The inquisitorial and the adversarialprocedure in a criminal court setting

Bruno De¤ains and Dominique Demougin

March 17, 2007

Abstract

We discuss a comparison of trial procedures, in particular, betweenadversarial and inquisitorial.

1 Introduction

Recent papers place at the heart of the explanation of economic develop-ment the quality of legal institutions (Rodrick, 2005, Acemoglu, 2004, LLSV,1998,...). The report Doing Business of the World Bank makes a clear dis-tinction between common law and civil law countries. This type of workspresents the great interest to investigate the role of the legal rules for laborand capital markets performances. However, they are essentially empiricaland generate some doubts on the deep reasons of the "superiority" of a cer-tain legal system. It is urgent to clarify some aspects of the debate on thecausal mechanisms of the relation between legal system and economic per-formance. From that point of view, the question of the procedures seemsessential insofar as the legal systems are characterized not only by the con-tent of the legal devices, but also by the way they are enforced. To illustrate,the di¤erences between the romano-Germanic and common law traditions arevery clear with regard to the domain of the proof. In French law, the judgetries to establish the truth in his judgment, whereas in the United States,the court confronts the arguments of the parties, in order to make triumphthe most probable to the audience. The analysis of the procedural designeproves to be necessary to approach the comparison of the legal systems. Be-sides the research of evidences, the debate must be about the complexity ofthe procedures, their costs or the judge�s role. From this perspective, theliterature is especially interested by the distinction between the inquisitorialand accusatory procedures.

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In the �rst case, the procedure is dominated by the judge who determinesthe appearances, assign the witnesses and the experts, interrogate them anddetermine the weight of the testimonies. In the second case, the judge onlydetermines the value of elements of proofs, the conduct of proceedings beingleft to the parties (to their lawyers who interrogate the witnesses). Thesenotions of inquisitorial and accusatory procedures must be handled how-ever with precaution insofar as they don�t perfectly capture the oppositionbetween common and civil law traditions (the distinction between "passivejudge" and "active judge" seems better to describe the main opposition be-tween the United States and France).It is not question to to propose a reform of the rules of procedures. But

it seems important to show in what manner the economic analysis can con-tribute usefully to the debate. The procedures are at the heart of the legaldevice and deserve this fact to be analyzed by the economists. We will starttherefore with raising the literature on the economics of the judicial proce-dures before concentrating us on the economic arguments on the nature ofthe capacity of initiative of the judge in the establishment of the facts. Thefollowing section analyzes the interest of the inquisitorial procedure, in amodel inspired by Dewatripont-Tirole (1999), when the parties are very un-equal in the expenses that they can engage for the presentation of evidence.As one saw, the inquisitorial procedure is characteristic of penal suits.

2 Literature

Cultural di¤erences between common law and civil law traditions are impor-tant with regard to the standard of proof. In French law, the judge is goingto establish the truth in his judgment, whereas in the United States the courtconfronts the arguments of each party, in order to make triumph the mostprobable to the audience. In any case, the production of the elements ofproof rests on the initiative of the parties. In the United States, these areindeed the lawyers that organize the debates, present the facts and gatherthe elements of proof... The judge has a neutral and passive role, assuringthe balance between the parties. Most countries of civil law tradition don�tknow procedures similar to the discovery of the common law. These coun-tries especially put the accent on the written proof and on the relative rulesof admissibility, whereas the countries of common law focus on the principleof the oral character. The common law sets on the rules of procedure so thatthe parts can confront themselves by cross-examinations.

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3 Strategies of the litigants

