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Prologue to Bill Maher & Larry Charles

 
TheAnal_lyticPhilosopher
 
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TheAnal_lyticPhilosopher
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05 October 2018 11:41
 

Harris is right to use Bayesian priors and evidential updating in order to hypothesize what is true in this case, for that is where Bayesian inference, as opposed to frequentist statistics, shines.  And he is right that for these priors it is more likely that Kavanaugh, not Ford, is lying.  For assuming the event did not happen, it is far less likely for a woman to lie and say it did than it is for man to lie and say it didn’t, when it in fact did.  This follows both empirically from what we know about sexual assaults and logically from what we know about lying.  But Harris makes, I think an error when he updates the possibility that Ford is lying, not Kavanaugh.

Harris is right that Kavanaugh’s outright lies and lies of omission only update the prior that he is lying about the sexual assault, but he is wrong that putting a witness to the event updates Ford’s prior towards telling the truth.  For Judge, in this case, is not a witness but an accomplice, and it is just as likely that an accomplice will lie as the main perpetrator, especially when lying is costless and uncatchable but telling the truth comes with a high cost.  In effect the two lies are one and the same lie, so a lie that puts an accomplice in the room neither costs the liar any risk nor gains the liar any credibility.  So Ford may be telling the truth, but placing a “witness” (actually an accomplice) in the room doesn’t update that probability in her favor.  And, the failure to corroborate from potential corroborators who were not also accomplices updates Ford’s prior toward lying.

I think Harris misses this because he’s intuitively convinced that Ford, not Kavanaugh, is telling the truth, based on his priors.  But true Bayesian inference should undermine, not be used to enforce, one’s initial intuition of the priors. 

Harris is right to invoke Bayesian reasoning here, but I think he’s wrong in how he goes about his updating.  It seems to me he’s interpreting new evidence in terms of his priors, not updating the priors in terms of it.  In this case even after considerable updating it’s unclear to me what Bayesian inference can tell us about who’s lying and who’s not.  Mostly what I see is people interpreting the evidence in terms of the priors they already have.

[ Edited: 11 October 2018 07:25 by TheAnal_lyticPhilosopher]
 
mapadofu
 
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mapadofu
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05 October 2018 17:12
 

Nope, P(Victim reports 1 accomplice present |she’s truthful, accomplice present) = 1

P(Victim reports 1accomplice | she’s lying, no assault) < 1 since at least some false reports involve 0 or 2 or 3… accomplices. 

Therefore the likelihood ratio between these two hypotheses favors the (truth, 1 accomplice) hypothesis over the (lying, no event) one.

 
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06 October 2018 04:45
 
mapadofu - 05 October 2018 05:12 PM

Nope, P(Victim reports 1 accomplice present |she’s truthful, accomplice present) = 1

P(Victim reports 1accomplice | she’s lying, no assault) < 1 since at least some false reports involve 0 or 2 or 3… accomplices. 

Therefore the likelihood ratio between these two hypotheses favors the (truth, 1 accomplice) hypothesis over the (lying, no event) one.

Um, all you’ve done here, if you’ve done anything, is compare the likelihoods from two different formulations of the posterior probability [P(lying)| statement) or P(truthful)| statement], which is what we want to know.  That’s neither a Bayesian nor a meaningful inference.  And in any case, your first iteration of the likelihood is also wrong.  If there was an attack and an accomplice, the probability of making a statement that there was an attack and an accomplice is not 1, for some victims omit the accomplice, even if being truthful about the attack.  Of course, if they make a statement reflecting the whole truth, as you stipulate, then the probability of that statement being what it is, if she’s being truthful, must be 1.  Then of course any statement being what it is if she is lying must be less than 1, for one can tell many different lies.  Hence the meaninglessness of your particular misstatement of the comparison of likelihoods (which isn’t all there is to Bayesian inference in any case). 

