# Odds vs. Guilt

In the current day US, the jury for a criminal trial is asked to deliberate and vote on their decision of “guilty” or “not guilty”. How they accomplish this is really up to them. There is no particular guard against a good salesman getting his way, nor of someone particularly stubborn (and hanging the jury) getting his.

Personally, I would argue that justice would be better and more reliably served if jurors were asked simply to state odds for each item of evidence.

For example, the prosecution brings forward a witness. The witness says that he saw the defendant running away from the scene of the crime, soon after the time that the crime is believed to have been committed. The defense points out that this might have been before the crime had taken place, that it was dark at that time, that eye witness testimony is unreliable, that it could have been someone else who looks similar, and that the police might have paid off the witness.

We shouldn’t, now, ask the jury to tell us whether the defense’s arguments open reasonable doubt. Of course they do. It’s always reasonable to doubt. We should instead ask, “What are the odds that the witness’s testimony is correct, versus that one of the defense’s possibilities is the real explanation? Would you bet with the witness 90% of the time? 50% of the time? What?” Each juror would then submit what he thinks is the most reasonable set of odds, and the trial moves to the next set of evidence.

There is accepted math for combining odds. For the one piece of evidence, the juries’ answered would be averaged together. At the completion of the trial, the probabilities would be multiplied. The sentencing would be a factor of the crime and the strength of the evidence.

If the one piece of evidence - the above witness testimony - was the only item of evidence in the trial and the jury’s response averaged out to 50%, then they’d be saying that so far as they were concerned, it is a toss of the coin either way as to whether the defendant is guilty; probably he should just be sent home. If there were 20 items of evidence and the product of their results is that there’s a one in a billion shot that the defendant is innocent; probably he should get the maximum sentence.

The results that I would expect from switching to such a system are:

1. More people would be proclaimed guilty (to some degree) than are at the moment.
2. While a larger percent of those people would be innocent than are today, they would be receiving minimal sentences.
3. Sentencing would become more even across judges.
4. Judgements would more fully be a result of the honest feeling of all of the jurors, rather than a select, outspoken few.

The only argument which I foresee against the method is that people will say that “a significant number of people can’t even figure out how to fill out a voter sheet or to perform basic algebra, how are you to expect them to figure out probabilities?” I don’t expect that most people would be able to understand nor perform probability multiplication, but that’s necessary for the jurors in this method. The court can do that. And I haven’t met the person who couldn’t understand “a flip of the coin”, “one in a million”, or “one in four”. If they can at least do that much, once you’re averaging over 12 people, you’re going to arrive at a pretty firm number, even though each individual in the jury might have to fudge their gut feeling by 12.5% to the closest probability they understand. Overall, I don’t think it’s really a big worry.

There are policy arguments against the method you suggested. The main objection to your suggestion is that our society finds it preferable to let some guilty individuals get away with criminal acts than to erroneously punish innocent individuals.

The only problem with this utterly retarded idea…

…sorry, let me restate that…

…The obvious problem with this utterly retarded idea, is that humans just don’t get probability very well. It’s bad enough as it is - but once you start trying to have them putting a number on things, you’re utterly screwed. Humans just won’t give statistically decent distributions using a likert scale of say 1-8 or 1-10. What on earth makes you think that adding another order of magnitude to the precision will acheive anything?

Hey, either he did it or he didn’t. That’s fifty/fifty.

This is also dangerously close to deciding by drawing lots which is specifically prohibited. The jury isn’t there to assess the odds of innocence, as a matter of fact they’re only supposed to convict if they are 100% sure that the person committed the crime. They don’t have to believe any particular piece of evidence at all. This would be a disaster. Among other things, it’s an inducement to have the prosecution flood the jury with evidence to throw the odds in their favor.

One problem with this approach is that the credibility of each piece of evidence doesn’t stand in isolation. Rather, some pieces reinforce each other, while others undercut each other. What matters is the totality of the evidence. How the pieces fit together is the main stuff of jury deliberations.