In the American system, all elements of proof presented to the judge arenormally known by the two parties before the trial. They must have anequal access to all information presented to the court. Yet, the accusatoryprocedure doesn�t guarantee that all applicable information will be revealedat the time of proceedings. Indeed, the incentive is strong for a party topresent informations only clearly to her advantage. Moreover, each partytries to cause some doubts on the revelations made by the adverse party. Itis the principle of the contradictory.The suit appears therefore above all like a means to feel the robustness of

the proofs and the veracity of the arguments brought to the attention of thecourt. The objective is not necessarily the research of the truth but ratherof the vraisemblance.The problem is that the demonstration of the proof is rarely free. For ex-

ample to the United States, the suits are reputed long and expensive becauseof the character contradictory of the procedure and the jury�s tradition. Inrelation to a suit before a judge, the suit before a jury entails an additionaldirect cost. According to a survey of the Rand Institute heart Civilian Jus-tice mentioned by Posner (1999), the additional direct cost of a suit beforea jury in relation to a suit before an unique judge is on average the order of$ 13.300. According to this same survey, the middle length of a federal suitbefore a jury is of 5,19 days, against 2,34 days before a judge.The trial is an expensive activity in time and in money that the parties

are going to mobilize. The literature concentrated therefore on the trial as arent seeking situation where the incentives of the parties essentially dependon their private gains. Shavell and Polinsky (1989) demonstrate indeed thata victim won�t opt for a trial if the amount of damages waited is superior tothe sum of the costs supported. Tullock (1988) proposes a model in whichthe probability of success depends on the expenses of the parts and describesthe accusatory procedure like a tournament of research of rents susceptibleto generate excessive expenses (cf infra). Katz (1988) focus on the relativeexpenses and endogenize the probability of success of the claimant. Theobjective consists in identifying the optimal level of expenses (i.e. of researchof proofs) for each party. He shows how the parties choose to make dissuasiveor agressive expenses according to their probability to win. Parisi (2002) alsoanalyzes the manner whose parts are going to provide this e¤ort to search forsome information and to maximize their waited gain. The incentive to searchfor evidences is function of the amount of the damage and the level of e¤ortprovided by the adverse part to �nd elements of proof. In this setting, thejudicial decision has some consequences redistributives merely. It justi�es a

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modelling in terms of rent seeking as well as the dissipation of a part of therent in expenses of justice.The problem with this kind of model is that they remain �nally quite

limited on the manner arguments brought to the attention of the court areinterpreted by the judge. They are also vague on the intrinsic value of thepretensions of the parts so that their utility to analyze the merits of the di¤er-ent procedures appears limited. A tentative to overtake has been developedby Froeb and Kobayashi (1996, 2001). These authors integrate a re�ectionmore deepened of the manner whose courts interpret the arguments of theparts as well as the possibility to see the elements of proof manipulated bythe parts. Even though the representation of the court stays naive enough, itis about a richer approach founded on a sequential research of the elementsof proof. The expenses are not predetermined and the elements presented tothe judge are going to orient his decision. The expenses of the parties becomeuncertain. This approach was the subject of developments by Farmer andPecorino (2000) and Daughety and Reinganum (2000).Another approach of the procedure based on the costs supported by the

parties appears in the perspective of the theory of the signal. In the analy-ses of the penal suits by Rubinfeld and Sappington (1987) or of Sanchirico(2001), the proof appears indeed like an expensive signal for the parts thatallows the judge to di¤erentiate the types of individuals, each capable to beguilty or innocent. The judge is going to deduct the behavior of the partsthe defendant�s type. The elements of proof don�t have an informationalcontent in themselves, it is the di¤erence of production cost that reveals thedefendant�s type. It is indeed more expensive for a guilty party to search forand to falsify some evidences to make the judge believe that he is innocentthat for an innocent to search for proofs and to demonstrate that it is re-ally innocent. As in the models of civil suit, the expensive character of theproduction of evidences plays a useful role because it permits to identify thetype of the players. The interest is here the trade-o¤ between the quality ofthe judicial decision and the costs of production of evidences by the parties.

4 Role of the judge

At the beginning of the suit, the judge doesn�t have any information to takea decision. He is in situation of informational asymmetry and he must gatherthe maximum of elements in order to approach the decision that would betaken in situation of perfect information. Thus, if the judge tries to minimizethe survenance of the misjudgements, he can take the elements that theparties are going to reveal to him or he can search himself the information.

