Can Typical Jurors Really Be Consistent Regarding Doubt? [Archive]

David Sklansky

05-31-2007, 03:39 PM

Almost everyone thinks that a 99 percent chance of guilt is beyond a reasonable doubt. Fine in theory. But do they mean it?

A hundred masked robbers invade Tiffanys, and clean them out. No one dies but some clerks are badly hurt. They run into an abandoned subway station where they have an escape planned. Its all captured from start to finish on multiple cameras.

The authorities thwart the escape completely. They are sealed off and trapped undergroung. And eventually marched out one by one. There is no physical evidence linking these individual people to the crime but there are multiple ways of proving that all hundred went underground and had no way of escaping. Period. A slam dunk conviction for everyone.

Except for one thing. When the police go down there they find 101 people. One guy was there exploring. They believe that because all 101 claim to be that guy. And there is nothing to indicate who the real innocent one is. (PLEASE don't bring up the fact that this is admittedly a farfetched assumption).

So now comes the trial. Perhaps for all 101 at once. The jury must convict or acquit them all. Would they do it? If they don't aren't they being inconsistent with their earlier pronouncements?

But the better question is what about if there were 101 different trials? What percentage would convict their one defendent on the one piece of evidence that he was underground? (Don't talk to me about who fidgets in their seats please.) Interesting question. More interesting yet though is the almost certain fact that some juries would convict and others wouldn't. With the undeniably exact same, doubt as to guilt. Do you think that's OK? Chezlaw does.

born2ramble

05-31-2007, 03:48 PM

Not Okay and I would find it very surprising that a jury would convict. In America, the vast majority would rather see 100 guilty men go free (unless some heinous violence occurred) than one innocent go to jail. In the earlier thread, I think everyone was working their way through the process of convicting a person and brought already-locked-in ideas to the table.

When you get to this trial though, and are certain you'd be putting an innocent in jail, extremely few (<.25%) Americans pull the trigger. You'd have to deal with putting an innocent man in jail for the rest of your life, media pressure, and other influences I'm probably not considering.

Make it 10,000:1, or add some more violence in this first case, and we've got a tough spot.

Scary_Tiger

05-31-2007, 04:04 PM

Did you watch Boston Legal last night? Same situation, two children are at home with their drunk of a father, one of them shoots him. In court, both claim it was the other who shot the father. It was actually at the suggestion of the lawyers, clearly a subversion of justice, but whatever.

Spoiler in white: <font color="white">The jury acquits both of them, lawyers drink and pat each other on the back. So according to Hollywood a 50% chance was enough, even for this more serious crime.</font>

As for the OP's example. I'd convict and feel 99.0099 last four digits repeating percent good about it. There would be far too few convictions and justice would not be served the vast majority of the time if the courts required what they say they do to convict.

chezlaw

05-31-2007, 04:57 PM

They should hope I'm on the jury because I'd vote not guilty. this would remain true even if there were an infinite number of them and one explorer.

You have to appaud there brilliance in avoiding any evidence that links them. Well done, next case.

If for ome bzarre reason they are tried individually then sure some will get lucky some unlucky. No point hiding the inherent variance in any justice system by spreading the luck equally amongst them.

chez

djames

05-31-2007, 05:09 PM

If there were enough cameras to capture the 100 villains, but not distinguish them from the 1 extra unknown captured in the subway, then I don't think it would be unreasonable for a jury to assume there were actually 101 villains with 1 escaping the cameras. In my opinion, the chance of 1 innocent explorer being in an abandoned subway station who can not provide an alibi seems more rare (using my gut probability model) than the chance that multiple cameras which could count but not identify 100 villains actually just missed the 101st villain.

So, I'd convict all 101.

btmagnetw

05-31-2007, 05:51 PM

[ QUOTE ]
If there were enough cameras to capture the 100 villains, but not distinguish them from the 1 extra unknown captured in the subway, then I don't think it would be unreasonable for a jury to assume there were actually 101 villains with 1 escaping the cameras. In my opinion, the chance of 1 innocent explorer being in an abandoned subway station who can not provide an alibi seems more rare (using my gut probability model) than the chance that multiple cameras which could count but not identify 100 villains actually just missed the 101st villain.

So, I'd convict all 101.

[/ QUOTE ]i hate answers like this.

what do you think about this moral qualm?
well, i'd change the situation in such a way that the dilemma did not exist, then answer it easily.

JMAnon

05-31-2007, 05:55 PM

[ QUOTE ]
In America, the vast majority would rather see 100 guilty men go free (unless some heinous violence occurred) than one innocent go to jail.

[/ QUOTE ]

I wouldn't be so sure. Most people will say something like that, but society has proven to be much more outraged when someone perceived to be guilty goes free than when someone innocent is wrongly punished. More social unrest and public outrage was evident after the Rodney King and OJ Simpson verdicts than when, for example, DNA evidence proves someone innocent after many years of incarceration (which has happened many times in recent years). I wouldn't underestimate the American lust for vengeance and punishment.

vhawk01

05-31-2007, 05:57 PM

[ QUOTE ]
If there were enough cameras to capture the 100 villains, but not distinguish them from the 1 extra unknown captured in the subway, then I don't think it would be unreasonable for a jury to assume there were actually 101 villains with 1 escaping the cameras. In my opinion, the chance of 1 innocent explorer being in an abandoned subway station who can not provide an alibi seems more rare (using my gut probability model) than the chance that multiple cameras which could count but not identify 100 villains actually just missed the 101st villain.

So, I'd convict all 101.

[/ QUOTE ]

Yeah, the OP forgot to mention that there was a sign on the subway that said exploring was a crime and that the punishment was the exact same as for robbery. So this is an easy one, convict them all, who cares which one gets the exploration charge and which the robbery charge.

gumpzilla

05-31-2007, 05:58 PM

[ QUOTE ]
i hate answers like this.

what do you think about this moral qualm?
well, i'd change the situation in such a way that the dilemma did not exist, then answer it easily.

[/ QUOTE ]

While you have a point, frequently questions about moral qualms are dumb because they are broken, unrealistic situations for which people have zero moral sense, and so attacking the realism of the situation is a perfectly valid response. I'm not saying this is necessarily one of them.

doucy

05-31-2007, 05:59 PM

[ QUOTE ]
If there were enough cameras to capture the 100 villains, but not distinguish them from the 1 extra unknown captured in the subway, then I don't think it would be unreasonable for a jury to assume there were actually 101 villains with 1 escaping the cameras. In my opinion, the chance of 1 innocent explorer being in an abandoned subway station who can not provide an alibi seems more rare (using my gut probability model) than the chance that multiple cameras which could count but not identify 100 villains actually just missed the 101st villain.

So, I'd convict all 101.

[/ QUOTE ]

If you're going to completely ignore the premises of the original question, then why don't you just say that you'll call Superman and have him stop the crime before it ever happens.

I'd probably vote not guilty.

vhawk01

05-31-2007, 06:01 PM

[ QUOTE ]
[ QUOTE ]
i hate answers like this.

what do you think about this moral qualm?
well, i'd change the situation in such a way that the dilemma did not exist, then answer it easily.

[/ QUOTE ]

While you have a point, frequently questions about moral qualms are dumb because they are broken, unrealistic situations for which people have zero moral sense, and so attacking the realism of the situation is a perfectly valid response. I'm not saying this is necessarily one of them.

[/ QUOTE ]

I think this is definitely not one of them, because I have to imagine some similar situation has happened before and will happen again. I'm sure its rare, but its not absurdly unrealistic (except the 100 bank robbers...pretend its 4 or something).

