>\n\n-- 23\npectedbenefitsfromgoodinteractions(F(v (d))g)—whicharenotinternal-\nG\nizedbyT—aregreaterthantheexpectedlitigationcostslandthelossofben-\nefit to S from blocking an interaction, i.e. F(v (d))E[v|v > l]. In fact, if\nG 2\ninvestments in quality are socially valuable, as is implicitly assumed in the\nliterature (e.g., Garoupa 1999a,b), then increasing damages within the inter-\nmediate range up to d will be desirable. This is because these higher dam-\n2\nages lead to a lower probability of disparaging remarks made against good\ntypes (as illustrated in Figure 2) and, thus, increase m , while still keeping\nG\nexpectedpayoffsfrombeingabadtypeatm = 0.Therefore,theextension\nB\nof our model with endogenous types resonates with Garoupa’s (1999a,b) in-\nsightsthatmoderatedamagescanincentivizeinvestmentsinbecomingagood\ntype.Moreover,ithighlightsthepotentialsocialcostsandbenefitsassociated\nwithsuchinvestmentmorespecifically.\nThediscussionherehighlightstheimportanceofinformationregulationfor\nbroadermarketdynamics.Theintuitionunderlyingourresultsarestraightfor-\nward.Extremelawsleadtoineffectivecommunicationequilibria.Incontrast,\nmoderatelawscreateanenvironmentwithmorereliableinformationregarding\ntypes, thus generating a greater gap between the payoffs obtainable by good\ntypesversusbadtypes.17Inrealisticsettings,providingsuchadditionalincen-\ntivesissociallydesirablewhenthepotentialinvestorisunderincentivizeddue\nto problems like information asymmetries. The gains from such investments\ninqualityshouldbeaddedtotheotherbenefitsofmoderatelawsthatwehave\nidentified.\n5.2 HonestSpeakersandEulogists\nExistinganalysesofdefamationlawtypicallyassumethatthespeaker’sneg-\native statement always harms the target, which is equivalent to the audience\nbeing na¨ıve. Moreover, these analyses (e.g. Garoupa 1999a,b and Bar-Gill &\nHamdani2003)considerstrategicspeakerswhobenefitfromdefamingthetar-\nget,andwhosebenefitsfromdoingsoareindependentoftheveracityoftheir\nstatements.Inreality,however,manyspeakersmaynothavesuchmotivations.\nQuite importantly, many people, when asked their opinion, provide an hon-\nest assessment of others. Moreover, there are also people who are motivated\nby doing the exact opposite of what the speakers in our model are motivated\nby; namely, promoting the relationship between the target and the audience.\nInwhatfollowswedistinguishbetweenthefirsttype,truthspeakers,thelatter\ntype,eulogists,andtheonesweformerlydiscussedinsection3asdisparagers.\nHere,webrieflyexplainwhatoccurswhenthesekindsofspeakersareincor-\nporatedintoouranalysis.\nInourdiscussion,weconceiveofthesetypesasfollows.Disparagers,aswe\nnoted,receiveapositivevaluefromblockinganinteraction;truth-speakersare\n17. Thisresultisreminiscientofthedeterrencereducingimpactsofjudicialerrorsobtained\ninthelawenforcementliterature(see,e.g.,Png(1986),RizzolliandGraoupa(2012),Mungan\n(2017), and Lando and Mungan (2018)) wherein judicial errors dilute the deterrence effect of\npunishmentbycreatingadisconnectbetweenpunishmentandbehavior.\nEElleeccttrroonniicc ccooppyy aavvaaiillaabbllee aatt:: hhttttppss::////ssssrrnn..ccoomm//aabbssttrraacctt==44118811889900\n\n<<PAGE_BREAK>>\n\n24 .V0N0\nindifferent with respect to whether the parties will interact but receive some\nvaluefromspeakingtheirmind; and,eulogistsreceiveavaluefromtherebe-\ninganinteraction.Therefore,solongascostsofsodoingarenothigh,dispar-\nagers will badmouth the target and truth-speakers will reveal their true type.