Blinded Justice

blindjusticeIt’s been “reasonable doubt” week here at The Big Questions. We’ve talked about recognizing reasonable doubt when you see it, about what the standard should be, and about what the standard for determining the standard should be.

This raises the question: What is the standard? Here’s the weird part: Nobody knows. The judges won’t tell you and neither will the legislators. If you’re on a jury, you’re on your own.

Now you might say that that’s a fine thing. We want to leave it to jurors to set this standard. Under that theory, a juror has two separate questions to answer. One is “How doubtful am I?” and the other is “How much doubt counts as reasonable?”. But I don’t believe anyone actually subscribes to that theory.

Here’s why I say that: Suppose that in a murder trial, the foreman of the jury reports back to the judge that the jurors have agreed that there’s a 15% chance the defendant is guilty, and that they consider 15% to be beyond a reasonable doubt. Therefore they have unanimously voted to convict. I am not a lawyer, but I will cheerfully bet you that in any such case, the judge would throw the conviction out in a hurry, on the grounds that 15% is not at all beyond reasonable.

In other words, the judge does not subscribe to the theory that it’s entirely up to the jurors to set the reasonable doubt standard. Moreover, the judge would throw out the verdict at 16% or 17% or 18% and so on up to …. what? Well, up to some number. That number is a standard that the judge is prepared to enforce. What is that number? I bet the judge won’t tell you. The question is: Why not? Why doesn’t the judge say something like “You should convict if you are at least 90% certain the defendant is guilty”?

Now you might respond that it’s often very difficult to be sure whether you’re more or less than 90% certain of something. I agree with that. But it’s also very difficult to be sure whether your doubt is more or less than “reasonable”. So jurors have a difficult job either way. But it’s easier to solve one hard question (“How doubtful am I?”) than to solve two hard questions (“How doubtful am I?” and “Is that a reasonable amount of doubt?”).

90% is a target. It’s often hard to know whether you’ve hit the target, but life is easier when you at least know what you’re aiming at.

Ideally the standard should come from the legislature, which, after all, is tasked with deciding matters of public policy. If we’re getting too many false convictions, the standard can be raised, and if we’re getting too many false acquittals the standard can be lowered. But the decision about what constitutes “too many” is a political decision, and therefore should, I think, be made by elected politicians.

Instead, the politicians shirk their duty and hand off this key decision to the judges, who in turn keep their standards a secret. Why? I strongly suspect it’s primarily to make the jury’s job as hard as possible so as to drag out the deliberations and make more work for judges. Judges may not be consciously aware of this motivation, but people in pretty much all walks of life are remarkably good at rationalizing crazy policies that just happen to have the side effect of making them more employable. Why else would they handicap the jury this way?


42 Responses to “Blinded Justice”

  1. 1 1 Jonathan Campbell

    My guess is that the judge would feel comfortable throwing out the conviction of the jury’s reported standard is anything less than 50%, and uncomfortable for any higher #. He might disagree with the jury that 51% is high enough (since “beyond reasonable doubt” seems to suggest “significantly more than 50% likely”, and 1% doesn’t seem too significant), but he might not have grounds necessarily to throw out the conviction.

    There are other examples where we have delegated responsibility to juries in a way that gives them the freedom to make dumb decisions: suppose the jurors all agreed that the defendent had clearly told 6 lies on the stand, outside of the question of whether he committed the murder, and that he may or may not have been lying on the question of whether he committed the murder. They agreed that it is always more likely for someone to tell an even # of lies in the courtroom than an odd #, so they acquitted. That would be dumb, but I don’t think it would violate any rules set by the judge.

    The jury is like a mini-democracy, and there are always instances where democracies (especially mini ones) can make stupid decisions.

  2. 2 2 JLA

    The jury is a check on the power of the legislature. If legislators began to dictate to juries how to make decisions, we would lose that check on power.

    Juries don’t face the right incentives, but the incentives legislators face are probably even worse. Putting more criminals in jail is always a huge boon to a politician. But, there are huge social costs to putting people in jail that politicians don’t bear.
    Therefore, politicians will likely favor too many false convictions over too many false acquittals.

  3. 3 3 Bennett Haselton

    I think it’s hard for criticisms of the legal system to gain traction, because insiders can just say that there are things that judges understand that experts in other fields just don’t get, yada yada yada.

