Back To The Shoe Argument

[PairTheBoard]

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If the blackness is a totally independent factor

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How would you know whether it was or wasn't? If you don't see how race relates to the rigorous points jason1990 has made, you aren't paying attention.

PairTheBoard

[jason1990]

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Firstly lets say that the jury originally believed that there was a 20% chance he was innocent. What precisely do I mean by that? It means that the jury thinks that if they were presented with a million identical cases with the exact same evidence, 200,000 of the defendents would be innocent. First make sure you understand that definition.

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. 200,000 are innocent. 2,000 have that shoe size. The other 198,000 are sent home. The trial now is for 802,000 defendents. All identical with the (adjusted) exact same evidence. Now the jury believes that one quarter of one percent of the defendents are innocent. (2000 out of 802,000).

Bringing it down to one defendent, the shoe evidence should change the juries probability of innocence from 20% to one fourth of one percent.

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Consider the following hypothetical. Across the country, in another town, a second trial is happening at the same time. The second trial is identical to the first, with one exception. In the second trial, a witness on the stand casually mentions that the defendant wears a size 13 shoe. Neither jury at that time knows about the footprint, so the second jury does not consider this testimony to be relevant. Nonetheless, it is part of the transcript of the trial. Both juries then deliberate, and both conclude the defendant is 80% likely to be guilty.

Then comes the footprint, a size 13 footprint known to be the murderer's. The second jury already knows the defendant wears size 13. The first jury immediately checks his shoe size and finds it is 13. So both juries are now in the same situation and they should weigh this new evidence in the same fashion.

But watch what happens when the second jury performs your thought experiment. They consider a million identical cases with the exact same (pre-footprint) evidence. However, for the second jury, the evidence includes the fact that the defendant wears a size 13 shoe. So all 1 million of their hypothetical defendants wear a size 13. It follows that none of their hypothetical defendants are sent home after the footprint is discovered, and their 80% assessment does not change. What went wrong?

[luckyme]

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But watch what happens when the second jury performs your thought experiment. ......

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It's not too late to delete is it?

luckyme

[RED FACE]

I didn't read all the other replies but what if the defense counters this new evidence by proving that the victim had an enemy who had a friend with this same shoe size and no alibi?

If the case is built on circumstantial evidence then such a fact is significant.

[jason1990]

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But watch what happens when the second jury performs your thought experiment. ......

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It's not too late to delete is it?

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Are you suggesting I said something stupid and should delete my post to avoid embarrassment? If I have made a blunder, I do not mind admitting it later. But I am simply illustrating something that David has already acknowledged. Namely, if the pre-footprint evidence points to the shoe size of the defendant, then it will affect the outcome of the mathematical analysis. However, it is clear in the hypothetical that it should not affect the outcome of the actual analysis. This is because, at every point in time, both juries possess the same set of relevant evidence.

If the two situations produce the same actual conclusions, but the math gives two different conclusions, then the mathematical model must be either flawed or incomplete. This apparent contradiction requires an explanation and, I think, demonstrates that things are not quite as simple as they may seem.

[PairTheBoard]

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This apparent contradiction requires an explanation and, I think, demonstrates that things are not quite as simple as they may seem.

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It especially requires explanation in consideration of the Race example. It's a hypothetical that the shoe size might be known prior to the late shoe imprint evidence. But the race of the defendent is clearly apparent to the Jury prior to the late witness evidence.

I could explain it but I'd like to see Sklansky do it. Maybe it will force him to take a second look at his hidden assumptions.

PairTheBoard

[luckyme]

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But watch what happens when the second jury performs your thought experiment. ......

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It's not too late to delete is it?

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Are you suggesting I said something stupid and should delete my post to avoid embarrassment? If I have made a blunder, I do not mind admitting it later. But I am simply illustrating something that David has already acknowledged. Namely, if the pre-footprint evidence points to the shoe size of the defendant, then it will affect the outcome of the mathematical analysis. However, it is clear in the hypothetical that it should not affect the outcome of the actual analysis. This is because, at every point in time, both juries possess the same set of relevant evidence.

If the two situations produce the same actual conclusions, but the math gives two different conclusions, then the mathematical model must be either flawed or incomplete. This apparent contradiction requires an explanation and, I think, demonstrates that things are not quite as simple as they may seem.

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Essentially you're swinging between attributes of this specific defendant and attributes of the actual murderer ( and therefore potential murderers)and morphing them. Their original Million potential murderers shouldn't have size 13 shoes just because this specific defendant does.

In your second trial the jury noticed that the man had red hair, tattoo on nose and his left eye missing but there was no testimony that the murderer had those attributes. Why would their Million alternates have those features. They've reached the 80% convinced of quilt stage on other evidence. None of their Million alternate accused should have those attributes because they are not attributes of the murderer. They should have the known attributes of murderer and could well be the same Million in DS's first case. Essentially, the Million alternates are blankfaced and shoeless until there is evidence that the murderer had X ( slightly simplified).

Late evidence of a video show a man looking like the defendant comes in. Are you sure their 80% confidence in quilt doesn't change?

Eyewitness testimony could never convict a person in your approach because they already knew what the defendant looks like. ??

luckyme

[David Sklansky]

"So it shouldn't matter whether the Shoe Size evidence comes early or late in the trial. And if it comes late in the trial it should not be subject to a premature opinion of guilt formed from incomplete evidence. After all the evidence is presented it should be weighed together"

It doesn't matter whether the shoe size evidence comes early or late. The end result is the same. If it was the absolutely first piece of evidence he would still be a fifty million to one UNDERDOG to be guilty at that moment (disregarding the fact he was arrested etc.). Then the rest of the evidence would bring him down up to 99.7%

The fact of the matter is that the mathematical technique that makes use of ratios of probabilities ( I won't use the B word) is very useful. And most people don't have a clue how to do this and therefore often make wildly wrong probability judgements. It is true that the technique makes assumptions but they are usually reasonable. And the errors made because of imperfect assumptions pale in comparison to the errors made by people who have no idea how to use the technique.

[David Sklansky]

Bingo. I take back everything I ever said about you.

Putting it slightly differently. First remember that I define evidence as "anything that changes the price". Now remember that I postulated a trial of 1,000,000 people where EVIDENCE is identical. Not everything about them. Including at this point the shoe size. Thus the million defendents would not all have to have the same size shoe as the defendent.

What's the chances that luckyme would find a flaw in a professional mathmetician's argument about Baye's Theorem? This tells me there may indeed be a God.

[BIG NIGE]

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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."

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.

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Okay your point is taken, but I am still skeptical of your premise that the footprint was just found after a likely lengthy period of time between the crime scene investigation and the end of the trial, and also that it was "definitely" the murderer's. How does something as obvious to look for as a footprint just go unnoticed? And even if it really did go unnoticed, how could one be sure that it was even there all along, and not a new footprint? If I was investigating and I saw a footprint at a crime scene weeks or months after the investigation, my first guess would be that someone probably steped there recently. I just don't see how a footprint could be "overlooked". Now sure it may be that it was barely detectable and you needed some advanced science to identify it and map it out, but the trial would never have reached its near conclusion without the footprint, if the prosecution thought it such a damning piece of evidence. The only thing I can think of is if this hypothetical scenario you propose is an allegory for a broader concept or idea, but if so then I don't know what that is. Although I didn't read the whole thread only the OP.