Lestat

05-31-2007, 06:31 PM

I've always found assessing doubt to be difficult. I play poker for a living and I STILL have a hard time deciding whether I'm 98% sure, or 89% sure that I'm beat when deciding to call a river bet. In other words, after exhausting any applicable Bay's Theorum, you think you're beat. So how does being 99% sure, feel any different than being 89% sure?

Now if I do this for a living and struggle with it every day, I'm sure a typical juror would struggle. However, I must be doing a somewhat comptetent job, because I haven't gone broke yet.

While I understand the math is extremely important in this area, I don't understand how to apply it when it comes to assessing doubt. Until someone can teach me the difference between what 98% sure and 90% sure FEELS like, I don't think I ever will.

andyfox

05-31-2007, 06:59 PM

I think most juries would be less likely to convict in your hypothetical case than they would be if they were 99% sure about an individual being tried for a crime he committed alone. That's because in the case of the individual, they're 99% certain he's guilty; they'd feel there's very little chance they convicted an innocent man. But in your hypothetical, if they convict, they'd be 100% certain they were convicting somebody who is 100% certain to be innocent.

I think most juries would be more likely to convict all 101 if the clerks died.

As for your "Do you think that's OK?" question in your last paragraph, that's a tough one. Ideally, we would want everyone judged equally. But how does one determine 99% certainty vs., say, 88% certainty? And how does one set a standard that's more concrete than the current "beyond a reasonable doubt?" What's reasonable to you might not be to me.

There have been similar situations posed in some movies. If memory serves, Inside Man and Quick Change had elements similar to the predicament you pose.

gumpzilla

05-31-2007, 07:07 PM

[ QUOTE ]
I think most juries would be less likely to convict in your hypothetical case than they would be if they were 99% sure about an individual being tried for a crime he committed alone. That's because in the case of the individual, they're 99% certain he's guilty; they'd feel there's very little chance they convicted an innocent man. But in your hypothetical, if they convict, they'd be 100% certain they were convicting somebody who is 100% certain to be innocent.

[/ QUOTE ]

This is an excellent point.

PairTheBoard

05-31-2007, 07:25 PM

[ QUOTE ]
I've always found assessing doubt to be difficult. I play poker for a living and I STILL have a hard time deciding whether I'm 98% sure, or 89% sure that I'm beat when deciding to call a river bet. In other words, after exhausting any applicable Bay's Theorum, you think you're beat. So how does being 99% sure, feel any different than being 89% sure?

Now if I do this for a living and struggle with it every day, I'm sure a typical juror would struggle. However, I must be doing a somewhat comptetent job, because I haven't gone broke yet.

While I understand the math is extremely important in this area, I don't understand how to apply it when it comes to assessing doubt. Until someone can teach me the difference between what 98% sure and 90% sure FEELS like, I don't think I ever will.

[/ QUOTE ]

This is why I think it loses a lot in translation when the Human Terms for Reasonable Doubt are translated to a number like 99%.

[ QUOTE ]
Proof beyond a reasonable doubt, therefore, is proof of such a convincing character that you would be willing to rely and act upon it without hesitation in the most important of your own affairs. However, it does not mean an absolute certainty.

[/ QUOTE ]

People can relate to and understand that. They have a Feel for that based on their own life experience. In most cases the evidence does not so clearly translate to a proability as in the OP.

From my understanding of the Reasonable Doubt as defined by the Court above, if I were about to cross a bridge which I knew had 1 chance in 101 of collapsing as I crossed and killing me, I would hestitate using the bridge until they fixed it. So I would have Reasonable Doubt for all defendants in the OP case.

There is definitely a difference between convicting 101 people where you Know you are sending 1 innocent man to prison, and convicting 1 man you know has only 1 chance in 101 of not being guilty. In the first scenario there is a 100% chance that an innocent man is being convicted. In the second scenario that is not the case. So I think it's understandable if Juries would decide differently. In fact, I think it is incumbent on the OP to make the case that this difference is an arbitrary psychological one rather than a substantive one. It seems to me it depends on the measure of Evil you place on convicting the innocent man. Is that the kind of measure on which you can make EV calculations? I think that's debatable.

PairTheBoard

Taraz

05-31-2007, 07:25 PM

David Sklansky

05-31-2007, 11:17 PM

David Sklansky

05-31-2007, 11:28 PM

"There is definitely a difference between convicting 101 people where you Know you are sending 1 innocent man to prison, and convicting 1 man you know has only 1 chance in 101 of not being guilty. In the first scenario there is a 100% chance that an innocent man is being convicted. In the second scenario that is not the case. So I think it's understandable if Juries would decide differently."

In other words a juror who will always vote to acquit if they are tried together might very well vote to convict if the facts remain the same but he is deliberating about only one of the defendents? You think that is OK? The innocent guy gets off under one scenario but often not under the other?

The proper mindset for the juror to have in an individual trial is to come to the same verdict as he would if they were tried together. As I'm sure your buddy Jason would agree.

PairTheBoard

06-01-2007, 12:25 AM

[ QUOTE ]
[ QUOTE ]
"There is definitely a difference between convicting 101 people where you Know you are sending 1 innocent man to prison, and convicting 1 man you know has only 1 chance in 101 of not being guilty. In the first scenario there is a 100% chance that an innocent man is being convicted. In the second scenario that is not the case. So I think it's understandable if Juries would decide differently."

[/ QUOTE ]

In other words a juror who will always vote to acquit if they are tried together might very well vote to convict if the facts remain the same but he is deliberating about only one of the defendents? You think that is OK? The innocent guy gets off under one scenario but often not under the other?

The proper mindset for the juror to have in an individual trial is to come to the same verdict as he would if they were tried together. As I'm sure your buddy Jason would agree.

[/ QUOTE ]

Why did you omit my sentences right after what you quoted David? They are the pertinent ones to your question and the ones you have to respond to.

[ QUOTE ]
It seems to me it depends on the measure of Evil you place on convicting the innocent man. Is that the kind of measure on which you can make EV calculations? I think that's debatable.

[/ QUOTE ]

Have you ever studied "Measure Theory" David? Do you know it is the foundation for mathematical probability? Do you know that in order to compute EV for a function you need it to be a measurable function from a probability space to some measure space? Do you know that not all Spaces are measurable? If you don't understand these things maybe you should step aside like the archaic baseball manager who is making decisions by the seat of his pants.

It's possible that the measure of Evil is not a measure space. It's possible that measures of Evil do not add up. It's possible that the measure of Evil for 100 convictions each with 1% chance of innocence does not equate to the measure of Evil for 1 100% Certain conviction of an innocent. And that's precisely what the Jurors might intuit.

Now argue against that if you like. But when you respond and quote me, please don't leave out the statements most pertinent to your response.

PairTheBoard

David Sklansky

06-01-2007, 01:01 AM

It's possible that the measure of Evil is not a measure space. It's possible that measures of Evil do not add up. It's possible that the measure of Evil for 100 convictions each with 1% chance of innocence does not equate to the measure of Evil for 1 100% Certain conviction of an innocent. And that's precisely what the Jurors might intuit.

Now argue against that if you like. But when you respond and quote me, please don't leave out the statements most pertinent to your response.

I won't for now, disagree with your argument that there is a difference between convicting one innocent person for sure or subjecting 100 innocents to a one percent chance. But your arguments don't apply here. Especially if we postulate that there are 101 trials, all the jurors think like you suggest, and they all know that there are one hundred equivalent trials going on. In that case the juror who would vote for conviction in a single trial is aware that equally thinking jurors will do the same. Which means that he is advocating the conviction of the innocent with his guilty vote, even though he would vote for acquittal in the one trial case.