    So, put the legal system on the defensive: Where is the evidence that the “experts” in the legal system (such as judges) are actually achieving the goals they claim to be achieving, and doing a better job than could be done by any reasonably bright college graduate? Forget hitting a target number for “reasonable doubt” — what’s one thing, *anything*, that judges can produce evidence that they are doing better than, say, the average math professor could do? (Let’s say, your average math professor after taking a crash course to learn the basic courtroom rules and procedures.)

    Judges undoubtedly think, for example, that they are better than average at telling if a person is lying. But there are experiments that can measure that ability, and most people tend to overestimate their true ability in that regard. A few tests using a random sample of judges would at least begin to answer the question.

    Doctors and mechanics and math professors, by contrast, can produce ample evidence that they are able to do many things that the average smart person could do (not even after a crash course to learn the “procedures”).

  4. 4 4 Tim C.

    Juries tend to go on what they “feel” anyway, and don’t necessarily subscribe to a number themselves unless told to do so. And if given a benchmark number, they tend to work around it to fit their “gut feelings” – but only if they know the effects of that number.

    I’ll give you an example from civil law. Most states operate civil negligence law under comparative fault regimes, in which plaintiffs’ contributing negligence is taken into account and assigned a percentage – by the jury. The plaintiff is allowed to recover (100-Plaintiff’s percentage) x damages. There are several versions of this regime, but most states adhere to the modified version, which sets a bar for plaintiff’s recovery – e.g., if plaintiff is more than 50 percent responsible, no recovery.

    One of the concerns with such a system is that juries will, like I said above, simply work around that number to get the outcomes they want – but only if they know the effects of going over or under certain benchmarks. A lot of judges, therefore, DO NOT instruct the jury about the benchmark itself. They simply tell the jury, “Find a percentage, I’ll do the math.”

    Of course, that’s perfectly consistent with Professor Landsburg’s theory. After all, if you tell a jury what happens if you go over or above a benchmark, then based on what I’ve said, they’ll make quick work of their verdict by choosing something over or under that number to fit their “gut feeling.” If the judge doesn’t tell them, on the other hand, they may sit back there a little longer and try to get more “accurate” numbers. Whatever that means.

  5. 5 5 Harold

    “Judges undoubtedly think, for example, that they are better than average at telling if a person is lying.”
    I would be surprised if this were the case – do they really think this? However, it is probably true that a great many people think they are better than average. I think 80% of drivers put themselves in the top 20%

  6. 6 6 Alan Gunn

    Juries are made up largely of people who have no notion of what a 90% likelihood of guilt might mean, people who. in a lot of cases, may think 90% means “more than likely.” A recent non-fiction book about a trial featured a juror who insisted that even if the jury found the defendant not guilty, he’d do serious time. Studies show that a large fraction of jurors think the phrase “proximate cause,” which relates to a concept the jury is supposed to rule on, means “approximate cause.” Before taking seriously the idea that jurors should try to quantify their notions about guilt, we should consider reforms that would guarantee that jurors can read, write, and count.

    My personal favorite jury story comes from a Federal trial of some accountants for professional malpractice. After several days of expert testimony, the jurors sent the judge a note saying that none of them understood any of the testimony. The judge’s response was to tell them to do the best they could.

    James Gould Cozzenzs put it well when he described his fictional jury in “The Just and the Unjust” as made up of people whose opinions you would never dream of asking for on any issue of importance.

  7. 7 7 Steve Landsburg

    Alan Gunn:

    Juries are made up largely of people who have no notion of what a 90% likelihood of guilt might mean, people who. in a lot of cases, may think 90% means “more than likely.”

    They are also made up largely of people who have no notion of what a reasonable doubt might mean. The difference is that it’s possible to explain the notion of a 90% likelihood and quite impossible to explain the nebulous notion of reasonable doubt.

  8. 8 8 Harold

    Given these stories from Alan Gun and others, it is amazing juries seem to do as well as they do.

    If you say top a jury “the doubt should be less than 90%”, then some people would throw up their hands and go blank. If you say “the doubt should be beyond reasonable”, then some people say “but what does that mean?”. We are advised that we should teach or coach to all learning styles, so you should present information in varying ways, knowing that some of them will mean nothing to some, but hopefully will be useful to others. It would be very helpful if the level of “reasonableness” was quantified, to give those members of the jury that think that way (and the judge) a good handle. The standard is primarily “reasonable doubt”, but we should be told what that means.