 

[ Edited: 11 October 2018 07:28 by TheAnal_lyticPhilosopher]
 
Scott Mayers
 
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06 October 2018 07:16
 
DEGENERATEON - 04 October 2018 12:36 PM

I agree with Sam’s points as to the lack of motivation for Ford to lie.  I don’t think she is fabricating a story.  But 35+ years ago?!  I don’t know anybody who hasn’t done something stupid in their past - something they probably regret and can look at and say “that isn’t who I am, that was strange even to me”.  Sam said something either in the prologue or podcast about the “stark encounter with the idiot you used to be”.  I’ve had that experience.  Hasn’t everyone?  Beyond all the political theater I just think it’s not fair.  You can’t destroy someone’s life over this.  It doesn’t matter if it’s a job interview or a criminal trial.  I’m also going with the assumption that something did happen (not rape or attempted rape) and it was in fact Kavanaugh. 
I’m also assuming that this is the only legitimate incident of this nature that happened in the 35+ years since.

But, WHY even accept what anyone simply ‘believes’ about hearsay regardless? I don’t get how even Sam can pick and choose when or where ‘belief’ about some person’s words are even sufficient as ‘evidence’ to third parties? All this means is that you might PREFER to trust the words of someone because they APPEAR more convincing according to your own standards. But then you require specific expansion on HOW you interpret whether one is or is not sincere and why you are somehow MORE of a better judge of character than others.

To me, this whole #metoo generation means nothing if the ‘me’ in it is exclusive of EACH ‘me’ in the world, including those being accused of something. Is the measure of how trustworthy someone is to be measured by how WE personally would or would not accuse another about something heinous? You can’t measure the actual trust of another based on your own capacity to trust (or distrust). It’s begging.

You also have to question how society places virtue in trusting mere appearances. Why anyone would even trust the words of a GOOD ACTOR/ACTRESS is beyond me (thinking of the accusations about the entertainment professions, for instance. Their primary skill is lying.)

I DON’T like many of the people being accused of sexual harassment often because they are the ones that people continuously FAVOR FOR their general aptitudes for being that way but by people who want vengeance AFTER the fact they’ve been burned personally, not because they would actually prefer nicer people. It’s a wink-wink kind of attitude. “Nice” only works if you first APPEAR “bad” but are expected to ACTUALLY be ‘nice’ in some hidden and personal way to those who want you to prove you are ‘worthy’ of being treated with exception.

This is all irrelevant. It is POLITICS that this guy is being counter-harassed for ONLY. And if you opt to decide differently, you are only proving you accept LYING to yourself as a justified rationale to measure others by.

 
mapadofu
 
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06 October 2018 07:27
 

Analytic, what exactly is your Bayesian model for Sam’s statement?

 
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06 October 2018 07:36
 
mapadofu - 06 October 2018 07:27 AM

Analytic, what exactly is your Bayesian model for Sam’s statement?

mapadofu, why do you ask?

 

[ Edited: 06 October 2018 07:45 by TheAnal_lyticPhilosopher]
 
mapadofu
 
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06 October 2018 12:09
 

Analytic,

I’m a bit surprised that my notional model worked out to such that likelihood ratio will come work out in favor of the “truthful reporting, event occurred as reported” hypothesis relative to any “untrue reporting” hypothesis, so if there are alternate formulations of the problem where this is not the case, I’d be interested to see them.

This might be a feature of the special feature of how I represented “truthful” in that, as you correctly noted, that I’m using that to represent true, accurate, complete etc.
Thus P(statement==actuality | true) = 1 for this meaning of “truthful”. 
In writing this up an observation that could, at least possibly, go either way: the observation of the time-gap between the event and the first time she related it to a loved one or other confidant.  Maybe the distribution for the time lag, given event occurred and truthful reporting, is highly concentrated at say <<1 year and maybe the distribution
for the time lag given no actual event, and lying is more spread out.  Then the significant, >1 year gap (don’t remember the exact gap) between the event and the first time she told anyone as I understand it, could result in a likelihood ratio that
that promotes the “no event, lying” hypothesis relative to the “actual event w/ 1 accomplice, truthful” one. 
This makes me wonder if there there is something special about valve-like nature of the problem as I’ve formalized it,  where, given truthful as I’m using it here, then the reported features of the incident itself exactly matches the feature of the event itself in a 1-to-1 way.


