In common criminal law in order for a defendant to be punished, they must be found guilty beyond all reasonable doubt. Hence, there is a threshold for the probability of guilt, beyond which the punishment is proportional to the offence and/or consequences.

I want to know if there is a legal system where punishment is proportional to the probability of guilt. For example, Alice and Bob are equally likely to have committed a known crime and one of them must have committed the crime. Hence, each faces 50% of the normal penalty. Such a legal system could be from anywhere in the world at any point in time, from modern roman legal systems, to small systems governing tribal communities. Any of these are interesting to me if researched.

I am also interested if such a punishment system has been investigated theoretically. Primarily, what the benefits are, but the ethical side is also of interest.

If anyone can help that would be most helpful, I have not been able to find any scholarly or other types of article. I am interested from a mathematical perspective, but I'd like to know whether such systems exist in reality.


Just to be clear, I am not asking whether there has been implemented a mathematically precise decision procedure, weighting level of punishment proportional to probability of guilt. But rather, if there is or has ever been an informal (i.e., imprecise) system.

There are good reasons for there not to be, I am asking whether there has been or is such a system.

Thanks for the answers so far, I just wanted to clarify that.

  • This is a duplicate of a prior question. I'll try and find it. Short answer: It is called plea bargaining.
    – ohwilleke
    Feb 28, 2017 at 17:51
  • Thanks if you can find the duplicate question. I cannot quite see how what I described coincides with plea bargaining, having searched. So if an answer sheds more light on the correspondence that would be helpful. Feb 28, 2017 at 19:51
  • Removed legal research tag which applies to how to do legal research and added criminal law tag.
    – ohwilleke
    Feb 28, 2017 at 23:07
  • Are you thinking of the probability question about reasonable doubt, law.stackexchange.com/q/14962/4501?
    – user6726
    Feb 28, 2017 at 23:33

5 Answers 5


A series of answers were proposed to similar questions in the world building forum.



The relationship to plea bargaining is as follows:

  • When the prosecution has a strong case with a high probability of winning, it insists on going to trial and will make only slight concessions relative to the result that could be obtained at trial.

  • When the prosecution has a case of typical strength with an intermediate chance of winning, it will normally make a significant concession in the severity of the offense charged or other agreements that impact the length of the sentence, relative to the result that would be obtained if the prosecution fully prevails at trial, rather than "roll the dice" and usually the defense will agree in exchange for a more lenient sentence.

  • When the prosecution has a case that is weak (but being ethical, believes that there is probable cause to support), it will normally make very deep concessions such as agreeing to a much less severe charge or for example to probation or a deferred judgment, to at least impose some punishment, in order to avoid going to trial, even when the potential punishment if the prosecution full prevails is very high.

Plea bargaining rates in the federal system are in the mid- to high 90%s, while plea bargaining rates in state systems are often in the 70% to 90% range (federal prosecutors can leave weaker cases to state prosecutors if they want to and have a stiff hammer due to high mandatory minimum sentences for many offenses and the sentencing guidelines, but state and local prosecutors have to take what their less elite law enforcement officers come up with). At trial, prosecutors typically win convictions well over 50% of the time (although not too much more, because the more clear cases are either dismissed by prosecutors as unproveable prior to trial or are plea bargained).

The net effect of the current system is that the severity of the sentence imposed in the vast majority of cases is proportional to the probability of the prosecution prevailing at trial times the likely sentence if it does prevail, as evaluated mutually by the prosecution and the defense. When there is not a sufficient consensus on the fair sentence in light of those factors the rare trial happens (and more often than not the defense rather than the prosecution overestimates its chances).

Unfortunately, this also means that the biggest penalties for going to trial are in the weakest cases in which the prosecution just barely manages to convince the jury and there is a strong probability that the defendant is actually innocent, as opposed to the cases where it is fairly clear that the defendant is guilty. And, people who are actually innocent of everything are most likely to roll the dice and go to trial, since people who are guilty of something know that in any fair resolution that are going to face the significant downsides of having any criminal conviction on their record, while people who are actually innocent may reasonably (although sometimes inaccurately) believe that the system will protect them and allow them to escape all consequences except the costs of defending themselves in court (if they can afford it).

Another option that prosecutors have in a case where proof beyond a reasonable doubt may be difficult or impossible, is to bring a civil lawsuit or to seek an administrative penalty, which may result in loss of a licenses or payment of a fine or compensation, rather than bringing criminal charges. In these cases, the prosecution only has to prove a case by a preponderance of the evidence in most cases, and usually, the defendant has no right to an attorney at public expense even if the defendant is indigent. These fines (or civil forfeitures) can also help fund the criminal justice system that pays prosecutors and other participants in the process.