    To do so is to openly acknowledge that you are willing to accept a certain number of innocents convicted. It would take a brave politician to admit this. If you say “the jury decides on reasonable doubt”, then it implies it would be unreasonable to expect any different. If you come right out and say “I want 10% of convicted people to be innocent”, that sends a very different message. You may not use those words, but that is how the media would put it. I don’t know if was ever any different, but it seems that today no politician has the courage to take on an issue like this. Or maybe some do, but they get destroyed before we ever get to hear about them.

  9. 9 9 Al V.

    There are many other ambiguities in our legal system, that make it difficult for juries to reach a consensus. In fact, it seems to me logical that these ambiguities lead to many of the hung juries and strange verdicts we read about in the press.

    Last year I was a juror in a case where a women was accused of Assault and Battery. It was quite obvious from the testimony that she had assaulted, but not battered (she had attempted to strike the other person, and gotten beaten up for her trouble, but none of her swings landed). We asked the judge if we could convict of Assault but not Battery. Rather than tell us, the judge read us the legal code regarding Assault and Battery. Since none of the jurors were lawyers, that didn’t help us at all and we were no better off after than before.

  10. 10 10 Harold

    AlV. – Very jhelpful judge when all you wanted was “yes” or “no”. What happened? or aren’t you allowed to say? I would assume you had to aquit, as she was not guilty of “Assault and battery” as charged.

  11. 11 11 Roger Schlafly

    Steve, you are really proposing a change in the responsibility of the jury. Instead of deciding guilt or innocence, you want them to estimate a probability. Seems undesirable and unworkable to me. Jurors are not good at estimating probabilities, and even if they were, it is not the ultimate decision that we want them to make.

  12. 12 12 Steve Landsburg

    Roger Schlafly:

    Instead of deciding guilt or innocence, you want them to estimate a probability.

    No, I just want them to estimate whether the probability is above or below 90% (or whatever other standard is set by the legislature). This gives them a more clearly defined (and hence easier) version of the task they’re already performing.

  13. 13 13 Clifford Nelson

    I think that while it is true that we can’t ever be sure 100% of anything in life we can be firmly convinced that a certain person was involved in a crime. So what is reasonable doubt? I would argue that if the jury was only certain that of the 100 possibly ways the crime was committed 99 involve the defendant, an acquittal must result because the jury cannot be firmly convinced of the defendants involvement. This is because the jurors also maintain a belief that he/she may not have been involved. That is reasonable doubt.

  14. 14 14 Steve Landsburg

    Clifford Nelson: So you’ve said that your cutoff is below 100% and above 99%. That’s a much higher cutoff than I’d have chosen, but it’s admirably precise.

  15. 15 15 Dave W.

    Here’s why I say that: Suppose that in a murder trial, the foreman of the jury reports back to the judge that the jurors have agreed that there’s a 15% chance the defendant is guilty, and that they consider 15% to be beyond a reasonable doubt. Therefore they have unanimously voted to convict. I am not a lawyer, but I will cheerfully bet you that in any such case, the judge would throw the conviction out in a hurry, on the grounds that 15% is not at all beyond reasonable.

    I would take that bet. I think the judge would tell the foreman that they must come out and render their verdict and only their verdict.

    the judge might or might not go a step further and order the jury to keep anything that happened during deliberations a secret, upon pain of contempt of court.

    It the judge did declare a mistrial (prior to receiving the verdict officially), it would be on grounds of juror misconduct, and the judge would probably not specify what the misconduct was, or sanction for it.

    One time I tried to argue, to Professor Orin Kerr, that “probable cause” should be reducible to a numerical probability because the word “probable” has a fairly specific and uniform meaning (unlike “reasonable”). He replied that this was impossible with a vague reference to “anchoring theory” (on which there does exist scholarly legal literature. Specifically, I argued that probable cause should be reducible numerically to better evaluate whether drug sniffing dogs can provide this “probable cause,” which seemed to me to be a place where a quantitative reduction of “hit” rates would be especially appropriate because, like, they’re dogs. But supposedly this “anchoring theory” somehow makes that not appropriate. He refused to discuss the matter further. Professors don’t like being argued with, except maybe by other professors. O, well.

