Since the 18th century，In order to meet the urgent needs of the theoretical system of the evidence law，Gilbert、Bianqin、Wigmore、McComis and other scholars focus on explaining the rules of evidence from academic theory。In the first wave of evidence law，The entire system of evidence theory is basically completed，Scholars have begun to pay attention to the formulation of evidence rules。By 1975，The US Congress promulgated the "Federal Evidence Rules"，The second wave of evidence of evidence。Scholars are more committed to rules research，A large number of important articles about evidence have emerged in legal reviews。But，Londbert thinks，Although these articles may have potential value，But the federal evidence rules are still similar to the time when formula，They rarely achieve the expected effect。So，Evidence Law is in a state of stagnation。

In the 1980s，The emergence of new evidence law has triggered the third wave of evidence research，In 1984 and 1988, the Joksman Organization of Oxford University organized two seminars in the legal field of probability and evidence，and 1986 The "Probability and Reference" seminar held by Tiller at the School of Law of Boston University is witness。They have changed the research direction of evidence law，Shit the scholars' attention from the rules of evidence to the proof process。The term "New Evidence Law" has covered all interdisciplinary research on all interdisciplinary and interdisciplinary，For example, the theory of evidence、The theory of Rong Gong、Relative theory of truth, etc.。New evidence Legalist firmly based on the tradition of rationalism，Seeking or critical mathematics model，Used as a proof mode or understanding the trial process。Mathematics becomes a research theme of the interdisciplinary interdisciplinary of evidence，and get support from the internationally renowned legal journal。

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New evidence Law was originally a series of arguments caused by the probability of the law。Among these disputes，One party advocates the role of Bayesia's inference model for understanding or application of laws，and the other party criticize bet365 live casino games or oppose this position。These problems mainly originated from the case of "People's Lorion" in 1968，This case encountered a problem when using the probability method to process statistics。Calculation error calculation based on the probability in this case，Scholars on the "how the probability theory should play a role in trial" starts fierce debate，In the Harvard Legal Review, it has triggered a well -known probability dispute。Finkstein and Felley believe in their article "Bayesian Method of Recognizing Evidence"，The real problem of the Collins case is not that the prosecution tries to use statistical reasoning，Instead, failed to provide statistical information to the jury in Bayesian theorem that failed to decide on the jury。But，But Bo pointed out in his famous "Through Mathematics"，The Bayes model used by Finkstein and Felley as a suspicious quantification method，Ignoring the legal value expressed by the judicial program，and the error risk it brings will increase the cost of litigation。

It is generally considered，But Bo won this special argument。Just as Allen advocated，Bayesian method can be used as a guide for rational thinking，Specific blueprints instead of decision -making。But，Dabo's paper does not eliminate the probability of the legal field，Instead, it has stimulated the greater interest of scholars on probability theory and evidence issues。Londbert emphasized in its far -reaching paper "Modeling Related"，For a jurist，Probability Analysis has many benefits in dealing with evidence。At the micro level，The grant -like model based on the Bayesian method can unify the correlation and proof of evidence。Since the Collins case，The research of the model of the model in the field of court science has caused a wave of upsurge，The "Court Scientific Reference and Statistics International Conference", which was created in 1990, was held in the United States and Europe.，attracted jurists、Lawyers and statisticians discuss the probability reasoning of scientific evidence of courts。Bayesian method and granting model are widely used in judicial practice in British and American law countries，Especially since 1990，The model of like grant ratio has become the standard method of scientific comparison in DNA courts。

On the macro level，Bayesian probability theory and judicial proof have inherent bet365 live casino games associations。With the help of Bayesian method，People can explore the evaluation of the authenticity of the case on the fact that the new evidence will change。This method can also help people understand the problems such as "why the pre -crime has not been significantly proved to the defendant's allegations" and other issues。As Kalison said，Comprehensive probability analysis of facts determined can provide better clues，What elements indicate that the elements will affect the facts of the facts。Use probability threshold，It can also be quantified to explain the standards，The standard of evidence of modeling advantages and exclusion of reasonable doubt standards is used to use the probability of modeling.。Probability threshold is the value obtained based on Bayesian decision theory，Its value range from 0 to 1。Kaye thinks，The probability threshold of the standard proven in civil lawsuits can be set to 0.5。Tires Profile，The probability threshold of the standard proven in criminal proceedings should be 0.95。Judge Weinstan agree with Tiller's point of view，And it is recommended to use clear language and quantitative statements to explain the rationality of these standards。

　Dilemma of judicial probability theory 

Following the probability of the "Harvard Legal Review"，The probability dispute on the "Criminal Legal Review" discusses a series of specific dilemma in the legal application，That is Kon's paradox。Cohen paradox is a research theme of judicial probability theory，Among them, the problem is the problem、Ticket escortae paradox and reference difficulties are the most famous "three major problems" in the Kane paradox。

The problem of the combination was initial。Combined difficulties include two versions。The first is the collection of evidence，In the case of considering multiple evidences at the same time，The probability of the facts of the case will be lower than the probability of only considering the case of only a single evidence。This contradictions with judicial practice，Because the proof of multiple evidence should be greater than that of a single evidence proof。The second is the facts of facts，In civil lawsuits，If the facts advocated by the plaintiff contain two or more branch requirements，Each branch of each branch must be established to ensure the victory。Allen pointed out，In the problem of acquisition，With the increase of the number of branch elements，The bet365 best casino games probability value required for each branch will also increase。The probability of giving the entire case by the entire case exceeds 0.5，So the probability of each branch must be far more than 0.5。This does not match the legal requirements，Because the law usually requires the plaintiff to prove every element of the case at a probability of slightly higher than 0.50。Actually，The paradoxes of these two versions are intuitive conflicts caused by informal misunderstanding of probability multiplication formula。As early as 1987，David through the reliability of witnesses、Priority probability and post -test probability to explain，It proves in the Bayesian framework that the problem of the closing problem is actually not existing。