Below that standard, prosecutors can seek search warrants, wire taps and arrest warrants in cases where there is merely probable cause to believe that a person committed a crime, which in addition to setting up future prosecutions can also be used as a form of punishment/harassment of someone prosecutors believe to be guilty of a crime even though they may not even have the evidence necessary to prove a civil suit, but the amount of impact that a search warrant, wire tap, or arrest can have on a suspect is much less than a full blowed prosecution.

  • 2
    +1 for showing how it actually happens in spite of not being in the books or accepted by legal theories.
    – Pere
    Jan 26, 2020 at 11:11

Interesting question.

We know from cases involving twins that even when you know for a fact one of two people committed a crime (say, because of highly incriminating DNA evidence), both twins will be found innocent because the standard of proof set is still "beyond reasonable doubt"

Examples of such a situation can be found quite often, this article talks briefly about the issue, and how many legal jurisdictions around the world (not just the US/UK) all come to the same conclusion that unless there is evidence to incriminate one twin over another, both will be set free.

I believe this all boils down to the standard of proof for criminal trials, proof "beyond a reasonable doubt" that someone is guilty. If we were to take the term to mean "99% certainty", then your answer seems to be a statement of the current situation, that you will get 100% of the punishment if you are 99% likely to have committed the crime in question.


No legal systems (officially) compute punishment based on strength of evidence for conviction. The reason is simple: justice is a relationship between an act and its consequences, not a relationship between evidence and a consequence. It would thus make no sense to lighten the punishment if there is a bit less evidence that a person did the deed, and to really pile it on when there is a lot of evidence. Moreover, if everyone is to be punished in proportion to the amount of evidence that they did the deed, you would end up with the absurd injustice that when a crime is committed, everybody in town is punished at least a little, because they had opportunity or motive. Instead, there is a threshold where the fact finder says "there is enough evidence to say he did it", or "there isn't enough evidence", and it does not matter whether there is one person or 100 being suspected.

The best model, a propos conviction, is a two-tailed test where the alternatives are "guilty" and "innocent". For hundreds of years, we have favored the requirement that the evidence must show the accused to be guilty – not innocent, and not in the middle zone where the evidence is balanced. The standard alpha of .05 is conceptually not so bad a view, and is reflected in Blackstone's formulation "It is better that ten guilty persons escape than that one innocent suffer".


I don't know of any such system, nor can I see how it would work.

"Reasonable doubt" and "balance of probabilities" (despite the name) are not measures of mathematical probability. Each finder of fact (judge or jury) decides what the threshold is and if their assessment of the evidence presented has met that threshold.

That includes deciding what evidence they believe and ascribing their own weighting to that evidence. Evidence is always conflicting and a jury that believes witness A would assign a different weighting to one that doesn't - if mathematical probabilities were assigned that could mean the difference between 0.99 and 0.01.


In a very strange way and fashion, Japan might qualify, but in an inverse way: You are (usually) not accused unless they can ensure to convict you. Japan's courts have a conviction rate of well over 99%. Allegedly, there are three reasons for this:

  • The prosecution allegedly really only brings their best cases, and everything that is not a sure case is dropped. The prosecution may even decide not to prosecute sure cases, because they may drop cases due to any circumstances they deem exonerating.
  • Judges might appear to be pressured that anyone that is charged is guilty, but there certainly are non-guilty verdicts. A research into those showed, that judges giving a non-guilty for proper grounds did not suffer consequences while those that made up excuses in political cases suffered consequences. The research showed that judges are not likely to be biased.
  • The system is such that cases can drag years through the system, with prosecution and defendant preparing for trial dates. The judge inquires into the presented case by both sides, then they schedule the next date. To the next trial date, both sides may and will bring further evidence. This results in many accused settling (for reduced punishment) and further pushes prosecutors to wait for the best evidence to conserve resources.

It is most likely the very harsh selectiveness of the prosecution that leads to the pattern: they can only prosecute the surest cases, which leads to the skewed "charged is guilty" result. In 2014, there were about 2000 state-employed lawyers in Japan serving as prosecutors out of about 35 000, with a population of 150 million. The US has about twice the population and more than 1.3 million lawyers - and at least a 5-digit number of state-employed lawyers.

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