  16. 16 16 Seth

    The ambiguous reasonable doubt standard is a healthy deterrent to criminal activity. The best defense is a good offense. Try hard not to put yourself in a situation where your fate is determined by a jury of your peers. If you do find yourself in such a situation, count yourself crazy or unlucky.

    Which brings something else to mind. Why is insanity a legitimate defense? Seems like that should be an automatic lockup. I’d much rather have calculated criminals walking around than insane ones.

  17. 17 17 ErikR

    I think reasonable doubt means that you are at the limit of your ability to distinguish any finer-grained probability of guilt. Maybe you cannot distinguish between 99% and 99.9%, but you can distinguish between 90% and 99%. In other words, reasonable doubt means that you are certain of guilt, to the best approximation of your ability to distinguish certainty.

    I think there really is no other way to explain how people feel. I certainly do not want to be directly responsible for killing an innocent person by voting guilty when I am not reasonably certain that they are guilty. You can argue about letting possible murderers go free and possibly murdering an innocent, but I do not think many people feel that they are responsible for killing someone in that case. Reasonable doubt means that people are reasonably certain of guilt, as certain as they are able to judge.

  18. 18 18 Clifford Nelson

    Professor Landsburg, I didn’t mean to say that my “cutoff is below 100% and above 99%.” What I meant to say is that if a juror is firmly convinced that a circumstance exists in which the accused did not involved in the alleged crime, reasonable doubt exists. This is so no matter how likely or unlikely. As I noted yesterday, one in a billion odds can result in a 90% chance of error (assuming 10 billion people on the planet). Thus, it is not an issue of how likely or unlikely. It is a question of existence, and if such a circumstance exists, you must acquit.

  19. 19 19 Steve Landsburg

    Clifford Nelson: Ah. So you are opposeed to all convictions, in which case we could of course dispense with the justice system altogether. That would at least save some money.

  20. 20 20 Æternitatis

    Excellent point, Prof. Landsburg.

    But it seems doubtful that the motivation for this popular irrationality is judicial self-interest (conscious or not). When I was a law student and an Olin fellow, I did research on related subjects and frequently made the same point you made in your post. I’m sorry to say that every single one of my interlocutors–very few of whom very judges–refused to see the light. But then I may not have been as eloquent as this post.

  21. 21 21 Clifford Nelson

    Professor, I am opposed to convictions where the jurors have a firm conviction that the defendant may not have committed the crime. Nothing more or less, and I am certainly not opposed to all convictions. Thanks for leading this discussion.

  22. 22 22 Æternitatis

    @Clifford Nelson “if a juror is firmly convinced that a circumstance exists in which the accused did not involved in the alleged crime, reasonable doubt exists”

    But such a circumstance exists in every single case! For example, a massive conspiracy between police, witnesses, prosecution, and defense could explain any set of evidence presented to the jury, even if the defendant was entirely innocent.

    And such conspiracies are not merely conceivable–in cases fortunately rare in civilized legal systems, they have actually happened.

    So unless a juror can positively exclude such a conspiracy–and how could he or she?–the verdict must always be “not guilty?”

  23. 23 23 David C

    I’m fairly comfortable with numbers, and I think I’d be hard-pressed to assign a numerical probability to my available evidence on a given day about whether one of my housemates stole a piece of clothing out of my laundry, the cats moved it, or I left it behind the bed and forgot to wash it, say. Maybe with practice I’d get better at doing so… but I can’t think of a good reason to believe the average juror is likely to have had such practice.

    “Reasonable doubt,” by contrast, at least sounds at first blush more tractable, to me. Perhaps it persists as a standard because it sounds tractable to *lawyers*. (I am not one myself; I’m just guessing.)

  24. 24 24 Thomas Bayes

    Thanks again, Professor Landsburg, for an interesting and educational post. My experience with decision theory predisposes me to assess decision (or detection) problems by evaluating the quality of the evidence (or measurements). This discussion has put the focus on assessing the reasonableness of the decision, which has been interesting to ponder.