\nEulogists, in contrast, would always want to praise the target, as there is no\nrecourse under defamation law for false positive statements (the question of\nwhythisasymmetryexistsgoesbeyondthescopeofourarticle).\nTheincorporationofthesetypesofspeakershasnoimpactontheobserva-\ntionthatextremelystrongdefamationlawsleavetheaudiencetoactupontheir\npriors. This follows, because once a critical threshold of damages is passed,\ndisparagers as well as truth speakers are deterred from making negative re-\nmarks.Thus,extremelystrongdefamationlawscausedisparagers,truthspeak-\ners, and eulogists alike to abstain from making negative statements, and the\naudiencehasnooptionbuttoactaccordingtoitspriors.\nThe same cannot be said, however, for extremely weak defamation laws.\nWhen damages are very low, targets lack an incentive to bring suit, making\ntalk cheap. Despite that, disparaging statements are still somewhat informa-\ntive:Giventheexistenceofsometruth-speakers,thereissomeprobabilitythat\nanynegativestatementistrue.Consequently,anaudiencethathearsanegative\nstatementevaluatesitscredibilitybasedontheratiooftruth-speakerstodispar-\nagers.Thus,inanassessmentwitha∗(z)=z,wecanformulatetheaudience’s\nconsistentbeliefthatthetargetisagoodtype,conditionalonanegativestate-\nment as x∗ = γ ∆ where τ denotes the proportion of truth speakers,\n1 ∆+(1−γ)τ\nand ∆ is the proportion of disparagers. On the other hand, non-disparaging\nremarksdonotnecessarilymeanthatT isagoodtype.Bysimilarlogic,there\nis some probability that any given praise is false given the existence of eulo-\ngists.Anaudiencewhichhearsapositivestatementevaluatesitsveracityasa\nfunction of the ratio of eulogists to truth-speakers. Thus, we can express the\naudience’sbeliefasx∗ =γ τ+ε ,whereεistheproportionofeulogists.\n0 γτ+ε\nUsing these observations it is easy to verify that, under lax laws, both dis-\nparaging and non-disparaging statements are somewhat informative of types.\nInotherwords,non-disparagingstatementsaremoreindicativeofgoodtypes\nthan no information at all (x∗ > γ), and disparaging statements are more\n0\nindicativeofbadtypesthannoinformationatall,i.e.x∗ <γ.Thus,iftheau-\n1\ndience’snecessarylevelofconfidenceforinteraction,(x),iscloseenoughtoγ\n(cid:98)\nsuchthatx∗ ⩾ x ⩾ x∗,onecanachieveanequilibriumwhereintheaudience\n0 (cid:98) 1\nmeaningfullyusestheinformationprovidedbyspeakers,evenwhenthereare\nnosanctionsforfalsestatements.If,however,x∈/ [x∗,x∗],thenlaxlawscause\n(cid:98) 1 0\ntheaudience toignore thestatement andact accordingto its priors, as inour\nanalysisinsection3.Thus,wefocusourremainingdiscussiontocaseswhere\nx∗ ⩾x⩾x∗.\n0 (cid:98) 1\nIncaseswheredamagesaremoderate, someoftheclaimsmadeinsection\n3 need to be qualified, whereas others remain intact. In particular, it is still\nthe case that moderate damages improve the reliability of information over\nextremedamages.Toseethis,consider,forinstance,theimplicationsofrais-\nEElleeccttrroonniicc ccooppyy aavvaaiillaabbllee aatt:: hhttttppss::////ssssrrnn..ccoomm//aabbssttrraacctt==44118811889900\n\n<<PAGE_BREAK>>\n\n-- 25\ningdamagesfromlowlevelsto l .Amongspeakers,thischangeonlyalters\n2qG\nthe incentives of disparagers, because these are the only speakers who have\naninterestinmakingfalsestatementsaboutgoodtypes,who,giventhislevel\nofdamages,bringalawsuitagainstthem.Thus,theproportionofdisparagers\nwho make false statements is reduced, which causes x∗ to fall and x∗ to in-\n1 0\ncrease,i.e.itcausesinformationsuppliedbyspeakerstobemoreinformative.