Lets rephrase that. A juror presumably thinks he is voting correctly. Thus he thinks that it would be right for other jurors to do the same. But then he would also think it right that the other jurors in all the other trials to vote the same. Which means he thinks it would be right to get 101 convictions. But that contradicts the claim that he would vote to acquit if all 101 defendents were presented to him at once.

Or yet another rephrasel. You are the one person jury, or if you like the judge. You supposedly would convict if one defendent is presented to you but would acquit if they all are at once. Instead they actually all presented to you one after another but you don't realize that and think each one is the last. Smoke clears, you convict them ALL. Even though had you known you would get all the case you would have acquitted them ALL. This absurd result has nothing to do with measure theory.

chezlaw

06-01-2007, 01:11 AM

[ QUOTE ]
Lets rephrase that. A juror presumably thinks he is voting correctly. Thus he thinks that it would be right for other jurors to do the same.

[/ QUOTE ]
If I understand you correctly this doesn't follow. Just because I think it correct for me to vote not guilty doesn't mean I think other jurors are correct to vote not guilty.

chez

PairTheBoard

06-01-2007, 01:28 AM

[ QUOTE ]
PTB -
It's possible that the measure of Evil is not a measure space. It's possible that measures of Evil do not add up. It's possible that the measure of Evil for 100 convictions each with 1% chance of innocence does not equate to the measure of Evil for 1 100% Certain conviction of an innocent. And that's precisely what the Jurors might intuit.

[/ QUOTE ]

[ QUOTE ]
Or yet another rephrasel. You are the one person jury, or if you like the judge. You supposedly would convict if one defendent is presented to you but would acquit if they all are at once. Instead they actually all presented to you one after another but you don't realize that and think each one is the last. Smoke clears, you convict them ALL. Even though had you known you would get all the case you would have acquitted them ALL. This absurd result has nothing to do with measure theory.

[/ QUOTE ]

Except that this is not how it's working. A Juror in one trial has no knowledge of anything except the evidence presented for the guilt or innocence of the defendant on trial. That makes each trial Independent. If you redefine the process so that it amounts to 100 seperate but Dependent Trials, in such a way that the 100 trials are equivalent to 1 trial for the 100, then you've Defined your conclusion to be true. You can't criticize one situation by redefining it to be a different situation. The L in your MSL is frayed.

PairTheBoard

David Sklansky

06-01-2007, 01:32 AM

So you are saying that you agree he should change his vote if he knew about the other trials?

Mason Malmuth

06-01-2007, 01:35 AM

Hi Pair:

Guess what, way back when in graduate school I did take a course in measure theory. I also took probability theory. There are some differences when you talk about a measure space in general, and specifically about a measure space that has a total measure of precisely 1, plus a few other specific properties. Thus introducing measure theory into this topic doesn't make any sense to me since what we have here is a basic straight forward probability measure/exercise that is framed by parameters that we are all familiar with. (By the way, I still have my copy of "Royden" if I'm remembering the author's name correctly.)

Best wishes,
Mason

PLOlover

06-01-2007, 01:44 AM

I have no doubt that in 101 seperate trials the juries would use irrational means (how innocent the guy looks, clean cut, etc., good testimony/story) to determine whether their defendant was the innocent one or not.

Over/under on how many get acquitted? I'd put the o/u at 8-10 unless the average age was over 30 then maybe less, the younger the men the better chance they have.

PairTheBoard

06-01-2007, 01:55 AM

[ QUOTE ]
Or yet another rephrasel. You are the one person jury, or if you like the judge. You supposedly would convict if one defendent is presented to you but would acquit if they all are at once. Instead they actually all presented to you one after another but you don't realize that and think each one is the last. Smoke clears, you convict them ALL. Even though had you known you would get all the case you would have acquitted them ALL. This absurd result has nothing to do with measure theory.

[/ QUOTE ]

[ QUOTE ]
So you are saying that you agree he should change his vote if he knew about the other trials?

[/ QUOTE ]

He would judge the first trial based only on the evidence presented on the guilt or innocence of the defendant in front of him. His job is to judge that trial Independently of anything else. If he were then asked to Judge a second trial for another defendant in the same case he would Recuse himself and refuse to judge it. The reason is because the second trial would be dependent on the first.

The proper analogy if you want the same Judge to judge 100 trials is to make them 100 different cases with identical evidence. You might notice that in that situation not only is it possible that the Judge sees 100 guilty defendants, but he could also see 100 innocent ones. They would be Independent. And that's the situation for the original Juror that you criticized. That's Juror's case is independent of any considerations other than the evidence in front of her for that one defendent. If you want to make up different scenarios to criticize, go ahead. But you can't criticize that one on the basis of another one.

PairTheBoard

PairTheBoard

06-01-2007, 02:09 AM

[ QUOTE ]
Hi Pair:

Guess what, way back when in graduate school I did take a course in measure theory. I also took probability theory. There are some differences when you talk about a measure space in general, and specifically about a measure space that has a total measure of precisely 1, plus a few other specific properties. Thus introducing measure theory into this topic doesn't make any sense to me since what we have here is a basic straight forward probability measure/exercise that is framed by parameters that we are all familiar with. (By the way, I still have my copy of "Royden" if I'm remembering the author's name correctly.)

Best wishes,
Mason

[/ QUOTE ]

Hi Mason,

Then I think you would have had an idea what I was talking about here,

[ QUOTE ]
It seems to me it depends on the measure of Evil you place on convicting the innocent man. Is that the kind of measure on which you can make EV calculations? I think that's debatable.

[/ QUOTE ]

I'm talking about measuring "Evil". Does the measure of Evil "add up" like a mathematical measure? Just because we have a function m on the measurable subsets of the space {1,2} that we might think of as a measure, doesn't mean we have a well defined Measure Space. For example,

m{1] = 1
m{2} = 1
m{1,2} = 100

Do we really know how "Evil" adds up?

That was my point. Let's not just assume that things always add up like EV's. Especially when we're talking about something so far afield from math as Evil.

PairTheBoard

David Sklansky

06-01-2007, 02:10 AM

I was talking about the juror who would not judge the other cases but realized that others were. And also realized that the exact same evidence would be presented against each of the 101 individually. Under these constraints you must surely agree that if she would acquit 101 she should acquit one.

David Sklansky

06-01-2007, 02:18 AM

"He would judge the first trial based only on the evidence presented on the guilt or innocence of the defendant in front of him. His job is to judge that trial Independently of anything else. If he were then asked to Judge a second trial for another defendant in the same case he would Recuse himself and refuse to judge it. The reason is because the second trial would be dependent on the first."

But that is logically RIDICULOUS. So WHAT if the second trial is dependent on the first. If he thought that the proper verdict for the first was guilty, so should he for the second. He might recuse himself because it was the law or because he is now worried he will have to judge all of them but if there was just one more defendent he has no reason to change or not render a verdict, given the identical evidence.

Before I continue this debate you will have to find me one other person who agrees with you.

PairTheBoard

06-01-2007, 02:19 AM

[ QUOTE ]
I was talking about the juror who would not judge the other cases but realized that others were. And also realized that the exact same evidence would be presented against each of the 101 individually. Under these constraints you must surely agree that if she would acquit 101 she should acquit one.

[/ QUOTE ]

You're not describing the reality of the court case situation. So you have divorced your model from anything that sheds light on the psychology of the real life juror.

PairTheBoard

PairTheBoard

06-01-2007, 02:25 AM

[ QUOTE ]
"He would judge the first trial based only on the evidence presented on the guilt or innocence of the defendant in front of him. His job is to judge that trial Independently of anything else. If he were then asked to Judge a second trial for another defendant in the same case he would Recuse himself and refuse to judge it. The reason is because the second trial would be dependent on the first."