You alluded to a “truthful but inaccurate” kind of possibility—how exactly to model that, especially in a way that results in P(report | true but inaccurate, actual event) < P(report | lying, actual-event didn’t happen); I’m not sure exactly what kind of conditional relationships you have in mind.

You also noted that I’ve picked out two specific hypotheses—“true, 1 accomplice” and “false, no event” that do not for an exhaustive set of possibilities.  I don’t have the time or inclination to really full model the whole gamut, but if you have, then I’d like to know. 

Another reason why I’m not worried about defining the entire ensemble is that my I interpret the bulk of Sam’s discussion regarding Dr. Ford reporting that there was another person in the room as being a discussion of (or would be formalized as) a statement regarding the likelihood ratio to we observe what we’ve observed (Dr Ford’s testimony that 1 other person was present) conditioned on the two hypotheses I spelled out.  Maybe you believe that Sam’s informal prose maps into a different probabilistic model.

[ Edited: 06 October 2018 12:42 by mapadofu]
 
TheAnal_lyticPhilosopher
 
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06 October 2018 14:05
 
mapadofu - 06 October 2018 12:09 PM

Analytic,

I’m a bit surprised that my notional model worked out to such that likelihood ratio will come work out in favor of the “truthful reporting, event occurred as reported” hypothesis relative to any “untrue reporting” hypothesis, so if there are alternate formulations of the problem where this is not the case, I’d be interested to see them.

This might be a feature of the special feature of how I represented “truthful” in that, as you correctly noted, that I’m using that to represent true, accurate, complete etc.
Thus P(statement==actuality | true) = 1 for this meaning of “truthful”. 
In writing this up an observation that could, at least possibly, go either way: the observation of the time-gap between the event and the first time she related it to a loved one or other confidant.  Maybe the distribution for the time lag, given event occurred and truthful reporting, is highly concentrated at say <<1 year and maybe the distribution
for the time lag given no actual event, and lying is more spread out.  Then the significant, >1 year gap (don’t remember the exact gap) between the event and the first time she told anyone as I understand it, could result in a likelihood ratio that
that promotes the “no event, lying” hypothesis relative to the “actual event w/ 1 accomplice, truthful” one. 
This makes me wonder if there there is something special about valve-like nature of the problem as I’ve formalized it,  where, given truthful as I’m using it here, then the reported features of the incident itself exactly matches the feature of the event itself in a 1-to-1 way.


You alluded to a “truthful but inaccurate” kind of possibility—how exactly to model that, especially in a way that results in P(report | true but inaccurate, actual event) < P(report | lying, actual-event didn’t happen); I’m not sure exactly what kind of conditional relationships you have in mind.

You also noted that I’ve picked out two specific hypotheses—“true, 1 accomplice” and “false, no event” that do not for an exhaustive set of possibilities.  I don’t have the time or inclination to really full model the whole gamut, but if you have, then I’d like to know. 

Another reason why I’m not worried about defining the entire ensemble is that my I interpret the bulk of Sam’s discussion regarding Dr. Ford reporting that there was another person in the room as being a discussion of (or would be formalized as) a statement regarding the likelihood ratio to we observe what we’ve observed (Dr Ford’s testimony that 1 other person was present) conditioned on the two hypotheses I spelled out.  Maybe you believe that Sam’s informal prose maps into a different probabilistic model.

As near as I can tell, all your “model” does is stipulate that when a person tells the truth, their statements are true with a probability of 1, and when they tell a lie, there is a probability less than 1 that they would tell that particular lie, therefore it is more probable than not that the person is telling the truth.  Just here you’re “modeling” that reasoning for the particular case of Ford telling the truth or lying.  That’s not even a Bayesian inference.  It’s just nonsense.  The alternative formulation of the problem would be to use Bayesian reasoning correctly.