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When the judge�s decision is oriented by the revelations of the parties,the procedure is accusatory, it opposes two visions of the same facts to maketriumph the version that appears the most believable. This type of procedureis anchored in the tradition of the Common Law. When the judge searchesfor himself of the information before taking his decision, the procedure isinquisitorial, closer to the procedures applied in the tradition of the Europeancontinental law.A fundamental di¤erence between these two logics is the role played by

the judge at the time of the suit. The judge of Common Law uses theaccusatory procedure to get some information. He is going to be based onthe testimonies of the antagonistic parties to take a decision while puttingin perspective the arguments of the claimant and the defendant. With thisdevice, the suit is directed by the parts. They spend their resources to getsome information and to present them to the judge whose role is neutraland passive. It essentially consists in insuring that the debate takes place"according to the rules". Each party try to orient the judge�s decision toher advantage. On the other hand, the judge of Civil law is more active.He directs himself proceedings, interrogate the witnesses and designate someexperts if need be to get the elements of proof.Is it preferable for a judge to have two partial sources of information or

one only impartial? For Posner (1973), the contradictory debate is preferablebecause it allows the parties that support the costs and the pro�ts of thesuit to direct the procedure. This arguing is criticized by Tullock (1988) forthat the accusatory procedure incites the parts to make excessive expenses tosearch for elements of proof and to deceive the judge in them favor. Accordingto this author, the inquisitorial procedure would be more e¢ cient to reducethe errors because a bigger part of resources is used to reveal the truth thatunder the régime of the accusatory procedure. For example, if an active judgemobilizes 80% of resources to lead some investigatings whereas each partyuses 10% each to make prevail her opinion, it is allowed to think that 90% ofresources invested in the suit serve to unveil the truth. Inversely, if the judgeis more passive only mobilizing 10% of the resources whereas every part uses45% of resources to build her strategy, then 55% of resources will be usedto unveil the truth and 45% to deceive the court. An inquisitorial procedureseems therefore more e¢ cient to allocate resources in order to reveal the truthon the circumstances of the con�ict opposing the parts. This procedure wouldminimize the losses bound to the costs of suit but would not guarantee foras much the obtaining of a complete information by the court.In the setting of these re�ections, the literature proposes to determine

the procedure susceptible to minimize the risk of error. The research wereinterested notably in the strategic behaviors of the plainti¤and the defendant

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when each part tries to persuade the court of the quality of her information.Using a game of persuasion, Milgrom and Roberts (1986) demonstrates thatif the parts are perfectly informed on the real state of the world, the judgecan get, in the setting of the accusatory procedure, the complete revelationof information preventing the survenance of errors. The revelations of theparties combined to the judge�s strategic skepticism drives to this result. Onthe other hand, if the information of the parties is imperfect, even with asophisticated decision-maker, the risk of opportunist behavior exists. Severalauthors propose games of persuasion to identify the conditions under whichthe parties are not going to reveal the information to the judge (to see notablySobel (1985), Shavell (1989) and Shin (1998)). From the moment the partieshave an incomplete access to information on the real state of the world,they can keep secret unfavorable information. It results from the fact thatto take his decision, the passive judge takes the revelations of the partssolely as a basis but doesn�t know in what measure the parties are informed,what can incite these last not to reveal information. Then, the judge cansearch for himself of the proofs to take hisdecision, as it is the case withthe inquisitorial procedure, in order to get impartial information and so toreduce the survenance of the errors.Is it better to collect information from interested parties or from an un-

biased agent? Shin (1998) compares the probabilities of error depending onwhether the judge uses the accusatory or inquisitorial procedure. He standsin a context where nor the judge, nor the interested parties are not in situa-tion of perfect information and put the hypothesis that information is gottenwithout cost. Dewatripont and Tirole (1999) and Palumbos (2000) comparethe procedures accusatory and inquisitoire in terms of costs to motivate theparts to produce and to share information. Froeb and Kobayashis (2001),in a very di¤erent model, also debate the arbitration between costs of theprocedures and quality of information gotten.Thin and Emons (2007) are going to pursue this type of analysis while

loosening the hypothesis that the parts can only �sh by "omission", in notunveiling everything that they know. In their model, the parts "can fal-sify" or "embellish" in their favor the proofs presented to the court. Thefalsi�cation of elements of proof imposes a cost however to the parts, a fewto the manner of the tournaments of pension research discussed previously.One recovers here a shape of arbitration between costs of the procedures andquality of information. The question is to know if a judge considering theprocedural costs, but also the quality of his decision, must take his decisionwhile listening two, one or no part concerned person. This problematic canbe connected to the one of Schrag (1999), that analyzes the role of the man-agerial judge introduces in the federal American system to limit the excess