A bigger problem, though, is that reasonable doubt isn’t a probability calculation. See What percentage probability would be considered “beyond a reasonable doubt?”, a 2002 thread, revived about two months ago starting at Post #35. As explained by various posters there (with cites, see especially Post #43), reasonable doubt is a judgment call by the jury which the courts uniformly refuse to define in quantitative terms. IOW, a key premise of the OP is flawed.

The Romans actually did something quite similar to this–they allowed for such a thing as “half guilty,” for example. The guilt was additive, so if enough people though there was a fifty-fifty chance he did it, well then, hasta la vista.

I wouldn’t trust a modern jury to realize the mathematics of probability. For instance, if someone thought the guy was probably guilty, they might say 80%, when that number would wrongly convict 20% of defendants even if they had the probability correct.

You have to consider that the state, wielding all of the power in a criminal proceeding, should necessarily bear a heavy burden of proof. “Probably guilty” should never equate to a verdict of anything other than “not guilty.”

And what about the reputation of people that are now “aquitted” which in the future will be “30% guilty”…?

There is also an issue of the weight given to each piece of evidence – should each piece really be of equal importance? Should five eyewitnesses to a rape outweigh a negative test result on a suspect’s DNA? What about four witness? Three? who is going to decide whether any particular pieces of evidence should be more or less important than others?

There’s two problems right there. In complex problems there is no “accepted math for combining odds.” Does a case depend on both voice and face ID (MULTIPLY probabilities) or would either suffice (ADD exclusive probabilities)? And “averaging probabilities” is not as appropriate as it may sound. Elsewhere I think I’ve shown my example of two weather predictors each predicting 90% chance of rain. Depending on their methodologies the inferrable chance may be less than or greater than 90%.

Not to mention other problems. Your method strongly tends to circumvent the jury deliberation which is at the heart of the jury concept. And, most importantly, you ignore that few people are adept at odds estimation. I’ve had expert circuit designers tell me with a straight-face that if there are only two possibilities the odds are 50:50.

If I were on a jury, probabilities would likely be prominent in my own thinking. For me, O.J. Simpson’s guilt was beyond reasonable doubt simply because no reasonable alternate theory was ever suggested.

You’re underscoring the other problem with the OP’s idea: juries aren’t rational. Even if they could flawlessly assess the probability of guilt, there’s no guarantee that would actually be a factor in their decision.

In the case of OJ’s trial, there could have been a video of OJ walking into a bar with Nicole Simpson’s head tucked under his arm, and him buying a round of drinks for everyone while shouting “I killed the bitch and the asshole who was fucking her!!!” while tossing her head in the air like a soccer ball, and that particular jury–with nine blacks, one Latino–and two whites–would never have voted to convict (one of the two white jurors wanted to deliberate for longer than the actual four hours they spent, but he was dissuaded by snarled death threats from other members of the jury).

So aside from the hopelessness of quantifying the probability of guilt, there’s no guarantee a jury would be objective anyway.

I’ll grant that I didn’t consider this. Correcting for it isn’t too difficult though. The defense attorney and the prosecution attorney will have to agree to some particular set of math. Where they can’t come to agreement, the judge decides.

Unless I’m missing something, you seem to be saying that because we have never done it this way and have never considered this to be the way that we are attempting to do things, it is bad and wrong.

The OP wasn’t written to say that we can achieve what we are attempting to do today in a better manner, it was written to compare an entirely different way of doing things to how we do it today.

To what benefit? Let’s say that putting someone into jail, when they didn’t deserve it, is equivalent to the crime of kidnapping someone. Kidnapping is worth 32 points, it seems. First degree murder, by comparison, is worth 43 points (it’s worse).