\nThisobservationrevealsanotherofourresultsthatcarriesoverinamodified\nway:onecanusedamagesequaltod <d todeteralldisparagersfrommak-\n2 3\ningfalsestatementsandalsoguaranteethattherearenolawsuitsbybadtype\ntargets.Inthiscase,itimmediatelyfollowsthatx∗ =0,suchthatadisparaging\n1\nstatementisperfectlyinformative.\nThe presence of eulogists, however, means that x∗ < 1. Thus, equilibria\n0\nthat are completely informative of the target’s type are no longer obtainable.\nStill,eveninthepresenceofeulogistsanddisparagers,imperfectlyinformative\nequilibria are possible. Moreover, these equilibria are optimal, because they\nlead to no litigation costs, cause all possible good interactions to take place,\nandachievemaximumdeterrenceofbadinteractions.\nWe conclude that the introduction of honest speakers as well as what we\ncalledeulogists—peoplewhowishtopromotethetarget—doesnotaffectthe\nsuperiorityofmoderatedamagesoverextremeformsofdamages.Whatdoes\nchangeisperhapssomewhatcounterintuitive: strictlawsturnouttobeworse\nthanlaxlaws.Strictlawsleadtocompletelyuninformativespeechinequilib-\nriumwhereaslaxlawsstillallowspeechtobesomewhatinformative,permit-\ntingeffectivecommunicationequilibria.\n5.3 CommitmentandPublicEnforcement\nOur analysis so far focused on private enforcement of defamation laws,\nwhere the target is the one to sue. However, private parties will only bring\nalawsuitifitpaystodosoex-post, andthiscalculusexposesthemtostrate-\ngicbehaviorbywould-bedefamers.Incontrast,someparties,typicallypublic\nagencies, maybeabletocommitex-antetosue, evenifitdoesnotpaytodo\nsoex-post.Infact,thisistheimplicitassumptioninvokedinmuchoftheeco-\nnomics of public law enforcement literature (see, e.g., Polinsky and Shavell\n2007 for a survey). Comparing private and public enforcement can be useful\ninunderstandingothercontextswhereinformationisregulated,andmayalso\nilluminatethereasonswhyprivateenforcementisusedindefamation.\nTohelpinthiscomparison,weconsiderasimplemodificationofouranal-\nysis wherein instead of the target, it is a public enforcement agency that can\nbring suit against disparaging remarks. The agency, however, is not privy to\nthetarget’sprivateinformationregardinghistype,whichisbyassumptionun-\nobservable,andsoitcannotconditionitsactiononT’stype.Theagencythus\nchoosessomeprobability,p∈(0,1),withwhichitwillbringalawsuit.Asthe\nchoiceofpdoesnotdependonanynewinformation,itischosenex-anteandis\ncommunicatedto,orobservedby,would-bespeakers.Thechoiceofpreplaces\np∗(t) in in the prior sections. We retain all other assumptions, including the\nEElleeccttrroonniicc ccooppyy aavvaaiillaabbllee aatt:: hhttttppss::////ssssrrnn..ccoomm//aabbssttrraacctt==44118811889900\n\n<<PAGE_BREAK>>\n\n26 .V0N0\nassumption that the probabilities with which the speaker will be found liable\nincourtareq andq ,whenshemakesdisparagingstatementsagainstgood\nG B\nandbadtypes,respectively.\nThissimplemodificationallowsustocalculatetheanalogsofthetwocrit-\nical damages pertaining to the best responses of S noted in (3). Specifically,\nthese two critical values now become d˜ ≡ 2v¯−pl and d˜ ≡ 2v¯−pl. Thus, in\neffectivecommunicationequilibriawith 2 d>d˜ 2pq th G espeake 4 rdoe 2 s p n q o B tmakedis-\n2\nparagingstatementsagainstgoodtypes,andrefrainsfrommakingdisparaging\nstatementsagainstbadtypeswhend > d˜.Itcanbeeasilyverifiedthateach\n4\nofthesevaluesislargerthantheircorrespondinganalogintheprivateenforce-\nmentcontext,i.e.d˜ >d andd˜ >d .\n2 2 4 4\nThe commitment to bringing a lawsuit also changes the speaker’s behav-\nior, as a lawsuit is possible even when expected damages are low. We next\nexplainthebehaviorofthespeakerineffectivecommunicationequilibria,un-\nder three different damages ranges, and subsequently compare them with the\ncorrespondingbehaviorunderprivateenforcement.