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of the discovery. These notions of active or managerial judge are to bringcloser of the one of the judge of the setting in state in French law and moregenerally to the role of the civil law tradition in the establishment of the facts(to see Langbein (1985) for a comparison with the Common Law). Thin andEmons (2007) also show that the incitements to "to falsify" depend on thevery progress of the suit, depending on whether the elements of proofs arepresented sequentially or simultaneously, that is without the parties havingthe opportunity to retort allegations of the adverse party.

5 Standards of proof

In the setting of a suit in Common Law, each party tries to demonstrate themerit of her arguments. The degree of persuasion of the court varies howeveraccording to the regime of proof. In the majority of the cases, the degreeof conviction required in a civil litigation is the one of the preponderance ofevidence. A fact is considered proved if it appears more probable than no.In some circumstances, a higher conviction level can be required under thestandard of clear and convincing evidence. Finally, in a penal suit, a thirddegree even more elevated exists "beyond a reasonable doubt". Sanctionsa¤ecting individual liberty generally require the most elevated convictiondegree.At the term of the trial, the court must decide even though it subsists

more doubts on the innocence or the defendant�s guilt. According to Brook(1982), the society is susceptible to accept that a decision is taken in spiteof the fact of the persistence of an uncertainty on the defendant�s type.In a certain manner, unavoidable errors inherent to the human and falliblecharacter of the judicial decision and to the opportunist behavior of theparties would exist.The standard of proof the more frequently used in a Common Law is the

preponderance of evidence. In application of this principle, the party thathas to prove a fact must demonstrate that the probability that the fact is trueexceeds the one that it is false. In a civil case, the jury must be convinced ofthe superiority of the claimant�s evidences. The standard requires thereforethat no proof is admitted if its probability doesn�t exceed 50%. The argu-ments of the two parties are put in competition in the accusatory procedure,the claimant and the defendant sharing the risks of the decision to 50-50.Standard of proof doesn�t exist strictly speaking in civil law tradition. As

regards to the principles, the "implicit" standard would be identical in a civilor penal procedure and would be close to the higher certainty degree usedin a penal suit in the United States. The frequent recourse to the notion of

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"intime conviction" refers to a moral obligation. These di¤erences make thata plainti¤ who wins the trial the Common Law could have lost it in a Civillaw country.However, the Code Civil doesn�t �x the research of the certainty as imper-

ative. Indeed, the articles of the Civil Code limit themselves to express thenecessity of a demonstration without precise de�ntition. However the articles1321 and 1322 indicate that must be considered like proved what makes fullfaith. But to make full faith is not synonymous of certainty. The recourseto the notions of information or presumptions clearly demonstrates it. Theepistemological statute of the proof refers to the notion of "vraisemblance"that the article 1387 requires when it establishes that facts have to be proba-ble. Certainly, this vraisemblance is insu¢ cient and must be completed. Butthe complement doesn�t have the e¤ect of making certain the arguments. Itse¤ect is to allow the accession to minimum threshold.The di¤erence with the American system of the preponderance of evi-

dence resides in the fact that the threshold is not �x in Civil law countries.Therefore, the degree of precision is not the same. In other words, in everysystem, the research of the probable is bound closely to the e¢ ciency of thestandard of proof used, that is to its characteristic in term of risk of error.From that point of view, a possible justi�cation of the preponderance

standard is that it distributes the risks of error symmetrically between the twoparties. The errors of type I (sanctionning an "innocent") and II (relaxinga "guilty party") an equal weight in this environment. This standard wouldcontribute to the minimization of the frequency of the errors: a decisionrule that rejects the least probable hypothesis minimizes the errors. Brook(1982) justi�es on this basis the standard of preponderance if the objectiveof the legal system would be to reduce the errors of type I and II, underthe hypothesis that the two errors have symmetrical costs for the society.Adopting this approach, the analysis of Davis (1994) tries to determine theoptimal standard when the judge tries to minimize the survenance of errors.He puts the interest of a �x rule to limit the judge�s power in the choice of thestandard. He agrees however to notice that the more stringent standard ofCivil law countries is better to reduce the probability of survenance of errorsagainst innocent people. With a standard of intime conviction, the risks oferror are not distributed fairly between the two parties.Finally, an arbitration could exist between the reduction of errors and