With some statistics work on crime rates, recidivism, etc. I should be able to find a certain minimum probability (say, 1 chance in 100 that you are innocent) at which we start to assign sentences such that for every one innocent who is convicted, the number of guilty who are also convicted is worth the cost. Society eats the -32 score but then makes it back by preventing an equivalent or higher quantity of crime. Overall, the world is a better and safer place.

Think of it like the draft. If society feels that sending you to your death is worth it to protect our way of life, then we have every right to do so. It might not be nice or fair, but it is part of your expected social duty. Going to jail when you did no wrong, to save two or three others from being murdered might suck, but you’re a hero for taking it like a man.

No that’s completely unacceptable. Only a jury – more accurately, each juror individually – can decide which pieces of evidence are more or less important than others. Do you really want a judge to tell a jury that one piece of outweighs another, and suggest or outright instruct them to ignore the less important evidence? The judge’s role in evidence is deciding whether a jury gets to see it at all, which is pretty fuckin’ important, not to tell them how much each piece is worth.

Seriously, if the judge does that, there is no need for a jury at all. A mathematical formula will determine guilt, and the judge gets to decide which numbers to plug into the formula.

Almost forgot … the prosecution and defense will never mutually agree on the relative importance of different pieces of evidence. It is completely against their interests. Because their agreement on any of this stuff will basically lock in a verdict.

*[citation needed]

There is nothing logically objectionable about the method you’re suggesting. However, it’s just unacceptable to most modern societies that place a significant value on personal liberty. Like I said, our society has decided that it’s better to allow some guilty individuals go free in exchange for higher assurances that the innocent will be less likely to be imprisoned. This is why criminal law assigns the burden of proof on the prosecution. It’s also why we require a higher standard of proof (beyond a reasonable doubt) in criminal cases.

Compare this to the lowered standard (generally a preponderance of the evidence) in civil cases, when personal liberty is not at stake.

By that logic, the government would never be able to pass a yearly budget because the Democrats and the Republicans will never be able to come to a mutual agreement since they have (by definition) diametrically opposed views. And yet, for the last 200+ years they have successfully done it because, well, eventually you want to be allowed to go home and get dinner.

This is a nonsensical comparison. Two opposing attorneys at trial are in an adversarial, and only an adversarial relationship. Legislatures are not supposed to work that way – members are supposed to work toward the same goals, which are laws to make things better for their constituency. Even if they are of different parties, they may still find common ground so each can feel the result is a net improvement.

If two opposing lawyers compromise and come to an agreement, that is called a plea bargain and there is no trial. More than 90% of criminal convictions are the result of plea bargains. The very fact of a trial happening is a strong indicator that compromise has already failed.

It was a certainty that someone would bleat, er, ask for this.

I distinctly remember that juror giving a television interview some months after the verdict. No, I don’t remember to whom or on what network he gave the interview. I looked, but I can’t find in on the internet.

So I must be imagining this, since if it isn’t on the internet, it doesn’t exist.

Sage Rat, I’m going to leave the debate to others. Frankly, I mainly posted because I recognized this as similar to the prior thread. And, since I had gone to the trouble of digging up the link, thought I’d save others who also recognized it the bother of doing the same.

There’s no way lawyers would have the math skills to do it, even if it did make sense otherwise (which it doesn’t). Nor would the judge.

Do any of you remember your probability courses, and how a seemingly simple problem could be unimaginably hard to set up properly. Intuition about how to simplify the problem was usually wrong. I only remember two times in my life where I really felt stupid; one was in probability class, and the other was a high school English class section on poetry. Fortunately, I wasn’t any stupider than any of the other students. And in essense, it really is SO simple (just count up the cases in the sample space and divide.)

Yup, it was hard enough, and that was for problems that are easy to quantify, like dealing bridge hands (how many bridge deals are there? Seems simple, right?) Now try to apply that to real world stuff that is difficult to quantify (that guy was SURE he’d seen the defendent, but might not have had his glasses on), and then factor in, as mentioned above, interrelationships between different evidence.

Good luck! It’s NOT a math problem.