But that is logically RIDICULOUS. So WHAT if the second trial is dependent on the first. If he thought that the proper verdict for the first was guilty, so should he for the second. He might recuse himself because it was the law or because he is now worried he will have to judge all of them but if there was just one more defendent he has no reason to change or not render a verdict, given the identical evidence.

Before I continue this debate you will have to find me one other person who agrees with you.

[/ QUOTE ]

Well you can create a model about Robots on Mars if you want. But if you create a model that has divorced itself from the reality of the situation you can't use it to draw conclusions about the real situation. It is fundamental to the court system that each trial be independent. You can't create a dependent model and then use it to condemn the actions of people operating on an independent model.

Yes, I agree, If you have Robots on Mars who you can direct to add things up the way you want them to, then they certainly should add things up the way you want them to.

PairTheBoard

PLOlover

06-01-2007, 02:27 AM

[ QUOTE ]
"He would judge the first trial based only on the evidence presented on the guilt or innocence of the defendant in front of him. His job is to judge that trial Independently of anything else. If he were then asked to Judge a second trial for another defendant in the same case he would Recuse himself and refuse to judge it. The reason is because the second trial would be dependent on the first."

But that is logically RIDICULOUS. So WHAT if the second trial is dependent on the first. If he thought that the proper verdict for the first was guilty, so should he for the second. He might recuse himself because it was the law or because he is now worried he will have to judge all of them but if there was just one more defendent he has no reason to change or not render a verdict, given the identical evidence.

Before I continue this debate you will have to find me one other person who agrees with you.

[/ QUOTE ]

I think if the same person was on all the juries (like getting dealt a pocket pair every hand and no one noticing)
and wanted to vote guilty every time,
if he was totally stubborn as a mule there would still be some hung juries,
and if he had some go along to get along in him there would be some acquittals too.

David Sklansky

06-01-2007, 02:28 AM

We have always been talking theoretically here. In real life it would never occur that they would seperate the cases, given the chance for different verdicts.

But the fact remains that if they did, and if the jurors were perfectly aware of the other trials, many would convict if the trials are seperate but not if they weren't.

We both actually agree on that.

What we disagree on is what it says about a juror who would vote differently simply because he personally isn't guaranteed to convict an innocent man.

PLOlover

06-01-2007, 02:32 AM

btw, referencing my over/under post, what chance do you think the actually innocent person has of being convicted?

from my over under post the average would be 90%, but I would put his chance *higher*, maybe even higher than 95%, in any case my point would be that the actually innocent person would be way more likely to be convicted than any of the really guilty.

PLOlover

06-01-2007, 02:44 AM

Lestat

06-01-2007, 03:03 AM

Someone help me out here. I'm sure this oversimplifies things and my thinking is off topic (and fuzzy), but here's the way I see it...

If you try all 101 people with the knowledge that one of them is innocent, you cannot meet the criteria of beyond a reasonable doubt, even if you are 99% sure that each man is guilty. On the contrary, you will be 100% sure an innocent man is being incarcerated. Hence, the only reasonable verdict is to acquit them all.

However, under independant evaluation, I see no reason why reasonable doubt cannot be sufficiently attained. The key is, a judge or juror cannot have prior knowledge to verdicts rendered in previous cases. If you insist that they do, then (I think) I see what PTB is saying, and you have divorced this from any real-world scenario.

There is a reason why jury selection is such a long and tedious process in this country, and why entire cases have been moved to different states if it's even suspected that a juror's conclusion may be biased or tainted by prior knowledge of a case. You simply cannot expect someone to try more than one person in this robbery case.

Although, I think David's contention is that under my scenario (trying each case seperately and in a vacuum), that an innocnet man will still very likely go to jail, and I'm not sure if he's saying that's unacceptable, or that it could be improved upon if jurors were more savvy in math. What I do know is...

No system of justice is perfect. From time to time, innocent people WILL be incarcerated, and guilty people WILL go free. But show me a better system than what the United States of America has come up with.

Now go ahead and tell me what I'm missing, cuz I'm sure there's alot!

PairTheBoard

06-01-2007, 03:05 AM

[ QUOTE ]
We have always been talking theoretically here. In real life it would never occur that they would seperate the cases, given the chance for different verdicts.

But the fact remains that if they did, and if the jurors were perfectly aware of the other trials, many would convict if the trials are seperate but not if they weren't.

We both actually agree on that.

[/ QUOTE ]

I'm not sure we do agree on that. It depends on what "perfectly aware" means. If they are really "perfectly aware" - since we're talking theoretically here - they could have the same experience of the situation as if they were sitting on one Huge Jury of 120 judging one Unified Case. That would "theoretically" be "perfectly aware". The only difference then with a normal case judging all 100 defendants is the number of Jurors. (Notice I'm simplifiying your example throughout to 100 with 1% chance of guilt each).

So it would only be if they were less than theoretically "perfectly aware" that they would judge differently. What would it theoretically mean for them to be partially aware? It would mean they viewed the case as partially Dependent on the others and partially Independent. That part they viewed as Independent would be subject to my observations for that situation in it's pure form. That is, the real life situation.

So this Theoretical "perfectly aware" term just muddles things between Dependent and Independent trials. We have a sense that they really could not be Theoretically Perfectly aware and would act partially as if the trials were independent. You then use that sense to conclude they are not behaving as they should according to your theoretical model. You have successfully muddled the issue.

[ QUOTE ]
What we disagree on is what it says about a juror who would vote differently simply because he personally isn't guaranteed to convict an innocent man.

[/ QUOTE ]

I don't think your theoretical model is practical for looking at this question. Your model muddles things between a theoretical "perfect awareness" and our sense that such a thing is impossible. If you would just look at my real life model where cases are judged as Independent I think you can examine this question. I actually haven't come to a conclusion about it myself. I've just set up the scenario. But if you try to make rigorous conclusions about it, I think you have to deal with the problem I pointed out about presuming Evil adds up like EV calculations.

Maybe it does, maybe it doesn't. If it doesn't then the jurors who change their vote because they are pretty sure they aren't actually convicting an innocent man, might be doing it in conformity with the way Evil works in this situation. I'm not sure I'm persuaded one way or the other. I think there's little doubt that the Juror psychology is going to be different. But Judging the fairness of that is something else again.

PairTheBoard

PLOlover

06-01-2007, 03:08 AM

[ QUOTE ]
On the contrary, you will be 100% sure an innocent man will be incarcerated. Hence, the only reasonable verdict is to acquit them all.

[/ QUOTE ]

that's a good point.

PairTheBoard

06-01-2007, 03:18 AM

[ QUOTE ]
Someone help me out here. I'm sure this oversimplifies things and my thinking is off topic (and fuzzy), but here's the way I see it...

If you try all 101 people with the knowledge that one of them is innocent, you cannot meet the criteria of beyond a reasonable doubt, even if you are 99% sure that each man is guilty. On the contrary, you will be 100% sure an innocent man will be incarcerated. Hence, the only reasonable verdict is to acquit them all.

However, under independant evaluation, I see no reason why reasonable doubt cannot be sufficiently attained. The key is, a judge or juror cannot have prior knowledge to verdicts rendered in previous cases. If you insist that they do, then (I think) I see what PTB is saying, and you have divorced this from any real-world scenario.

There is a reason why jury selection is such a long and tedious process in this country, and why entire cases have been moved to different states if it's even suspected that a juror's conclusion may be biased by prior knowledge of a case. You simply cannot expect someone to try more than one person in this robbery case. If they were all tried together, then I think anyone would agree they all should be acquitted.