prevention of incentives. Demougin and Fluet (2005) show that the waythese objectives are pursued by a country can re�ect the features of its legalsystem. When the priority is to provide incentives, the legal system wouldadopt rules similar to those of the Common Law. When the priority is thereduction of errors, a more stringent proof standard will be required and

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would be closer to the Civil law system.

6 Inquisitorial versus Adversarial

In this section, we discuss the comparison between the inquisitorial and theadversarial procedures in the case of a criminal court setting. As mentionedin the introduction, there is a small albeit important theoretical literatureinitiated, in particular, by the �advocate�paper by Dewatripont and Tirole(1997) referred to hereafter as DT. In that paper, the inquisitorial procedureis identi�ed as a situation where a sole investigator must gather informationfor both parties in the trial; the defense and the prosecution. In contrast, theadversarial procedure stands for the case where the respective evidence mustbe investigated by separate individuals. The comparison concludes in favor ofthe adversarial procedure for situations of moral hazard in the investigativee¤ort. Intuitively, the rent associated with aligning e¤ort for both causes inthe case of a single investigator is larger than the sum of the rents when thetasks are split.In the following section we introduce two conceptual changes to the DT

framework. First, we assume that the party �nancing an investigation candesign the incentive contract, thereby controlling the e¤ort undertaken. Inthat respect, we identify the inquisitorial procedure as a situation where thecontracting for evidence for the defense and the prosecution is �nanced bypublic fund whereas with the adversarial procedure the state only controlsthe design of the contract inducing evidence for the prosecution. Second, weassume an excess burden of taxation, speci�cally, paying $ 1 out of publicfund imposes a costs of $ (1 + �) with � > 0.By construction, the setup implies that for any pair of investigating e¤ort

the inquisitorial procedure generates higher social costs. First, defense costsare higher by the factor � because there are �nanced by public instead ofprivate funds. Second, due to the moral hazard inducing investigative e¤ortfor the defense means paying out an informational rent. In the case of anadversarial procedure that rent is just a transfer between individuals, thusimposing no social costs. However, with an inquisitorial procedure societyis forced to �nance the informational rent, thereby increasing social costsnot because of the transfer but because of the excess burden associated withpublic funding.Despite the higher costs for given investigating e¤orts the inquisitorial

procedure may nevertheless perform better. The argument is that with an ad-versarial procedure the social planner does not control defense expenditures.Assuming that the objective of a person accused of a crime is to minimize

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the likelihood of a prison term, the level of defense expenditures will dependon the �nancial resources of the individual. As a result, a wealthy personwill spend more than would be socially e¢ cient. In contrast, an accused withlittle or no �nancial resources will spend less than would be socially desir-able. The ine¢ cient behavior of the accused has also a feed back e¤ect onthe investigative e¤ort of the prosecution. Indeed, the two sides play a kindof Stakelberg game where the defense is �rst mover. In either case, socialcosts are not minimized.We consider the following representative case. A person is accused of a

major crime. There are some objective facts which implicitly yield society�spreferences for or against a prison term. In order to capture the problemwe use a setup resembling the DT model. Speci�cally, we use �D 2 f0; 1gto yield the objective information for or against the defense where �D = 0means that reasonable doubt is justi�ed and �D = 1means it is not. Similarly,�P 2 f0; 1g captures objective information favorable or disfavorable to theprosecution; respectively �P = 1 and �P = 0. Society�s preferences are thensummed up by the variable

� = �D � �P 2 f0; 1g (1)

where � = 0 implies either evidence evidence presented by the prosecutionis by itself not convincing or there is a reasonable doubt that the accuseddid not commit the crime. In either case, we assume that society wouldprefer not to punish the individual. In contrast, � = 1 means punishment ispreferred outcome.Society delegates its decision to a court. The court would always want

to decide according to society�s preferences. Its di¢ culty however is thatobjective informations are not readily available, i.e. � is not known. Denoteby �i 2 f0; 1g ; i = D;P the court�s information regarding the case of defenseand the prosecution respectively and