\nAsunderprivateenforcement,itfollowsthatwhendamagesareveryhigh,\ni.e.,d>d˜,alldisparagingremarksaredeterred.However,whend∈(d˜,d˜),\n4 2 4\nthe speaker refrains from disparaging good types, but disparages bad types\nwheneverhervaluefromblockinginteractionsissufficientlyhigh(i.e.v˜ (d)≡\nB\np(q d− l) < v)whichhappenswithprobability1−F(v˜ (d)) > 0.Thus,\nB 2 B\nin this range, a disparaging remark conclusively reveals to the audience that\nthetargetisabadtype;andanon-disparagingcommentisaninformative,but\ninconclusive,signalthatthetargetisagoodtype,i.e.x∗ =0<γ <x∗.When\n1 0\ndamages are low, i.e., d < d˜, the speaker is no longer necessarily deterred\n2\nfrom disparaging good types, and chooses to defame the target if her value\nfrom blocking interactions exceeds v˜ ≡ p(q d− l). Thus, it follows that\nG B 2\n0<1−F(v˜ (d))<1−F(v˜ (d)),and,therefore,0<x∗ <γ <x∗ <1.\nG B 1 0\nWe can now compare defamation laws under public and private enforce-\nmentregimes.First,effectivecommunicationequilibriaarenotpossibleunder\neither regime when damages are extremely high (i.e. higher than d˜ and d\n4 4\nin the public and private regimes, respectively). Thus, our previous conclu-\nsion regarding the ineffectiveness of high damages in supporting informative\nstatementsextendstothepublicenforcementcaseaswell.\nSecond, unlike private enforcement, public enforcement can sustain effec-\ntivecommunicationequilibriaevenwithlowdamages.Underprivateenforce-\nment, the speaker will anticipate that the target will not sue if damages are\nsufficiently low. This can lead the speaker to disparage regardless of the tar-\nget’s type, which would make statements non-informative. With public en-\nforcement, however, there is always a risk of a lawsuit, thus deterring some\nwould-bedefamersandsustainingthereliabilityofsomestatements.Thisim-\npliesthat,unlikeintheprivateenforcementcontext,verylowdamagescanbe\nusedtosupporteffectivecommunicationequilibria—atleastwhenthethresh-\noldbeliefoftheaudience,i.e.xˆ,isnottoofarfromitspriors,i.e.whenγ−xˆ\nis not large, because then xˆ ∈ [x∗,x∗]. Note that this means that low dam-\n1 0\nEElleeccttrroonniicc ccooppyy aavvaaiillaabbllee aatt:: hhttttppss::////ssssrrnn..ccoomm//aabbssttrraacctt==44118811889900\n\n<<PAGE_BREAK>>\n\n-- 27\nagescanbesuperiortohighdamagesinfacilitatingeffectivecommunication\nbetweenthespeakerandtheaudience.\nThird, and quite importantly, it is impossible to obtain an equilibrium that\nalwaysrevealsthetarget’stypewithpublicenforcement: asnotedabove,any\ndamages below d < d˜ result in good types being disparaged with a proba-\n4\nbilityof1−F(v˜ (d)) > 0,badtypesbeingdisparagedwithaprobabilityof\nG\n1−F(v˜ (d))<1,orboth.Thisimmediatelyimpliesthatprivateenforcement\nB\ndominatespubicenforcementintermsofitswelfareconsequences.Thediffer-\nence in the welfare obtainable under the two regimes is enhanced further by\nthefactthatunderpublicenforcement,theenforcementagency’scommitment\nresultsinlitigation.\nThelastpointhighlightsamoregeneralandimportantadvantageofprivate\nenforcementoverpublicenforcement.Specifically, privateenforcementdele-\ngates the decision to litigate to the party with the best information about the\nmeritsofthecase.Moderatedamagescanbecraftedtoseparategoodandbad\ntypes based on their willingness to sue, and this enables the speaker’s state-\nmentstobemoreinformativeofthetarget’stype.