Important Evidence Evaluation Scenario/Question

[RJT]

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Logically, the judge is completely correct to reassess his opinion based on new information. There is no way to know if his reevaluation results in a more accurate judgement.

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The revaluation will be more accurate. Can we quantify it is the question. And if so, how?

[RJT]

Or should we look at it his way:

On a scale of 0-10 rate each piece of evidence and then combine them in some formula:

2 dead bodies = a
Car chase = b
Shoe prints = c
Glove = d
Prior history = e
Race = f

Originally the judge combined all the evidence and came up with 5% chance of innocence. We now know that with new shoe print information he gives the chance of innocence to be 1% (ignore, well below 1% - that makes it harder than need be for now). Can we derive his original formula from this information?

I don’t think we can. We need more information. But if we have his original formula then with the new information, we can check his math.

His formula will be say an average of all the numbers or the mean of the numbers or the square root of the mean or whatever.

Again, the OP offers a new way to look at things. Can such things be looked at in such a manner? Does our brain actually look at things in such manners already and we don’t realize it? Can we use statistics in evaluating evidence.

For example, when 2 dead bodies are found dead at the home of an ex-spouse, how often is the ex-spouse the murderer. When a glove is found near the crime scene - if the gloves fits the defendant, how much weight do we give this? Do we need to know if the glove is new or covered in dried blood? What are the chances of the glove fitting if it covered in dried blood?

[leaponthis]

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No. It is not essentially correct and will not be until you change the premise of the hypothetical to something that affords the opportunity to examine facts as individual quantifiables rather than a collective of nuanced abstracts.


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Well, that's not true. The shoes and their value are indeed quantifiable. The judge quantified them when he determined that coupled with other evidence they led him to believe that there was a 5% chance that the defendant was guilty. When he recieved the new evidence he went through it is as he had done before. He reweighed the evidence and given his criteria reduced his findings. He set the criteria and told you by declaring his findings in both instances that he gave concrete weight to the shoe size. He is the judge and he has the right to employ his methods.

leaponthis

[leaponthis]

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There is no mathematical formula that the Judge used to change his number from 5 to well below 1%. This is purely subjective quantifying. Therefore, there can be no such proof.

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Not true. There has to be a math formula else the judge could not use % to describe his findings. He would have to say something like "somewhat" or "just about" but he cannot quantify if he does not use a formula.

leaponthis

[LandonM]

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Well, that's not true. The shoes and their value are indeed quantifiable. The judge quantified them when he determined that coupled with other evidence they led him to believe that there was a 5% chance that the defendant was guilty. When he recieved the new evidence he went through it is as he had done before. He reweighed the evidence and given his criteria reduced his findings. He set the criteria and told you by declaring his findings in both instances that he gave concrete weight to the shoe size. He is the judge and he has the right to employ his methods.

leaponthis

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No.
The value of the shoe size may be 'quantifiable' in the sense that it could be assigned some sort of theoretical "percentage" formula, however, just because 'one quantifies' does not mean the ultimate quantification itself is valid.
DS asked if the judge was correct in his decision from the standpoint of pure logic (without any regard to the legal implications) Logically, you cannot quantify ANY evidentiary components by merely reducing them to a likelihood or a "percentage", lest you fail to acknowledge the occurrence or possibility of anomaly as a matter of procedure (which in and of itself offends against a universally understood concept of justice, thus stands as logical fallacy when it occurs)

I was simply stating that if DS wanted to isolate the logic he seems to be striving for, he would be better served by posing it in a hypothetical where the finite quantifiables (i.e- The likelihood of a certain shoe size) aren't held liable at every turn by abstractions (i.e- the fact that likelihood or unlikelihood does not, in and of itself, mete a conclusion).

[LandonM]

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Not true. There has to be a math formula else the judge could not use % to describe his findings.

leaponthis

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The spirit of DS' question isn't "could" or "couldn't", but rather "should" or "shouldn't". Your contention presumes that the theoretical "percentage formula" is valid by default, thus any conclusion he draws from said formula is logically cogent so long as the "math adds up".

My interpretation of the question as it has been posed by DS leads one to question the logical application of the "formula" itself much more than it does whatever conclusion might result from it.

[ALawPoker]

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Would one be correct in saying that IF the shoe size of 12 B is one tenth as common as 10D, and IF you were assuming it was 10D when you estimated the chances of innocence THEN

you must cut your estimate of his innocence by approximately ten REGARDLESS of the factors that you originally used to come to your first estimation.