� = �D � �P . (2)

The (statistical) quality of the information presented to the court is thoughtto depend on investigative e¤orts. Speci�cally, we have may

Pr [�P = 1j�P = 1] = p and Pr [�D = 0j�D = 0] = d (3)

In either case, the probability measures the likelihood of the investigator�nding evidence favorable to its case given that the objective informationis itself favorable. Unlike DT, we assume that a party can �nd evidence infavor of its case even if the objective situation does not give it. For example,

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we assume that with high investigative e¤ort the defense may be successfulin �nding reasonable doubts even though objectively �D = 1. Speci�cally,we assume

Pr [�P = 1j�P = 0] = �p and Pr [�D = 0j�D = 1] = �d; 0 � �; � < 1 (4)

Investigation is costly. We denote with C(d) and C(p) the respectivee¤ort costs; C(0) = 0; C 0; C 00 > 0. Closing up the model requires to de�nethe likelihood of the �i; i = D;P and whether the random variables arecorrelated. For the sake of argument, we assume in the remainder thatPr (�i = 0) = 1=2 and that the events are independent. Moreover, we impose� = 0, i.e. the persecution is thought to never be able to convince a court ofthe validity of her case if �P = 0. It is easily veri�ed that the intuition of theensuing results extend to these cases.Objectively there are 4 possible cases. First, we could have �D = �P = 0

implying � = 0. With � = 0, no matter what level of p-e¤ort, �P = 0 implying� = 0. Second, suppose �D = 1; �P = 0 again the court would observe� = 0. Third, with �D = 0; �P = 1 society�s preferences are characterized by� = 0. However, given �D = 0; �P = 1 the court can nevertheless sees � = 1with probability (1� d) p. Finally, given � = 1, the court observes � = 1with probability p (1� �d). We take it as given that the court will �nd itadvantageous to punish � = 1 and not punish otherwise.1

Altogether, courts make with probability 14p (1� d) a type I error pun-

ishing an innocent and with probability 14[1� p (1� �d)] a type II error al-

lowing a criminal to go free. To keep the mathematics to a minimum, weassume in the remaining, and solely to exemplify the idea, that the errorcosts associated with both types of judicial miscarriage are equal and mea-sured by L. Thus expected social costs associated with judicial errors become14f[1� pd (1� �)]gL. Total social costs further include investigation costsand costs associated with the excess burden of public funding where the lat-ter costs depend on the organizational form and the rent accruing to theinvestigator.

6.1 Aligning incentives

Unlike DT, we ignore the multitasking issue assuming that even in the case ofinquisitorial procedures the court could easily hire two investigators that areboth expected to directly report to the judge their respective information.

1Two remarks are in order. First, we can �nd analytical conditions which would guanteethis outcome. Second, society (court) can always adjust the level of punishment dependingon the likelihood of errors.

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Thus the distinguishing feature of the di¤erent procedures is determined bywho �nances thereby designing the incentive contract.Otherwise we follow DT by assuming that wage payments to the inves-

tigators can only be conditioned on the outcome of the trial and not on theinformation �i; i = D;P .2 We denote with CP (p) the costs of aligning the in-centive of the investigator researching information in favor of the prosecution.Moreover wi stands for the wage of the investigator if court concludes � = i.The unconditional probability of outcome � = 1 is 1

4[p (1� d) + p (1� �d)]

where the �rst term captures the likelihood of a type I error and the secondterm that of a correct guilty verdict. Altogether, we have

CP (p) = minw0;w1

�1� p

4[2� d (1 + �)]

�w0 +

�p4[2� d (1 + �)]

�w1 (I)

0 = (w1 � w0)1

4[2� d (1 + �)]� C 0(p) (IC)

0 � w0; w0 + w1 (NNC)

where (IC) gives the incentive compatibility constraint and (NNC) the nonnegativity condition of wages; i.e. we assume that the investigator face a lim-ited liability requirement. Substitution of the (IC) in the objective functionof the principal implies

CP (p) = w0 + pC0(p) (5)

making it optimal to set w0 = 0. Using the above notation CP (p) includesinvestigation costs C(p) and the investigator�s rent RP (p) = CP (p) � C(p).C(0) = 0 together with the convexity condition guarantees that with p > 0the rent becomes strictly positive. A similar results obtains for the investi-gation activity toward the case of the defense.