    Someone has probably ‘invented’ this already, but here is a proposal for a method people might use to assign a level of reasonable doubt to a posterior probability. If Pg is the posterior probability of guilt based on the evidence and priors, then we might quantify the ‘reasonableness’ of the probability as:

    R = -log2(1-Pg)

    To judge Pg, then, we could ask how likely it would be to pick up a fair coin and show ‘heads’ on R successive tosses. R will not always be an integer, but the idea still applies. Here is the relationship between Pg and R for some values of Pg:

    (probability of guilt; reasonableness)
    (0.50; 1.00)
    (0.60; 1.32)
    (0.75; 2.00)
    (0.80; 2.32)
    (0.90; 3.32)
    (0.95; 4.32)
    (0.96; 4.64)
    (0.97; 5.06)
    (0.98; 5.64)
    (0.99; 6.65)
    (0.999; 9.97)

    A probability of 0.97 would have about 5 units of reasonableness, and 5 units of ‘reasonableness’ would mean that you believe the alternative (innocence) is as unlikely as tossing a coin 5 times and seeing heads on every toss.

    We might motivate this conversion by the Weber-Fechner Law, which states that intuitive human sensations tend to scale as logarithmic functions of the stimulus.–Fechner_law#The_case_of_numerical_cognition

    I wouldn’t be surprised to learn that someone has already proposed this and tested it on human subjects. Any references?

  25. 25 25 Alan Gunn

    “They are also made up largely of people who have no notion of what a reasonable doubt might mean. The difference is that it’s possible to explain the notion of a 90% likelihood and quite impossible to explain the nebulous notion of reasonable doubt.”

    But what would be the point of explaining something to people who, for the most part, would be incapable of understanding the explanation? Especially when many of those who would be doing the explaining don’t understand it either. Many people go to law school because they can’t do math. I’ve had more than one law student tell me they couldn’t calculate two percent of 100 without a calculator. I once heard a very distinguished and quite famous law professor express puzzlement about why anyone would ever enter a lottery with a small prize when lotteries with bigger prizes were available. Someone tried to tell him about odds, and his reaction was befuddlement. He seemed to think it was just a matter of you either won or lost, so why not go for the big bucks. (Alas, he was not a poker player or I’d be rich today.) You want these people to instruct people who are even dumber than they are about probability?

    A good deal of appellate practice consists of arguing about the meaning of jury instructions that few if any jurors can reasonably be expected to understand. The reality of the trial process is that juries are given particular problems to deal with when it’s not possible for the courts to make rules about them. The courts are saying something like “we don’t know what the rules should be here, so we’ll let a panel of laypeople decide on the basis of their gut reaction” A famous legal scholar once put it sort of like this (in the context of tort, not crime): the law of negligence consists of a process for determining whether someone is negligent but it has almost no rules about what negligence is.

    All this jury business was originally a historical accident. At first, juries were people who could be expected to know whether the defendant did it or not, unlike the judges, who came in from out of town and didn’t know what had happened. Over the centuries this evolved into a system in which any sort of knowledge relevant to the case rules you out as a juror.

    Anyway, if we did assign a particular probability to reasonable doubt (or any other standard of proof), it would be apparent to almost everyone that the legal system sometimes produces the wrong result. Although sophisticated people know this, uneducated people have an amazingly naive view of the system’s accuracy. Many of them think that failure to charge and convict someone of a crime means that person didn’t do it. Why this happens, I don’t know; maybe it has something to do with the fact that on shows like “Law and Order” the truth always comes out in the end. I don’t think many judges would want to shatter this illusion.

  26. 26 26 Dave W.

    btw, two of my family members have served on juries in the last five years and both juries acquitted even though they thought it highly probable that the defendant did what the defendant was accused of doing. In one case the defendant had a small jackknife which was illegal under state law because the blade was springloaded. the defendant was not threatening anyone or likely to threaten anyone — probably did not know the knife was illegal. In the other case a woman slapped her much larger and drunken husband (who’s antics had gotten the police called in the first place). In both cases the juries felt that the charges had nothing to do with public safety and were being brought to pad police / prosecutor stats. In neither case did the jury feel that police had falsified evidence, but chose to deem a small margin of objective doubt as “reasonable” doubt in view the ridiculousness of the prosecutions. I don’t think these were cases of what lawyers would call “jury nullification.” I think the knife jury wanted the knife law to stay on the books, and the slapping jury wanted domestic violence laws to stay on the books. however, in each case, a sense of the totality of the equities cause the jury to regard probabilistically small doubt as reasonable.

    I would not have agreed with the approach of these juries 5 years agao, but I think my thinking has evolved so that now I think the juries did good.

    So maybe that is why “reasonable doubt” is best not reduced to numbers. I still think “probable cause” and “reasonable suspicion” should be reduced to numbers. “Preponderance of the evidence” already is reduced to a number (that is 0.5).