Is the above statement essentially correct or not?

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I can't come to terms with accepting that this is an accurate re-evaluation. The common match should mean nothing in terms of proving his innocence. So when the match becomes less common, it shouldn't make a difference, because whatever data he had that proved innocence in the first place will still exist in its entirety. If there was, for whatever reason, a 3% chance he was at work that day and thus incapable of committing the murder, then obviously he could wear a matching size 26Q space shoes and unless you're willing to alter your judgment of how likely he was to be at work, then you can't drop your estimation to below 3%.

I guess what you're saying is he summed up all the circumstantial evidence to properly calculate the 5%. He can't simply slash it by 10 when he learns that the shoe size is 10x more rare. Maybe people with shoe size 12D are 100 times more likely to own a knife. The judge must re-do his entire formula, and is wrong to ignore everything else.

Maybe I'm still not seeing what you're getting at. I think I officially retire from this thread.

[johno]

This is my rather limited understanding!

Baye's theorem states that the probability of a hypothesis (innocence) given a piece of new evidence (the shoe print) is dependent on -

1) pre-evidential probability (innocence without knowledge of the shoe print).

2) ratio of the probability of the evidence 'ocurring' given the hypothesis is true to the probability of the evidence occuring for all hypotheses (guilty or innocent in this case).

In theory the effect of the new evidence can be quantified - the applicability of this result depends on the accuracy in variable quantification-

1) The accuracy of determining the probability of innocence without the shoe print evidence - this may be very difficult to assess, if for example only people with that shoe size were considered suspects.

2) The accuracy in assessing the probability of the evidence 'occuring' if the defendent is guilty. If you assume that the murderer definitely made the footprint then this is easier - otherwise you need to attach some kind of weighting or probability to the possibility that it is a random footprint.



In addition, you need to believe that Baye's theorem is applicable to the degree of a person's belief in a proposition, and have a view on the degree of subjectivity required to apply the theorem in this situation.


An aside - if the prisoner is left to rot in jail, is he serving 'sklansky years'?

[leaponthis]

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The value of the shoe size may be 'quantifiable' in the sense that it could be assigned some sort of theoretical "percentage" formula, however, just because 'one quantifies' does not mean the ultimate quantification itself is valid.


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Yes, it does mean the quantification is valid if you are the one setting the criteria for validation, which the judge was in this case.

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Logically, you cannot quantify ANY evidentiary components by merely reducing them to a likelihood or a "percentage", lest you fail to acknowledge the occurrence or possibility of anomaly as a matter of procedure (which in and of itself offends against a universally understood concept of justice, thus stands as logical fallacy when it occurs)


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Ouch. That is one HEAVY statement. I'm a bit aprehensive in trying to tackle it but...Sklansky does refer to me as an oaf, so here goes. Whether or not you fail to acknowledge some anomally does not affect the logic of assigning a % to a factor that one weighs to determine it's value. If the judge fails to consider something, it in and of itself does not make his decision, in and of itself illogical. It might lead to a poor decision or it might not but his method can still be considered logical.

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I was simply stating that if DS wanted to isolate the logic he seems to be striving for, he would be better served by posing it in a hypothetical where the finite quantifiables (i.e- The likelihood of a certain shoe size) aren't held liable at every turn by abstractions (i.e- the fact that likelihood or unlikelihood does not, in and of itself, mete a conclusion).

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DS is nothing if not a math guy. Logic, smogic! DS wants proof not morality based on logic. He gave us what he believes was concrete "evidence" and expected us to multiply it into proof heaven. I do not speak for DS but as you can tell from this forum he doesn't speak very often for himself either. I love your reply and though I have my own opinion of what Sklansky wants, I do not discount your views. You are probably right.

leaponthis

[leaponthis]

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My interpretation of the question as it has been posed by DS leads one to question the logical application of the "formula" itself much more than it does whatever conclusion might result from it.

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I love you. But, I love most people that are smarter than me. However,this statement has me perplexed. "Question the logical application"...I see your point., but I'm wondering if the judge applying the results of his formula is a moral issue and not a logical one. Maybe he has a moral obligation to not be as speculative as his method appears to be but why is his method not logical? He has circumstantial evidence, he assigned a probability to each bit of evidence, he added up the percentages and assigned an overall probability to innocence. I'm, admittedly, not a logician but that procedure sounds logical to me.

leaponthis