6.2 Social costs and procedures

In the case of an adversarial procedure, social costs include costs associatedwith judicial errors, the investigation costs as well as the excess burden as-sociated with the case of the prosecution. Altogether, we have

SCAdv(p; d) =1

4f[1� pd (1� �)]gL+ (1 + �)C(p) + �RP (p) + C(d) (6)

2Note that in reality investigators do not report a variable �i but a vector of informationwhich may or not convince the court. Of course convincing must be seen in the broadercontext of the entire trial. Conditioning on the outcome of the respective �i may beimpossible simly because it may be ex-post impossible to disentangle what caused thecourt to decide one way or an other (for example some jurors may �nd reasonable doubtwhile others were not convinced by the case of the prosecussion).

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Observe that the SCAdv do include the entire rent paid to the agent investi-gating the case of the prosecution, but the excess burden associated with thetransfer of rent.3 In contrast, social costs associated with the inquisitorialprocedure social costs include in addition the excess burden of public fundingfor the cause of the defense, i.e.

SCInq(d; p) = SCAdv(p; d) + ��RD(d) + C(d)

�(7)

Thus, for positive investigative e¤ort on behalf of the defense, we conclude:Result 1: For all d > 0; SCInq(d; p) > SCAdv(p; d).In some sense, we �nd a similar conclusion than DT in that the social

costs associated with any speci�c pair of investigative e¤orts are always largerunder a inquisitorial rather than adversarial procedure. However, the resultdoes not automatically imply that the latter organization of trials is prefer-able. Indeed the inquisitorial procedure has an obvious advantage in thatthe social planner can directly control defense expenditures.In contrast under the adversarial procedure, it is the accused who controls

the incentive contract for the defense and the level of defense expenditures.Assuming that the objective of the accused (whether guilty or not) is to avoida condemnation at all costs , we would expect the ensuing d to be larger thanis socially optimal if the accused is wealthy and smaller than is desirable inthe case of a poor individual. To allow for a geometric argument, we de�ne

SCAd(d) = minpSCAdv(d; p) and SCIn(d) = min

pSCInq(d; p) (8)

Under conditions guaranteeing convexity throughout, we the social cost func-tion have a shape as represented in the �gure. In particular it is easily veri�edthat for either procedure investigation e¤ort for the prosecution reacts posi-tively to an increase in d. Intuitively, raising d increases the marginal bene�tof p in terms of error costs. As a result, for small d investigation e¤ort is toosmall for both sides in the trial and error costs are high. Vice et versa for dtoo large where the social planner is induced to generate too much e¤ort forthe case of the prosecution.The �gure re�ects result 1. However, it also points out that for individuals

that are su¢ ciently poor �d < dp �we have SCAd(d) > mind SCIn(d). Thiscase is characterized by low costs of investigation, but large error costs. Atthe other end of the wealth scale � d > dw �, wealthy individual spend�too�resources (from a social point of view), inducing the social planner toexcessively raise his own research for the case of the prosecution. Here socialcosts are too high because of investigation costs.

3Observe that the functional form of (6) imposes some parameter restrictions forSCAdv(p; d) to be convex throughout. We assume the condition is satis�ed.

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)(dSC Ad

)(dSC In

)(dSC Ad

)(dSC In

d1*Add wdpd

L

)(dSC Ad

)(dSC In

)(dSC Ad

)(dSC In

d1*Add wdpd

L

Figure 1: Social costs: inquisitorial versus adversarial

Result 2: With large inequalities in the income distribution, the inquisitorialprocedure minimizes social costs.The analysis raises an additional moral and ethical issue with respect

to the adversarial procedure in that it generates di¤erent level of justicedepending on individual wealth.

7 Conclusion

8 Bibliography

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