  27. 27 27 Steve Reilly

    A timely series of posts. For me, at least, since I just finished up with jury duty this week. And, yes, New York’s definition of “reasonable doubt” is as silly as it gets. An honest doubt for which there is a reason. A real doubt, not an imaginary one. A doubt that a reasonable person would be likely to entertain.

    @Alan Gunn, the jury I was on included one man who refused to accept the legal definition of the phrase “in concert with” and instead supplied his own. He wanted to vote guilty for one man on a few charges simply because the man happened to have been near a friend who was committing a certain crime. The juror eventually gave up trying to convince us to convict the man, but only because we’d all decided that he was guilty of a different crime, and so “we’ve got him for something else so it’s not that important”.

    @Seth, why is an ambiguous reasonable doubt standard more of a deterrent than an unambiguous one? It’s not like criminals will figure out a surefire to commit crimes that make jurors 80% but not 90% certain of their guilt.

  28. 28 28 Clifford Nelson

    Æternitatis: I don’t agree with your conclusion. A firm conviction must be based upon evidence. So if a prosecutor meets his burden in presenting the case a conviction should properly result unless the defendant presents proof that creates a firm conviction that one or more other persons may be responsible. A firm conviction must be based upon evidence.

  29. 29 29 Steve Landsburg

    Alan Gunn:

    Many people go to law school because they can’t do math.

    But we’re not talking about doing math. We’re talking about drawing a simple line like “Convict if you think that out of 100 similar cases, at least 90 of the defendants would be guilty.” The only math involved is in understanding the numbers 90 and 100. If jurors can’t count to 100, then we’re truly in trouble.

  30. 30 30 Jeff Semel

    About the motivation of judges for not making explicit the standard for reasonable doubt, convicting innocents is politically unpopular. An elected judge or prosecutor is likely to want the number of false convictions to be obscured, not made more salient to the voting public. A judge without any bias on the issue might (reasonably) decide as Steve did that the responsibility for assigning an explicit probability to “reasonable doubt” belongs to the legislature, and therefore do nothing.

    I doubt the politicians would do any better.

  31. 31 31 Clifford Nelson

    Professor, I think the question is why you think the 10% are not guilty. If it is because as a mathematical certainty the evidence cannot exclude other persons … then it is merely a guessing game and not the administration of justice. I would say these types of cases should not be prosecuted. That is quilt by type (where the type has a high likelihood of guilt) and is highly prejudicial.

    On the other hand, it may be that the evidence leaves you with doubt even though the evidence excludes all other persons. In that case, I think the question is not the amount of doubt in terms of a percentage, but whether it is reasonable for you to doubt at all. If it is reasonable for you to doubt to any extent, then you should acquit.

  32. 32 32 Steve Landsburg

    Clifford Nelson:

    So here we have a group of 100 cases where, based on one sort of evidence, we believe that 98 of the defendants are guilty. And a here we have a group of 100 other cases where, based on a different sort of evidence, we believe that 97 of the defendants are guilty.

    And you are telling me that depending on the sort of evidence, you can be more comfortable with convicting the second group than the first — sending three innocent people to jail instead of two.

    It’s a pretty serious thing, sending an innocent person to jail. What do you think you’re accomplishing by it?

  33. 33 33 JDC

    Part of the problem is the origin of the “reasonable doubt” standard. In Whitman’s thoughtful book _The Origins of Reasonable Doubt: Theological Roots of the Criminal Trial_, he convincingly argues that the reasonable doubt standard developed in a period when jurors were far more concerned with the dangers of passing judgment than the need for factual certainties. He finds that jurors feared eternal damnation for convicting a defendant and were reluctant to pass judgment, even in cases of clear guilt. To overcome that problem, priests developed the reasonable doubt standard to “comfort, coax, and prod anxious and reluctant Christians.” Whitman further concludes that the standard is perverted because it’s unrelated to its original purpose, and instead serves as a standard of proof designed to protect the innocent.

    Furthermore, there is a generous literature on the statistical nature of the standard, and of course, cases that get the math all wrong.

    Bottom line: there are few (no?) bright-line rules in the law. Why should this be an exception?

  34. 34 34 Cos

    I think you have a fundamental misunderstanding of how people think. There is no percentage, because they can’t determine it, and I suspect most juries don’t model it that way in their head. “Reasonable” refers to both halves of your question.