\nInsum,thiscomparisonilluminatetherelativevalueofpublicversuspublic\nenforcement.However,asourfocushereisoncommitment,weabstractfrom\notherrelevantconsiderations, suchastherelativecostsoflearningaboutdis-\nparagingremarksorproducingevidence.Inasmuchaspublicagenciesemploy\ndiscretion, they are also susceptible to capture and other public choice prob-\nlems.Theseconsiderationsshouldalsobetakenintoaccountincomparingthe\nrelative social desirability of pubic versus private enforcement in regulating\nspeech.\n5.4 InaccurateCourts\nTo keep our analysis focused, we presented results obtained in the case\nwherethecourtisrelatively‘accurate’inrenderingdecisions,inthesensethat\nitcommitserrorswithlowfrequency(i.e.q <q ( l/2 )).Themainroleof\nB G 1−l/2\nthisassumptionistoguaranteetheexistenceofarangeofmoderatedamages\nwhichleadstoseparatingequilibria.\nWe relax the assumption that courts are accurate in a prior version of this\narticle,18 which reveals that most results we presented extend to this case. A\nnotableexceptionisthattheremaybenoeffectivecommunicationequilibrium\nwhichleadstogreatersocialwelfarethanwhentheaudienceislefttoactbased\nonitspriors,andthisistrueevenwhentherearenodamagecaps.Thereason\nforthisisthatthesmallestdamageswhichincentivizetypeB targetstobring\nsuit(i.e.d )arethensmallerthanthesmallestdamagesthatdeterthespeaker\n3\nfrom disparaging type G targets. This causes there to be no damage amount\nwhichislowenoughtodisincentivizefrivolouslawsuitswhilealsocompletely\ndeterring defamatory speech. Thus, effective communication equilibria can-\nnoteliminatefalsestatements.Thiscancauseverylowdamagestobeoptimal,\nduetothesamerationalesthatemergewhendamagesarebounded(seesection\n18. SeeArbel&Mungan2020.\nEElleeccttrroonniicc ccooppyy aavvaaiillaabbllee aatt:: hhttttppss::////ssssrrnn..ccoomm//aabbssttrraacctt==44118811889900\n\n<<PAGE_BREAK>>\n\n28 .V0N0\n4.2).ThisresultfurtherhighlightstheimportanceofBayesianaudiences.With\nana¨ıveaudience,standardeconomicmodelswouldpredictthatoptimaldam-\nagesaremoderate, becauselowdamageswouldinvitetoomuchfalsespeech\ntowhichtheaudiencelendscredence.\n6. Conclusion\nExisting economic analyses of defamation law typically assume that there\nare no obstacles in the way of a person who wishes to harm another person\nthroughdefamatorystatements.However,forsuchharmstoberealized,people\nmust find the derogatory statements made by the person credible. The credi-\nbility of these statements, in turn, depend on what types of consequences a\nspeaker faces by making such statements. Defamation law is a tool that can\nbe used to alter these consequences, and therefore the credibility of negative\nstatements.Wehaveformalizedthisdynamicbystudyingthebeliefformation\nprocessofpeoplewhoaretherecipientsofsuchinformation.\nOur analysis has revealed several interesting dynamics. When courts are\naccurateandthemaximumrecoverabledamagesfromthedefendantarelarge,\nonecanlargelyeliminatefalsespeech.However,whentheseconditionsdonot\nhold,itispossiblefortheregulationofspeechthroughdefamationlawtocause\nmore harm than benefits. This may occur because the credibility of speech\nobtainedthroughweakorinaccurateenforcementofdefamationlawcanlead\ntoanincreaseinfalsenegativespeechwhichisbelievedbytheaudience(and\nthismayalsoleadtosignificantlitigationcosts).Inothercases,itpossiblefor\nthe increased informativeness obtained through defamation law to outweigh\nits social costs. Which of these two cases is obtained depends, among other\nthings,ontheharminflictedtothetargetofspeech.