Back To The Shoe Argument

[SNOWBALL]

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For example, if the defendant admitted to being at the crime scene, the shoe-print is practically irrelevant. That's why I said it depends on so many other factors.


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did you read the OP?
DS said they know they footprint belonged to THE MURDERER.

[Taraz]

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For example, if the defendant admitted to being at the crime scene, the shoe-print is practically irrelevant. That's why I said it depends on so many other factors.


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did you read the OP?
DS said they know they footprint belonged to THE MURDERER.

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LOL, wow I'm blind.

[bunny]

The guy is obviously more likely to be guilty the rarer the shoe size. How is this even debatable?

[BIG NIGE]

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I need to resurrect it with all this mathematical wrangling going on about evidence. I forget what people's original answers were.

Suppose a man is on trial for murder and the jury is on the verge of acquitting him in spite of their strong suspicion of guilt because the evidence leaves room for reasonable doubt. But at the last minute a footprint is uncovered at the murder scene. It is definitely the murderer's. And it is the same size as the defendent. If it wasn't, its instant acquittal. But since it is the jury is now contemplating a conviction.

Do you agree or not that the rarer the shoe size, the greater the reason for the jury to convict?

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No. The jury should acquit no matter what unless the footprint is so large or small (or have any other kind of unique identification marking) that there's no other person in the area who could *reasonably* have it, thus removing the reasonable doubt. Of course, the whole premise of this question, or argument as you call it, is highly questionable, because it is hard to imagine a circumstance in which the footprint would "definitely" be the murderers, not to mention that it is HIGHLY improbable that an entire trial would go on and then all of a sudden a footprint is found after investigators have combed the area thoroughly multiple times, as is the case in murder investigations. At that point it would be almost as likely that while he was in jail or out on bail during the trial, he himself or someone else took the defendant's shoe and just planted it there.

[jason1990]

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OK, now assume that the shoe size fits one percent of the population. Now lets go back to the million identical defendents. 800,000 are guilty. All 800,000 have that shoe size.

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Okay.

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200,000 are innocent. 2,000 have that shoe size.

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Not necessarily. If these 200,000 people were an unbiased random sample from the population at large, then yes, 2,000 would have that shoe size. But they are not a random sample. They are 200,000 people who are on trial for murder, who are faced with the same set of evidence against them (whatever that evidence may be), and who happen to be innocent. The proportion of them with the murderer's shoe size need not be 1%. It could be anything and would depend on a number of factors. For example, suppose the evidence indicates that the police suspected early on that the murderer was a large man. They therefore ruled out suspects that were of small to average stature. Hence, in those 200,000 instances where they picked the wrong man, their choice would have been biased toward larger men whose shoe size is larger than average.

Besides all this, though, there is another issue. There are not 1 million defendants. There is only 1. When you hypothesize 1 million identical defendants, you are simply building a probabilistic model. And you have built assumptions into that model. In this case, you assumed 2,000 out of the 200,000 innocents would have the murderer's shoe size. This may not be a good assumption. You could replace it with a different assumption if you like, but in the end, you will still only have a model of the situation which is based on subjective assumptions. It should be recognized as such, and not seen as some indisputable truth. The math may be indisputable, but the model is not.

[LooseCaller]

score another one for realizing that pure probablistic models will always be flawed when imposed on reality.

[PLOlover]

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Bringing it down to one defendent, the shoe evidence should change the juries probability of innocence from 20% to one fourth of one percent. The fact that juries may not think that way is neither here nor there.

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I don't think most people think that way (.2)*(.01)=about1/4 of one percent

but rather people look at it like he's about 80% guilty, this new evidence points to 99% guilt, but the 80% guilty is an amalgamation of guilt approximations (66,70,90,95,50,45,88,90...)
so
when you throw in that 99 to the above data it won't sway it as much as you think.

I guess I'm saying that in your example you're giving the shoe data point as much weight as all the other evidence combined, 50% shoe, 50% rest.

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Here's a counterexample that brings the 20% innocent down to 2.5%, which I would argue is "beyond a reasonable doubt".

instead of a shoeprint, at the last moment a witness comes forth who is certain of only one thing, the murderer was black. The defendant is also black. Let's say the percentage of blacks in the population is 10%.

OK, now assume that the RACE fits ten percent of the population. Now lets go back to the million identical defendents. 800,000 are guilty. All 800,000 have that RACE. 200,000 are innocent. 20,000 have that RACE. The other 180,000 are sent home. The trial now is for 820,000 defendents. All identical with the (adjusted) exact same evidence. Now the jury believes that 2.5% of the defendents are innocent. (20,000 out of 820,000).

[David Sklansky]

I was going to point out that I am assuming that there is nothing about the case that would in any way point to the defendants shoe size. But I didn't want to make the lesson any more complicated. It appears you don't dispute that this technique is valid if the shoe size is independent. And you surely realize that most of those who would still argue against conviction are doing so not due to the technicalities you bring up, but rather because they have no clue how to apply the general math principles. But rather than fix that ignorance, they read your post and think they don't have to.

[David Sklansky]

"No. The jury should acquit no matter what unless the footprint is so large or small (or have any other kind of unique identification marking) that there's no other person in the area who could *reasonably* have it, thus removing the reasonable doubt."

That's just wrong. And even the courts realize that, since they allow prosecutors to argue, when they have several pieces of independent but not by themselves totally damning evidence, that the PARLAY is damning. I think they may use different words though.

[PLOlover]

let me put it another way. say the jury is 50-50, which is of course way reasonably doubtful. Let's put the threshhold at about 95% for conviction.

If at the last moment, a witness comes forward and says it was a black man, and the defendant is black, and blacks are about 10% of population, then presto, theyve reached the 95% threshold (ok approximately, but you see my point).

So a guy who was 50-50 gets convicted just because he's black?