  35. 35 35 Roger Schlafly

    Yes, the type of evidence matters. It would be nice to have 99% certainty, but if the type of evidence does not allow it, it may be beneficial to settle for less.

    I do think that your proposal to require juries to use statutory probabilities is a very bad idea. It is contrary to the whole idea of a jury trial.

  36. 36 36 Clifford Nelson

    Well …actually I am saying I could never be comfortable and would never convict someone based solely upon a “high” (say 90% – 99.9%) mathematical probability. It must be definitive (100%) and thus limited solely to the defendant for me to convict. In my mind it is either no doubt or a reasonable doubt with this type of evidence.

    It is more difficult if evidence is presented that connected someone directly to a crime. In that case, I have to evaluate the proof and be firmly convinced of the defendant’s guilt. It is not that I would accept a higher error rate (by moving away from the 100%). It is more that, in the above example, if I moved away from 100% the next step (that is the evidence points to two individuals) is a 50% chance of error. Thus, it is either 100% or reasonable doubt (since 50% is a lot of doubt).

  37. 37 37 dave

    i like 95%. it goes well with the normal distribution of the accused.

  38. 38 38 mcp


    What you are saying makes no sense. I think you are just uncomfortable with the idea of quantifying how sure you are. You cannot “deduce” truth from nothing. You must start with two things. First, you must have, in the courtroom situation, “the evidence.” In what situation is there evidence so compelling that it could not have been falsified? Even ignoring that, don’t you think there is always a positive probability of mistakes being made in laboratories, say, when dealing with blood evidence? Say it’s 1%. Then even if it is tested 10 times, to “make sure it’s right,” there is still a .000000000000000001% chance that a mistake was made each time. For any number of checks, this number is greater than zero. I assume, based on your posts, that you disregard blood evidence, DNA evidence, and everything other type of evidence which suffers from this problem, as there is no way to deduce guilt from it.

    The second thing you must have, in order to make logical deductions, is a set of rules for making logical deductions. This is a finer point, but I do not see how one may be totally confident that the rules of logic are sound. Do they seem self-evident? Yes. But what system do I have for formally evaluating them? Even if we did have such a system, which proved the correctness of first order logic, how would we know that the system that did the proving was sound? we could not, without repeating the procedure and running into the same problem. (I am compelled to ignore all the issues presented in this paragraph in my day to day life, but then, I am comfortable with approximation, because I think it is the best thing available.)

    Basically, in all of life, courtrooms included, we are guessing. Where it does not seem like we are guessing, we have guessed before, which creates the illusion that our current guesses are in fact more than that. We find some guesses more likely than others, but we are still guessing. I see no way to call the process something else.

  39. 39 39 Clifford Nelson

    mcp: You have to separate the error rate which attaches to a test from the result. My argument was the result had to point solely to the defendant. You can take another look if you like. I did not discuss the error rate of a test. However, since you asked, I do not think the error rate of the test need be absolutely perfect to convict.

    Further, although we must guess in life, my point was that in court a juror should base his/her decision on information. In the case we were discussing, that information (the mathematical probability of defendant’s involvement) fails to provided a basis from which a juror could decide to convict or acquit. Thus, it is pure guess work.

  40. 40 40 Steve Landsburg

    Clifford Nelson:

    a juror should base his/her decision on information. In the case we were discussing, that information (the mathematical probability of defendant’s involvement) fails to provided a basis from which a juror could decide to convict or acquit

    The mathematical probability is not the information; it is an *expression* of the information.

  41. 41 41 Thomas Bayes


    If stastical decision theory really was pure guess work, then cell phones and the wireless connection I’m using right now wouldn’t work. And in a very important way, the concept of ‘information’ is completely connected to the concept of probability. The amount of information you receive through some message or observation can – and should – be quantified by the amount it reduces your uncertainty.

    Jurors begin a case with much uncertainty about a defendant’s guilt. All of the ‘information’ they receive reduces their uncertainty. At some point their uncertainty could be low enough to convict. It is reasonable to ask that that threshold be quantified.

  42. 42 42 Harold

    Presumably the juror starts with total uncertianty. The prosecution then presents its case. The certianty should then rise to conviction levels, otherwise the prosecution should not have been brought. The defence then presents its case, and the cerainty may or may not drop below whatever threshold is in the jurors mind.

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