Now go ahead and tell me what I'm missing, cuz I'm sure there's alot!

[/ QUOTE ]

You are right on point Lestat. And maybe the reason David is still talking to me.

PairTheBoard

David Sklansky

06-01-2007, 03:29 AM

[ QUOTE ]
[ QUOTE ]
On the contrary, you will be 100% sure an innocent man will be incarcerated. Hence, the only reasonable verdict is to acquit them all.

[/ QUOTE ]

that's a good point.

[/ QUOTE ]

But if that is true it can't be right to convict all of them individually. And it certainly isn't fair to convict only some of them.

Mason Malmuth

06-01-2007, 03:33 AM

Hi Pair:

You're saying the problem is not well defined. That may be the case and is often a difficulty with these type of problems. However, that doesn't have anything to do with measure theory.

Best wishes,
Mason

PLOlover

06-01-2007, 03:38 AM

[ QUOTE ]
Quote:

Quote:
On the contrary, you will be 100% sure an innocent man will be incarcerated. Hence, the only reasonable verdict is to acquit them all.

that's a good point.

But if that is true it can't be right to convict all of them individually. And it certainly isn't fair to convict only some of them.

[/ QUOTE ]

what if the added axioms of jury duty are like
a) you cannot convict a man if you are certain he is innocent
b) you cannot acquit a man if you are certain he is guilty

then you would have to find the group innocent. It would have no impact on the individual trials.

As to the individual trials and any concept of fairness, in a trial it is an adversarial system and fairness plays no part in it really, both sides try to win basically at all costs.

PLOlover

06-01-2007, 03:44 AM

[ QUOTE ]
what if the added axioms of jury duty are like
a) you cannot convict a man if you are certain he is innocent
b) you cannot acquit a man if you are certain he is guilty

then you would have to find the group innocent. It would have no impact on the individual trials.

As to the individual trials and any concept of fairness, in a trial it is an adversarial system and fairness plays no part in it really, both sides try to win basically at all costs.

[/ QUOTE ]

and btw, b) is usually mentioned in the judges instructions (judge the facts, not the law), and I think a) is pretty much understood as a given.

David Sklansky

06-01-2007, 03:49 AM

Think of it this way. What would the public say if when all the trials were over, some were convicted and some were acquitted? Would there not be an outcry? And if they were all convicted they wouldn't accept that either if they agreed they should be convicted if they were tried together.

PLOlover

06-01-2007, 04:02 AM

[ QUOTE ]
Think of it this way. What would the public say if when all the trials were over, some were convicted and some were acquitted? Would there not be an outcry?

[/ QUOTE ]

no different than everybody thinking OJ is guilty but he got off.

[ QUOTE ]
And if they were all convicted they wouldn't accept that either if they agreed they should be convicted if they were tried together.

[/ QUOTE ]
?, but I doubt there would be much outrage for the one innocent guy convicted because many people have been refused to be let out of prison despite universally agreed upon exonerating DNA evidence, and no one really seems to care.

PairTheBoard

06-01-2007, 04:12 AM

[ QUOTE ]
Hi Pair:

You're saying the problem is not well defined. That may be the case and is often a difficulty with these type of problems. However, that doesn't have anything to do with measure theory.

Best wishes,
Mason

[/ QUOTE ]

It does if the thing that's being assumed but is not well defined is a measure space which upon closer inspection turns out not to be a measure space at all. In this case, the measure of Evil.

PairTheBoard

David Sklansky

06-01-2007, 04:14 AM

But OJ theoretically could be innocent. It is impossible for only some of them to be guilty.

PLOlover

06-01-2007, 04:21 AM

[ QUOTE ]
But OJ theoretically could be innocent. It is impossible for only some of them to be guilty.

[/ QUOTE ]

who was the count somebody who killed his wife in New york city in the 80's I think. Klaus von Bulow I think.

There was some controversy because he admitted killing her or something but he still got off.

Ok, what about Nixon? lolololololol

tshort

06-01-2007, 04:37 AM

[ QUOTE ]
However, under independant evaluation, I see no reason why reasonable doubt cannot be sufficiently attained. The key is, a judge or juror cannot have prior knowledge to verdicts rendered in previous cases. If you insist that they do, then (I think) I see what PTB is saying, and you have divorced this from any real-world scenario.

[/ QUOTE ]

The evidence itself is dependent upon the known innocence of 1 of 100 suspects. So I think the evidence itself disallows a logical juror to independently try a suspect to be guilty. He knows that if his trial is repeated over all suspects one of them is guaranteed to be innocent.

Obviously, for a truly independent trial the evidence would have to just be there is a 99% chance he is guilty (however we know that, assume God said it to you ... b/c he likes to gamble of course). The juror knows as similar trials are repeated over and over again the likelihood that there was an false-guilty charge continually increases but is never known for certain to be true.

This is obvious, but the later is the realistic scenario of a trial.

[ QUOTE ]
What we disagree on is what it says about a juror who would vote differently simply because he personally isn't guaranteed to convict an innocent man. (David)

[/ QUOTE ]

Of course given the evidence as presented in OP the juror is wrong and illogical.

Change the evidence to apply independently to each subject being 99% guilty and we are never guaranteed to convict an innocent man (just more and more likely that we have).

The scenario to allow for the point I believe you are trying to say David is (as PTB stated) pretty unrealistic.

[i]Edit: The juror is wrong because he doesn't realize his logic will guarantee an innocent conviction.

Even with true independent trials the jurors should understand any amount of doubt realistically leads to innocent convictions. Now it's just a morality issue.

jason1990

06-01-2007, 10:09 AM

I do not think that, ideally, the question of how evil their verdict is should enter into the deliberation of the jury. It is not their job to determine the relative evil of convicting the innocent versus acquitting the guilty. They are simply supposed to decide on a verdict of guilty or innocent for the charges that come before them. They must decide this within the rules and framework of the court system. If they think these rules will lead to something they regard as evil, then the place to correct that is, ideally, not in the jury box. The place to correct that is in the legislature (or wherever it is that one might change the system).

jason1990

06-01-2007, 11:24 AM

So we are imagining a juror faced with these two scenarios:

A. He is deciding on the guilt of a single defendant (call him Joe, for ease of notation). The juror knows nothing about the other trials, not even their existence. He votes guilty.

B. He is again deciding on Joe's guilt, but this time knows about all the other trials. He votes not guilty.

You claim the juror is being inconsistent. Your proof uses probability. Let me paraphrase it in my own words in order to isolate the thing I want to comment on. (Again, with my "agenda".) Here is your argument:

Suppose the juror quantifies his doubt by assigning a number to the probability that Joe is innocent. Whatever number he chooses, he should also choose it for the other 100 defendants, since there is the same set of evidence against them all. Since these numbers must add up to 1, he must say the probability that Joe is innocent is 1/101. Since this does not depend on the juror's knowledge of the other trials, the juror is being inconsistent.

But what if the juror chooses not to quantify his doubt with a number? In that case, your argument for inconsistency is not applicable. My impression is that you believe a juror who does not quantify his doubt with the number 1/101 is being irrational or illogical. Am I wrong?

I claim that refusing to quantify his doubt is not only rational, it in fact may be a superior response. By analogy, imagine that I take a quarter and I bend it with pliers. I do not show you the quarter. I force you to choose a number for the probability that this coin will come up heads. You can do no better than to choose 50%. But you are almost certainly wrong. By saying 50%, you are saying the coin is fair. The coin is almost certainly not fair. A smarter answer would be to say, "there is not enough information." Another analogy: an unknown person has selected a positive integer less than 11, written it on a piece of paper and sealed it in an envelope. What is the probability that the number is 7? Again, if you are forced to choose a probability, then you can do no better than 1/10, since you have no information. But this is not necessarily true. Perhaps the person's favorite numbers are 3 and 7, and he flipped a coin to decide between the two. A better answer would be, "there is not enough information."