\nOnereasonwhytheseconclusionshavenotbeendevelopedinthevastlegal\nliteratureonthetopicispresumablytheinsufficientattentionpaidtotherole\nof audiences, which have typically assumed to be na¨ıve. We believe that our\nbasic insights are also applicable to many other areas of law where the goal\nis to regulate the veracity of information. Although our analysis represents a\nstepforwardinunderstandingimportantdynamicsinthesecontexts,wewere\nunabletoincorporatemanyotherpossibilitieswhichmayyieldadditionalin-\nterestinginsights.Wehighlightsomeissueswehaveabstractedfromwiththe\nhopeofhighlightingsomeavenuesforfutureresearch.\nWe have focused, for instance, exclusively on plaintiffs who bring suit to\nincreasetheirmonetarywell-being.But,therearemanyplaintiffswhoaremo-\ntivatednotbythedamagestheymayrecover,butbytheprospectofadvancing\nthetruth.Inthesecircumstances,largerexpecteddamagesmaycrowd-outthe\nintrinsicmotivationsofthepotentialplaintifftobringsuitbymakingitharder\nforthirdpartiestoidentifythetruemotivationsoftheplaintiff.Similarly, we\nconsideredahomogenousaudienceandassumedthatthespeakerhasperfect\ninformationregardingthetarget’stype.Relaxingtheseassumptionsmaycause\na greater wedge between the results obtained with na¨ıve audience members\nand with Bayesian audience members. We hope that the framework we have\nEElleeccttrroonniicc ccooppyy aavvaaiillaabbllee aatt:: hhttttppss::////ssssrrnn..ccoomm//aabbssttrraacctt==44118811889900\n\n<<PAGE_BREAK>>\n\n-- 29\nFigure5\ndeveloped here can be used as starting point to incorporate these additional\nconsiderations.\n7. Appendix\nGameTree\nFigure5depictstheinteractionsbetweentheplayers.Itsummarizesthepar-\nties’payoffsattheterminalnodesonthebottomintheorderS,A,T.Thereare\ntwographicallimitationsofFigure5.First,itdoesnotshowinformationsets\ndescribing A’s knowledge regarding S’s type, due to the depiction difficulty\ncausedbyS drawinghertypefromacontinuum.Second,foreaseofexposi-\ntion, Figure5doesnotdepictNature’sv drawdeterminingS’sinclinationto\ndisparage.\nPerfectBayesianEquilibriumRequirements\nInformalizingtherequirementsforaPBE,wefirstspecifytheunconditional\n(orexante)probabilitywithwhichSwilldisparageT givenanystrategy,s,as\nfollows:\n(cid:90) 1\nµ(s)≡ [γs(G,v)+(1−γ)s(B,v)]dF(v) (1)\n0\nWhen µ(s) ∈ (0,1), we can use Bayes’ rule to calculate the probability\nofT’stype, goodorbad, conditionalonthestatementmadeaboutT.Onthe\notherhand,whenµ(s) ∈ {0,1},itfollowsthatS isplayingastrategywhere\nhe(almost)always avoidsdisparaging(0)ordisparages(1) T, inwhichcase\nBayes’rulecannotbeusedtocalculatetheprobabilityofT beingaparticular\nEElleeccttrroonniicc ccooppyy aavvaaiillaabbllee aatt:: hhttttppss::////ssssrrnn..ccoomm//aabbssttrraacctt==44118811889900\n\n<<PAGE_BREAK>>\n\n30 .V0N0\ntype, conditional on the strategy which is (almost) never played by S. Thus,\nwedenotebothpossibilities,asfollows:\n(cid:82)1s(G,v)dF(v)\nγ 0 if µ(s)̸=0\nΓ(t=G|z =1,s)≡ µ(s) (2)\nΥ otherwise\n(cid:82)1(1−s(G,v))dF(v)\nγ 0 if µ(s)̸=1\nΓ(t=G|z =0,s)≡ 1−µ(s) (3)\nΥ otherwise\nHere, the symbol Υ indicates that the strategy in question is (almost) never\nchosenbythespeaker.\nGiventhisnotationwemaycharacterizePBEasanassessmentconsistingof\nthestrategyprofilea∗,s∗ andp∗ alongwithasetofbeliefsx∗ andx∗,which\n0 1\nsatisfiesthefollowingfourrequirements.\nRequirement1(R1): Ahasnoprofitabledeviationgivenitsbeliefs:\na∗(z)=0 if x >x forz ∈{0,1}\nz (cid:98) (4)\na∗(z)=1 if x <x forz ∈{0,1}\nz (cid:98)\nR1statesthatAinteractswithT onlyifAbelieves,givenS’sstatement,that\nthe probability that T is a good type exceeds the threshold probability of x.