Ticket escort paradox is a typical case often cited by new evidence legalists。Assuming 499 people pay the admission fee for the performance competition，But 1,000 people watched the game，The remaining 501 people secretly went in to watch。If the boss of the performance site filed a lawsuit against all audiences，Only provide statistical data without other evidence，We intuitively think that the boss cannot get compensation from any audience，Although the probability of the defendant in each case is more than 0.50。Tickets have caused two problems in the paradox: one is whether pure statistical evidence has a proof value for legal ruling，For example, cases such as fugitive paradox and similar red and blue buses and prisoners' cases，Their common point is that the whole case is only statistical information，Is the information sufficient to prove it as a judgment; the second is whether the Bayesian probability theory is consistent with the determination of the judicial facts，or how to maintain the same，This problem has aroused fierce debate by new evidence jurists。Probability Theory Scholars provide a variety of solutions to solve such paradoxes，One of the solutions is，Subjective probability is obviously different from objective probability，The fact that the subject is the subjective probability of the defendant as the defendant must be less than 0.50，Therefore, you need to make a favorable instructions to the defendant。

Bayes has the probability of maintaining a balance between subjective evaluation and rational analysis，But facing the dilemma of reference class selection。bet365 best casino games Reference choices will directly affect the accuracy and rationality of the accuracy and probability reasoning of probability value calculation。If you can’t determine the appropriate reference class，It is impossible to get related frequency data，This will have an impact on the reliability of evidence assessment and belief.。Allen deeply recognizes the reference class problems in probability reasoning，And in his paper "The Value of the Mathematics Model of Evidence", the reference class issues faced when the use probability method evaluation evidence is evaluated by six cases.。Actually，This is a common problem，Not only does it exist in the judicial certificate，And when determining the probability of an individual that has some attributes may involve reference class selection。So，Franklin proposed three feasible principles to determine the reasonable reference class，Principles related to attributes、Common degeneration principle and intersection principles。

Cohen paradox is the core issue of the discussion of new evidence law。To solve this paradox，Evidence jurist proposed various solutions，Including legal probabilityism、Bayesian decision theory and relatively true theory。These solutions can be classified as two paths，is probabilityism and interpretism。where，Legal probabilityism and Bayesian decision theory belong to the former，The theory of relatively true nature belongs to the latter。Lipton advocates probabilityism and interpretism should be closely integrated。He thinks，Bayesian formula provides a constraint for the reasonable distribution of faith，This constraint is consistent with the perspective of interpretism。Explanationism believes that explanation considerations play an important role in the process of belief update，and is committed to forming a way to form a constraint belief，but not very successful。Because of this，probabilityism and interpretism should become friends。In recent years，These two paths begin to become consistent，Blending each other's concept。2020，Welch conducted a substantial correction of the relatively true theory through Bayesian decision theory，Defending and improving the relatively true theory。At the same time，Probability Theory Scholars on the basis of relatively true theory，Powerful defense of the bet365 Play online games probability method, that is, legal probabilityism and Bayesian decision theory。

　　Key technology of legal technology 

The practice of judicial certification is the ruler of the appropriateness of the mathematical model。But，Excessive requirements of the formalization of probability theory itself，Probability reasoning has risks such as calculating complexity and prosecutor fallacy in the applicable legal field，This is the primary reason for the probability of Bayesian in the law industry。The second reason is the misunderstanding and misuse of the probability method itself in the law of the law.。For example，Bayesian theorem needs to be input at the first test probability.，But it is difficult to obtain accurate priority probability in reality，Set the legal principles that the probability of first verification is contrary to the legal principles of innocence; not all evidence can be evaluated in a probability manner;、Reference class selection、Pure statistics such as evidence;。The third reason is the disciplinary barriers and field differences between law and mathematics。Obligatory symbols in mathematical models、Complex operations and the lack of language descriptions make law scholars see it as "evil"，This hinders the application of mathematical models in legal practice。

But，Compared with the iterative update of technology，Legal artificial intelligence requires mathematical models to achieve automatic legal reasoning，For this，Judicial probability method is grand debut。In the era of continuous development of artificial intelligence，Probability theory has long been algorithmized and embedded in software tools，Sugenarisk、Genie and other software。In this context，Intelligent probability reasoning has made the basic theory of mathematics for technical modeling and algorithm programming，No need to start from the basic theory of mathematics.。This means that the legal person has been liberated from the complicated probability operation，Scientific calculations through the mode of human -machine collaboration。Fanton、Tang Noni and others made a lot of important contributions to promoting the use of Bayesian artificial intelligence software auxiliary trials。They use this type of software program to build Bayesian network model，and analyze the real case，Rulousa Deberk case and Simonhafin Bet365 app download Murder Case，Disapt many probability of reasoning fallacy。

Use of Bayesian artificial intelligence software，Successfully eliminated technical obstacles in judicial certification and probability reasoning，Fundamentally overcome the calculation complexity problem faced by the legal person，Then it helps to resolve judicial disputes in the union of law and mathematics。2016，The International Joint Community "When the Bayesian reasoning is applied and when it is not applicable" and "how to make the probability results be accepted in court，There is no need to explain in detail the two core issues of mathematical basic principles. "。Judicial proof as a kind of practical activity，Have uncertainty。Bayesian probability theory in mathematics is the advantage of，It not only effectively describes the facts inference and the expression of beliefs，It also provides a systematic framework for handling this uncertain reasoning。

　　(The author is Professor of Wenbo College of East China University of Political Science and Law)