Similarly, if you ask the juror, "what is the probability that Joe is innocent?" and he responds by saying that there is not enough information, then he is giving you a correct and rational response. Based on this response, he would be unable to quantify his doubt in the way you are suggesting.

It may be true that the juror in question is being inconsistent. But probability does not prove it. And it is also not necessarily true that this juror is "99% certain" that Joe is guilty.

I think your threads are doing an excellent job of demonstrating that mathematics and probability theory, by themselves, are not adequate for deciding the results of jury trials. I cannot tell if these are just fun thought experiments you are posing, or if you really believe you can assign a probability to everything. Since you are a professional gambler, I would guess it is the latter. Some people have a serious misconception about probability. They think that science and/or logical deduction will let us answer those questions in which there is certainty; probability is there to answer everything else. I hope at least some people will read my posts and be dissuaded from this idea. Some things even probability cannot say anything about. For some things, the best answer is "not enough information."

David Sklansky

06-01-2007, 02:28 PM

Your comments do not apply to the people on this thread. They are all willing to quantify chances of guilt at 1/101. You agree that they therefore ARE being inconsistent if the give two different verdicts. Had to say that before PTB jumps all over this.

As to your general comment, I really need to know your background at this point. Because, ironically, I want to practice what I preach and adjust the probabilities that what I plan to say is correct.

In other words I have thoughts in my head. The chances that they are correct change based on whether YOU went to Harvard or the University of Indiana. Sorta funny.

Phil153

06-01-2007, 03:08 PM

Let's get some clarity here.

It's obvious that the two situations are logically equivalent. If an impartial jury will acquit a man under one scenario and not under another, where the differences have no bearing on the likelihood of guilt, then something is wrong in the way they think.

The options in either case are:

- Let 100 guilty men go free as well as the innocent man
- Convict 100 guilty men as well as the innocent man
- Convict some fraction of a innocent man in the same proportion of the fraction of guilty men
- Let some fraction of guilty men go free in the same proportion of the fraction of an innocent man.

The situations are completely logically equivalent. If you don't see that, or think a fraction of a guilty man is absurd, consider trying 100 of these 101 man cases. You come to the same spot.

If you would acquit under one scenario and not another, there is a flaw in your thinking. Period. You can quibble all you like with the circumstances set out in the OP, but under those prescribed circumstances your answers to both questions should be identical.

BTW, boundary conditions such as the above are useful, precisely because they isolate relevant factors and expose sloppy thinking that might otherwise get lost in complexity or Pair-the-Boardian feel-gooderies. Everyone needs to man up and admit Sklansky is right before (rightly?) tearing his hypothetical to shreds.

Also, crimson is for suckers.

PairTheBoard

06-01-2007, 03:28 PM

Sklansky can set up a probabilty model, say with 100 equally likely outcomes. Probablity statements on Events within that model are then beyond debate. But Sklansky then takes the outcomes, events, and probabilities for that model and assigns words to them like, Yada, Yida, Yippe, Boopboop, Slimslam, etc. Those words are words we commonly use in real settings. Slansky can then make statements with those words according to the way he has identified them with the Probability Model and force us to admit statements like,

"The Yida must be concluded to be Yada when the slimslam boopboops."

The sentence sounds like something in real life but there's no necessary connection between the slam dunk must be true statement, "The Yida must be concluded to be Yada when the slimslam boopboops" and anything we recognize as reality. The statement is just an artificial adjoint to the raw Probability Model.

This does not necessarily isolate any fundamental principles. In fact it can be very misleading.

PairTheBoard

PLOlover

06-01-2007, 03:29 PM

I think I can boil it down even more.

100 have already been convicted, the last man is on trial now.

The defense lawyer brings up (and is allowed to bring up) the fact that the state admits that only 100/101 of the group were guilty.

The prosecution says their evidence is overwhelming in this case and the innocent man must already have been (wrongfully) convicted. They further state that if the jury acquits this defendant then the real innocent man will probably never be able to successfully appeal his convicition.

You're the juror, you personally think there is enough evidence to convict this specific person.

Phil153

06-01-2007, 03:32 PM

[ QUOTE ]
But what if the juror chooses not to quantify his doubt with a number?

[/ QUOTE ]
Therein lies the heart of the problem Sklansky is exposing

People rely on feel instead of hard numbers. Relying on feel is tremendously important in weighing complex decisions and non-quantifiable evidence. But sometimes it's flawed. People use it EVEN in scenarios where hard numbers produce more consistent and accurate results.

I think Sklansky would be better served by coming up with powerful real life examples of people failing to use Baye's Theorem. Examples abound but are not obvious to most.

These hypotheticals he keeps putting out are certainly amusing, but lead to an almost religion-like backlash against what is actually a valid critique. People don't like being told their best judgment is flawed, and react pretty strongly to it. Especially when it comes from a certain mr. Do You See Why.

jason1990

06-01-2007, 03:32 PM

[ QUOTE ]
Your comments do not apply to the people on this thread. They are all willing to quantify chances of guilt at 1/101. You agree that they therefore ARE being inconsistent if the give two different verdicts. Had to say that before PTB jumps all over this.

[/ QUOTE ]
My present opinion is that they are being inconsistent even if they do not quantify chance of guilt. Existence of other trials is not evidence in the trial at hand and should not affect deliberations. (Although I agree with everyone who describes your hypothetical as absurdly unrealistic.) I really just wanted to seize another opportunity to preach against unwarranted quantification.

[ QUOTE ]
As to your general comment, I really need to know your background at this point. Because, ironically, I want to practice what I preach and adjust the probabilities that what I plan to say is correct.

In other words I have thoughts in my head. The chances that they are correct change based on whether YOU went to Harvard or the University of Indiana. Sorta funny.

[/ QUOTE ]
Is there even a University of Indiana? There is an Indiana University, and it is actually a very good school for mathematics. It is tied with Duke University for #34/#35 in the NRC rankings. Russell Lyons ( http://mypage.iu.edu/~rdlyons/ ) is at Indiana University and is a top notch probabilist.

At any rate, the community of probabilists is smaller than you might think. So I will not name my institutions. But I will tell you that the school I went to is below Harvard and above Indiana University on this list: http://math.wlu.edu/GradRank95.pdf

Really, though, why not just post your ideas and have an open discussion about them? Why do this Bayesian pre-analysis on the probability that your ideas are good ones?

Phil153

06-01-2007, 03:36 PM

PTB,

Why are you so violently opposed to Sklansky's ideas? I know that probability models are vile and impersonal, but they're also effective when properly understood. Should we give the final word to feelings, even in cases where the data is hard and properly quantifiable?

I personally believe that's just sloppy thinking. A kind of hope that somehow justice will prevail if only we don't close our hearts.

djames

06-01-2007, 03:49 PM

Jason, I applaud you taking the high-road in response to Sklansky's unnecessary arrogance. After such a lucid and logical post, it was unfortunate to read inquiries into your educational history rather than an acknowledgement of the content of your post. I guess that's par on this course though.

chezlaw

06-01-2007, 03:57 PM

[ QUOTE ]
Let's get some clarity here.

It's obvious that the two situations are logically equivalent. If an impartial jury will acquit a man under one scenario and not under another, where the differences have no bearing on the likelihood of guilt, then something is wrong in the way they think.