\n(cid:98)\nSimilarly, if A believes that T is a good type with a probability that is lower\nthanx, AdoesnotinteractwithT.Intheexceptionalcasewherex = x, A\n(cid:98) z (cid:98)\nisindifferentbetweeninteractingwithT andnot,and,thusitmayplayeither\nstrategy.\nRequirement2(R2):T hasnoprofitabledeviationsinsub-games:\n0 if q d<l/2 fort∈{B,G}\np∗(t)= t (5)\n1 if q d>l/2 fort∈{B,G}\nt\nR2statesthatthePBEstrategyofT mustbesuchthatinsubgameswhereS\ndisparageshim,T litigateswheneverthecostsofdoingso(l/2)arelowerthan\ntheexpecteddamagerewardsthathecanobtainfromlitigation.Conversely,T\nchoosesnottolitigatewhenthecostsarehigherthanexpecteddamages.Inthe\nexceptionalcasewhereq d=l/2,T isindifferentbetweenlitigatingandnot.\nt\nRequirement3(R3):Shasnoprofitabledeviations:Forallt,vpairs,s∗(t,v)\nmaximizesplayerS’spayoff,whichcanbeexpressedas\nl\nU ≡a∗(s(t,v))(v−p∗(t)s(t,v){q d+ }) (6)\nS t 2\nThe requirement with respect to S appears more complex than the re-\nquirementsthatpertaintoT andA’sstrategies,becauseS choosesheractions\nin anticipation of the other players’ actions. Still, the requirement is simply\nthat,givenherowntype,T’stype,andtheanticipatedbehaviorofAandT,S\nmustchoosethecourseofactionthatwouldmaximizeherpayoff.\nRequirement4(R4):A’sbeliefsareconsistent:\nx∗ =Γ(t=G|z,s∗)wheneverΓ(t=G|z,s∗)̸=Υforbothz ∈{0,1} (7)\nz\nR4 simply states that A’s beliefs must be consistent with the implied condi-\ntionalprobabilityofT beingaparticulartypebasedontheequilibriumstrategy\nEElleeccttrroonniicc ccooppyy aavvaaiillaabbllee aatt:: hhttttppss::////ssssrrnn..ccoomm//aabbssttrraacctt==44118811889900\n\n<<PAGE_BREAK>>\n\nREFERENCES 31\nof S. This requirement is applicable only to strategies which have a positive\nprobabilityofbeingplayedbyS.\nProof of Proposition 2: The proof begins with part (iii), which is used in\nprovingpart(i).\n(iii) We show that the audience ends up always interacting with T, in all\nequilibria where the actions of the audience are not described by a∗(z) = z\nforz ∈{0,1}.\nSupposethereisaPBEwherea∗(z) = 0forallz.Bydefinition,theaudi-\nencealwaysinteractsinsuchassessments.\nSuppose there is a PBE where a∗(z) = 1 − z for all z, then per R3,\ns∗(t,v) = 0 for all v and t, and, therefore, µ(s∗) = 0, which implies that\nΓ(t = G|0,s∗) = γ.ThisimpliesviaR4thatx∗ = γ,which,inturnimplies\n0\nviaR1that a∗(0)=0,whichcontradictstheassumptionthata∗(0)=1.\nSuppose there is a PBE where a∗(z) = 1for all z. If µ(s∗) = i ∈ {0,1},\nthen Γ(t = G|i,s∗) = γ, which implies via R4 that x∗ = γ. This implies\ni\nviaR1thata∗(i)=0,whichisacontradictionwiththeinitialsupposition.If,\non the other hand, µ(s∗) ∈ (0,1), observe that, per R4, x∗ ⩽ γ implies that\n0\nx∗ ⩾ γ, because x∗(1−µ(s∗))+x∗µ(s∗) = γ. Thus, x∗ ⩽ γ implies that\n1 0 1 0\nx∗ ⩾γ >x,whichisacontradictionwiththeimplicationofR1thatx∗ ⩽x.\n1 (cid:98) 1 (cid:98)\n(i) Consider damages d < d , and suppose a∗(z) = z for all z. It follows\n1\nviaR2thatp∗(t)=0forallt.Thus,R3impliesthats∗(t,v)=1forallvand\nt, and, therefore, x∗ = γ due to R4 . Thus, in equilibrium, the audience acts\n1\naccordingtoitspriors.\nNext, consider damages d > d . It follows per R2 that p∗(t) = 1. Thus,\n4\nperR3,s∗(t,v) = 0forallv andt,becaused > d .ThisimpliesviaR4that\n4\nx∗ =γ.Thus,inequilibrium,theaudienceactsaccordingtoitspriors.\n0\nTheanalysisofthesetwocasesdemonstratesthatwhend ̸∈ [d ,d ],inall\n1 4\nPBE where a∗(z) = z for all z, the audience acts according to its priors. In\naddition, part (ii) of this proposition demonstrates that the audience acts ac-\ncordingtoitspriorsinallPBEwheretheaudience’sbehaviorisnotdescribed\nbya∗(z) = z.Thus,wheneverd ̸∈ [d ,d ],theaudienceactsaccordingtoits\n1 4\npriorsinallPBE.\n(ii)Thediscussionofseparatingequilibriainsection3.4demonstratesthat\nsuchdamagesexist.\nReferences\nAcheson, D. J. and A. Wohlschlegel. 2018. The Economics of Weaponized\nDefamationLawsuits.47SouthwesternLawReview335-384.\nArbel, Y. and M. Mungan. 2019. The Case Against Expanding Defamation\nLaw.71AlabamaLawReview453-497.\nArbel,Y.andM.Mungan.2020.RegulatingInformationwithBayesianAudi-\nences,GeorgeMasonLaw&EconomicsResearchPaper19-28.\nEElleeccttrroonniicc ccooppyy aavvaaiillaabbllee aatt:: hhttttppss::////ssssrrnn..ccoomm//aabbssttrraacctt==44118811889900\n\n<<PAGE_BREAK>>\n\n32 .V0N0\nArbel,Y.2021.AStatusTheoryofDefamationLaw.AlabamaWorkingPaper\nSeries2021.\nArbel,Y.2022.TheCredibilityEffect,AlabamaWorkingPaper.\nBe´nabou,R.,andJ.Tirole.2006.IncentivesandProsocialBehavior.96Amer-\nicanEconomicReview1652-1678.\nBe´nabou, R., and J. Tirole. 2011. Laws and Norms. National Bureau of Eco-\nnomicResearchNo.w17579.\nBar-Gill,OrenandAssafHamdani.2003.OptimalLiabilityforLibel.2Con-\ntributionsinEconomicAnalysis&Policy,1-26.\nCrawford, V. and J. Sobel. 1982. Strategic Information Transmission, 50\nEconometrica1431-1451.\nDalvi, M. and J. Refalo. 2008. An Economic Analysis of Libel, 34 Eastern\nEconomicJournal74-94.\nDeffains,B.andC.Fluet.2020.SocialNormsandLegalDesign,36TheJour-\nnalofLaw,Economics,andOrganization136-169.\nGaroupa,N.1999.TheEconomicsofPoliticalDishonestyandDefamation,19\nInternationalReviewofLawandEconomics167-180.\nGaroupa, N. 1999. Dishonesty and Libel Law: The Economics of the ”Chill-\ning”Effect,155JournalofInstitutionalandTheoreticalEconomics284-300.\nGaroupa,N.andM.Rizzolli.2012WrongfulConvictionsdoLowerDeterrence\n168JournalofInstitutionalandTheoreticalEconomics224-231.\nHemel, D. and A. Porat. 2019. Free Speech and Cheap Talk, 11 Journal of\nLegalAnalysis46-103.\nHemel,D.2020.EconomicPerspectivesonFreeSpeech.OxfordHandbookof\nFreedomofSpeech,118-136.\nHeymann, L.2012. TheLawofReputation, andtheInterestoftheAudience,\n52BostonCollegeLawReview1341-1439.\nLando,H.andM.Mungan.2018.TheEffectofType-1ErroronDeterrence53\nInternationalReviewofLawandEconomics1-8.\nMungan, M. 2016. A Generalized Model for Reputational Sanctions and the\n(Ir)relevance of the Interactions between Legal and Reputational Sanctions,\n46InternationalReviewofLawandEconomics86-92.\nMungan,M.2017.WrongfulConvictions,Deterrence,andStigmaDilution25\nSupremeCourtEconomicReview199-216.\nEElleeccttrroonniicc ccooppyy aavvaaiillaabbllee aatt:: hhttttppss::////ssssrrnn..ccoomm//aabbssttrraacctt==44118811889900\n\n<<PAGE_BREAK>>\n\nREFERENCES 33\nPennycook, G., Bear, A., Collins, E., and D. Rand (2020) The Implied Truth\nEffect: Attaching Warnings to a Subset of Fake News Headlines Increases\nPerceivedAccuracyofHeadlinesWithoutWarnings,66ManagementScience\n4944-4957.\nPng,IvanPL.1986.OptimalSubsidiesandDamagesinthePresenceofJudi-\ncialError6InternationalReviewofLawandEconomics101-105.\nPolinsky,M.andS.Shavell.2007.TheTheoryofPublicEnforcementofLaw\nin1HandbookofLawandEconomics403-454.\nPosner, R., 1986. Free Speech in an Economic Perspective, 20 Suffolk Law\nReview1-54.\nPosner,R.1973.EconomicAnalysisofLaw,1sted.\nPost,R.1986.TheSocialFoundationsofDefamationLaw:Reputationandthe\nConstitution.74CaliforniaLawReview691-742.\nRasmusen,E.1996.StigmaandSelf-fulfillingExpectationsofCriminality,39\nTheJournalofLawandEconomics519-543.\nSunstein,C.2021.Liars:FalsehoodsandFreeSpeechinanAgeofDeception.\nEElleeccttrroonniicc ccooppyy aavvaaiillaabbllee aatt:: hhttttppss::////ssssrrnn..ccoomm//aabbssttrraacctt==44118811889900"

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