The options in either case are:

- Let 100 guilty men go free as well as the innocent man
- Convict 100 guilty men as well as the innocent man
- Convict some fraction of a innocent man in the same proportion of the fraction of guilty men
- Let some fraction of guilty men go free in the same proportion of the fraction of an innocent man.

The situations are completely logically equivalent. If you don't see that, or think a fraction of a guilty man is absurd, consider trying 100 of these 101 man cases. You come to the same spot.

If you would acquit under one scenario and not another, there is a flaw in your thinking. Period. You can quibble all you like with the circumstances set out in the OP, but under those prescribed circumstances your answers to both questions should be identical.

BTW, boundary conditions such as the above are useful, precisely because they isolate relevant factors and expose sloppy thinking that might otherwise get lost in complexity or Pair-the-Boardian feel-gooderies. Everyone needs to man up and admit Sklansky is right before (rightly?) tearing his hypothetical to shreds.

Also, crimson is for suckers.

[/ QUOTE ]
I admit it. Notwithstanding the fact that some disagree it seems trivially true. Its the application and implications that are dubious at times.

chez

PairTheBoard

06-01-2007, 04:05 PM

[ QUOTE ]
[ QUOTE ]
But what if the juror chooses not to quantify his doubt with a number?

[/ QUOTE ]
Therein lies the heart of the problem Sklansky is exposing

People rely on feel instead of hard numbers. Relying on feel is tremendously important in weighing complex decisions and non-quantifiable evidence. But sometimes it's flawed. People use it EVEN in scenarios where hard numbers produce more consistent and accurate results.

I think Sklansky would be better served by coming up with powerful real life examples of people failing to use Baye's Theorem. Examples abound but are not obvious to most.

These hypotheticals he keeps putting out are certainly amusing, but lead to an almost religion-like backlash against what is actually a valid critique. People don't like being told their best judgment is flawed, and react pretty strongly to it. Especially when it comes from a certain mr. Do You See Why.

[/ QUOTE ]

I agree with you here Phil. I too am interested in making the case especially to young people that a better knowledge of MSL will benefit them in ways they can't imagine. But there should be plenty of real world examples that illuminate that case which are not muddled up with all sorts of controversial difficulties. Sklansky seems to insist on dwelling on ones which illustrate something almost in opposition to that case. That is, that analogies to mathematical models can often be misleading.

PairTheBoard

PairTheBoard

06-01-2007, 04:36 PM

[ QUOTE ]
PTB,

Why are you so violently opposed to Sklansky's ideas? I know that probability models are vile and impersonal, but they're also effective when properly understood. Should we give the final word to feelings, even in cases where the data is hard and properly quantifiable?

I personally believe that's just sloppy thinking. A kind of hope that somehow justice will prevail if only we don't close our hearts.

[/ QUOTE ]

I will take a bit of the low road here phil, and tell you that I did 4 years graduate studies specializing in probability at a school in the top 20 of jason's list. Jason's school ranks significantly better than the one I went to. I am competent in the subject but Jason is a real talent. He has fluent working expertise in a wide range of mathematics related to probability, which he specializes in. I know this from having followed his posts for some time now both here and in the probability forum.

So I hardly think probability is vile. I find it a fascinating subject and one which everybody should learn more about, including David. What I object to is misapplication of the theory, not just for how such misaplication can mislead us in other areas but because it actually degrades the crediblity of probability for proper application. When Sklansky tries to cram these speculative analogies to probability down our throats he actually does harm to the goal of showing people how useful probability can actually be when properly applied.

PairTheBoard

chezlaw

06-01-2007, 04:48 PM

[ QUOTE ]
Quote:
--------------------------------------------------------------------------------

But what if the juror chooses not to quantify his doubt with a number?

--------------------------------------------------------------------------------

Therein lies the heart of the problem Sklansky is exposing

[/ QUOTE ]
This thread makes my head hurt but its seems its got nothing to do with quantifying doubt with numbers or probabilities of anything.

Its a straight choice between letting 100 guilty men go free or convicting one innocent man. (I don't think anyones arguing for anything inbetween). I don't need to know anything about probability to decide that. Its a pure question of what we believe about justice.

Then there seems lots of confusion caused by talking about trying them together or one at a time which doesn't make any difference if we have the full picture and is irrelevent if we don't.

chez

Jetboy2

06-01-2007, 05:03 PM

[ QUOTE ]
Its all captured from start to finish on multiple cameras.

[/ QUOTE ]

I'm figuring that the Tiffany cameras are pretty damn good. Unlike, say, the grainy, nasty pictures you'd get at a 7-11.

[ QUOTE ]
Except for one thing. When the police go down there they find 101 people.

[/ QUOTE ]

Ok. So you can narrow it down using the excellent camera evidence from Tiffanys.

Probably not logical, but realistic...

David Sklansky

06-02-2007, 01:56 AM

But you are a mathmetician? And a specialist in probability to boot? I ask this because it seems I have a simple refutation to your points about bent coins and not enough information. But if you are an expert you most have dealt with it already.

Also one more last question. Do you think Persi Diaconis would agree with all your criticisms?

David Sklansky

06-02-2007, 02:03 AM

"I think Sklansky would be better served by coming up with powerful real life examples of people failing to use Baye's Theorem. Examples abound but are not obvious to most."

You can do that too you know. False positves in tests for very rare diseases being perhaps the best example. But what does that have to do with this thread. It wasn't about teaching math. It was about inconsistent jurors.

Phil153

06-02-2007, 03:31 PM

[ QUOTE ]
But what if the juror chooses not to quantify his doubt with a number? In that case, your argument for inconsistency is not applicable. My impression is that you believe a juror who does not quantify his doubt with the number 1/101 is being irrational or illogical. Am I wrong?

[/ QUOTE ]
The original post states that the only available information is a defendant's presence in the subway. What other possible model is more accurate than probability when limited to information that is purely mathematical?

I think a lot of the fuzzy thinking has come from not taking David's conditions on board. You can argue black and blue that the real world never fits these conditions (which is an interesting debate), but your other objections do not make sense to me.

[ QUOTE ]
I claim that refusing to quantify his doubt is not only rational, it in fact may be a superior response. By analogy, imagine that I take a quarter and I bend it with pliers. I do not show you the quarter. I force you to choose a number for the probability that this coin will come up heads. You can do no better than to choose 50%. But you are almost certainly wrong. By saying 50%, you are saying the coin is fair. The coin is almost certainly not fair. A smarter answer would be to say, "there is not enough information." Another analogy: an unknown person has selected a positive integer less than 11, written it on a piece of paper and sealed it in an envelope. What is the probability that the number is 7? Again, if you are forced to choose a probability, then you can do no better than 1/10, since you have no information. But this is not necessarily true. Perhaps the person's favorite numbers are 3 and 7, and he flipped a coin to decide between the two. A better answer would be, "there is not enough information."

[/ QUOTE ]
That's true. But what if you are forced to make a decision based solely on the facts that you know? Then you would indeed use a probability model, and anyone who didn't would be insane. Example: someone offers you odds on the flip.

[ QUOTE ]
Similarly, if you ask the juror, "what is the probability that Joe is innocent?" and he responds by saying that there is not enough information, then he is giving you a correct and rational response.

[/ QUOTE ]
The juror is required to convict, or not. Both choices have consquences. Saying "I don't have enough information" is not a useful response unless you also argue that this is grounds for an acquittal. In which case 100 guilty men go free. And we're back to square 1.

[ QUOTE ]
It may be true that the juror in question is being inconsistent. But probability does not prove it. And it is also not necessarily true that this juror is "99% certain" that Joe is guilty.

[/ QUOTE ]
I may be mistaken, but I believe David was trying to show a logical inconsistency - not an issue with probability models. The probabilities given in the OP would be agreed by everyone.

jason1990

06-02-2007, 05:26 PM

[ QUOTE ]
[ QUOTE ]
I claim that refusing to quantify his doubt is not only rational, it in fact may be a superior response. By analogy, imagine that I take a quarter and I bend it with pliers. I do not show you the quarter. I force you to choose a number for the probability that this coin will come up heads. You can do no better than to choose 50%. But you are almost certainly wrong. By saying 50%, you are saying the coin is fair. The coin is almost certainly not fair. A smarter answer would be to say, "there is not enough information." Another analogy: an unknown person has selected a positive integer less than 11, written it on a piece of paper and sealed it in an envelope. What is the probability that the number is 7? Again, if you are forced to choose a probability, then you can do no better than 1/10, since you have no information. But this is not necessarily true. Perhaps the person's favorite numbers are 3 and 7, and he flipped a coin to decide between the two. A better answer would be, "there is not enough information."

[/ QUOTE ]
That's true. But what if you are forced to make a decision based solely on the facts that you know? Then you would indeed use a probability model, and anyone who didn't would be insane. Example: someone offers you odds on the flip.

[/ QUOTE ]
If someone offers me a wager on any of these events, I could easily say, "There is not enough information and I refuse to wager." Depending on the exact structure of the wager, this could in fact be the wisest decision.

Forcing someone to wager is equivalent to forcing them to quantify their opinion on the probability of the thing being wagered. They are automatically using a probability model when they do. So your statement is practically a tautology.

[ QUOTE ]
The juror is required to convict, or not. Both choices have consquences. Saying "I don't have enough information" is not a useful response unless you also argue that this is grounds for an acquittal.

[/ QUOTE ]
To clarify, they are saying "I do not have enough information to form a probability model." That is different from saying "I do not have enough information to come to a verdict in this case." The present legal system does not require a juror to quantify his doubt with a probability. (Of course, it does not forbid it either.) There is a non-mathematical definition of "reasonable doubt" which they are supposed to use. This definition is applicable, even for a juror who concludes that there is not enough information to form a probability model.

[ QUOTE ]
I may be mistaken, but I believe David was trying to show a logical inconsistency - not an issue with probability models.

[/ QUOTE ]
You may be right. My comments were directed only at the issues related to probability models. In the context of David's other recent threads, I thought this was relevant.

John21

06-03-2007, 04:42 AM

[ QUOTE ]
The juror is required to convict, or not. Both choices have consquences. Saying "I don't have enough information" is not a useful response unless you also argue that this is grounds for an acquittal. In which case 100 guilty men go free. And we're back to square 1.

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Hey Phil,

I'm not sure if the jurors are technically required to convict or not. What they're charged with is determining if the State provided enough "proof" that the defendant is guilty beyond reasonable doubt. It's really not on the jurors to dole out justice, they merely decide if the prosecution's case reached a certain threshold or not.

In DS's example, there's simply no conclusive "facts" pointing towards guilt. There's no fingerprints, video, etc., incriminating this particular defendant - it's all circumstantial. Whether it's 101:100, or 50:1, is irrelevant. What matters is the 101:100 is exculpatory evidence, and it carries the same weight with circumstantial evidence as 50:1.

In other words, when weighing circumstantial evidence, the quantity of it doesn't factor in. Whether 100 people robbed the store and 101 were caught, is seen in the same light and given equal weight, as if 1 robbed the store and 50 were caught. And that would hold true whether they were tried together or separately.

Like I said, it's not the jury's job to ensure that justice is being served, that's for the prosecutor. So while it might seem like the prosecutor is presenting a case, he's really just trying to remove reasonable doubt in the minds of the jurors, as to the defendant's guilt. And in this case he won't be able to do it. They must acquit. Or to put it more poetically, "if it doesn't fit, you must acquit".

Take care,
John

Phil153

06-03-2007, 05:25 AM

Thanks for the thoughts, you make some good points. If I ever pull a jewelry heist, I'll be sure to have 100 men in ski masks, one poor sod pulled along for the ride, and you as my lawyer /images/graemlins/grin.gif

jogger08152

06-03-2007, 09:13 AM

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Almost everyone thinks that a 99 percent chance of guilt is beyond a reasonable doubt. Fine in theory. But do they mean it?

A hundred masked robbers invade Tiffanys, and clean them out. No one dies but some clerks are badly hurt. They run into an abandoned subway station where they have an escape planned. Its all captured from start to finish on multiple cameras.

The authorities thwart the escape completely. They are sealed off and trapped undergroung. And eventually marched out one by one. There is no physical evidence linking these individual people to the crime but there are multiple ways of proving that all hundred went underground and had no way of escaping. Period. A slam dunk conviction for everyone.

Except for one thing. When the police go down there they find 101 people. One guy was there exploring. They believe that because all 101 claim to be that guy. And there is nothing to indicate who the real innocent one is. (PLEASE don't bring up the fact that this is admittedly a farfetched assumption).

So now comes the trial. Perhaps for all 101 at once. The jury must convict or acquit them all. Would they do it? If they don't aren't they being inconsistent with their earlier pronouncements?

But the better question is what about if there were 101 different trials? What percentage would convict their one defendent on the one piece of evidence that he was underground? (Don't talk to me about who fidgets in their seats please.) Interesting question. More interesting yet though is the almost certain fact that some juries would convict and others wouldn't. With the undeniably exact same, doubt as to guilt. Do you think that's OK? Chezlaw does.

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Granting all your assumptions:

Not Guilty.

jogger08152

06-03-2007, 09:33 AM

jogger08152

06-03-2007, 10:11 AM

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I've always found assessing doubt to be difficult. I play poker for a living and I STILL have a hard time deciding whether I'm 98% sure, or 89% sure that I'm beat when deciding to call a river bet. In other words, after exhausting any applicable Bay's Theorum, you think you're beat. So how does being 99% sure, feel any different than being 89% sure?

Now if I do this for a living and struggle with it every day, I'm sure a typical juror would struggle. However, I must be doing a somewhat comptetent job, because I haven't gone broke yet.

While I understand the math is extremely important in this area, I don't understand how to apply it when it comes to assessing doubt. Until someone can teach me the difference between what 98% sure and 90% sure FEELS like, I don't think I ever will.

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It does feel different. I'm not sure what the smallest probability interval dinstinguishable "by feel" is, but in at least some cases, it's fairly small.

Example:

Roll two (six-sided) dice. Before you do, make each of the following statements:

"I'm pretty sure I won't roll a 12 here."
"I'm pretty sure I won't roll a 7 here."

Obviously, you probably understand the actual probabilities before you make the roll in this instance, but do the two statements really "feel" equivalent to you? If not, you're able to "feel" the difference between ~97% and ~83%.

Obviously you could make the case that your "feelings" are tainted by your knowledge of the probability; if you think that's an issue, just reflect on the difference between, "I'm pretty sure I'm beat" and "There's no f*cking way that guy raises me on that river without the stone nuts." Again, you're looking at something like 75 and 99 (because of course, despite your feeling, it's certainly POSSIBLE he'll raise you on the end, especially if he thinks you're the type who just might fold), and you (or at least I) *can* "feel" the difference.

Fun aside: Twice recently in local live games, I've seen super-passive nitty old ladies initiate action with with hands I'd never have believed (one had been calling down with top pair (J) against a pfr and bet into him when a 3rd flush card came on the river; the other bet a 4-card straight (K-Q-J-9) on the turn with AQ in the hole after both failing to raise preflop and checking through on the flop.