(In technical terms what you are doing is taking the “likelihood” (P(statement| truthfulness))—a part of the Bayesian formula (along with P(statement) and P(truthfulness))—from two ways of stating the posterior probability (either in terms of truthfulness or lying: P(truthfulness| statements) or P(lying| statements).  Then you are comparing (invalidly) these two likelihoods in order to get what should be the probability that Ford is telling the truth (the posterior probability, P(truthfulness| statements).  And I’m saying that’s not Bayesian reasoning, only a distortion of part of it.)

I don’t mean this to be harsh here.  It looks to me like you are working in good faith.  But from what I understand about Bayesian statistics, you are working in error.

 

 
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06 October 2018 15:48
 

Abalytic, you’ve said I’m wrong but have not described your model.

 
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06 October 2018 16:48
 

Here’s are more fleshed out version of the model I’m working from:

Variables:
- T: with boolean states, true -> the witness truthfully and accurately reports the number of accomplices
- A: the configuration of attack, with a special “no attack” state a_null, and then states for a_0 for 0 accomplices, a_1 for 1 accomplices, a_2 for 2 accomplices and so on
- R: the number of accomplices reported: r_null = no event reported at all,  r_0 = event but no accomplices reported, r_1 for reporting the event occurred with one accomplice etc.

The joint distribution P(T,A,R) can be factored into P(R|T,A)P(T,A).
My assumed properties for P(R| T,A) are:
- p(r_x | T=true, a_y) = 1 if x==y and 0 otherwise; this is the perfect reporting model
- p(r_x | T=false, a_null) = let’s just say it is a geometric distribution with a mean value 0<mean<1 for r_0, r_1… and 0 for r_null. I tend to think that the probability distribution needs to be monitonically decreasing.  This is the distribution for the number of accomplices reported in false accusations.
- p(r_x | T=false, a_y) = 0 if x==y (if the victim mis-represents the count,  he/she can’t report the true number).  Other than this, I don’t have any intuitions about how this distribution would look; however it doesn’t matter.

Again, my interpretation of Sam’s prose is that he’s just talking about specific features of the of the conditional relationship, specifically p(r_1 | true, a_1) and p(r_1 | false, a_null), and how they play into the posterior for the relative likelihood between the two hypotheses (true, a_1), (false, a_null).  This is pretty straightforward Bayesian hypothesis testing stuff.

[ Edited: 07 October 2018 05:02 by mapadofu]
 
DEGENERATEON
 
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07 October 2018 19:22
 
Scott Mayers - 06 October 2018 07:16 AM
DEGENERATEON - 04 October 2018 12:36 PM

I agree with Sam’s points as to the lack of motivation for Ford to lie.  I don’t think she is fabricating a story.  But 35+ years ago?!  I don’t know anybody who hasn’t done something stupid in their past - something they probably regret and can look at and say “that isn’t who I am, that was strange even to me”.  Sam said something either in the prologue or podcast about the “stark encounter with the idiot you used to be”.  I’ve had that experience.  Hasn’t everyone?  Beyond all the political theater I just think it’s not fair.  You can’t destroy someone’s life over this.  It doesn’t matter if it’s a job interview or a criminal trial.  I’m also going with the assumption that something did happen (not rape or attempted rape) and it was in fact Kavanaugh. 
I’m also assuming that this is the only legitimate incident of this nature that happened in the 35+ years since.

But, WHY even accept what anyone simply ‘believes’ about hearsay regardless? I don’t get how even Sam can pick and choose when or where ‘belief’ about some person’s words are even sufficient as ‘evidence’ to third parties? All this means is that you might PREFER to trust the words of someone because they APPEAR more convincing according to your own standards. But then you require specific expansion on HOW you interpret whether one is or is not sincere and why you are somehow MORE of a better judge of character than others.

To me, this whole #metoo generation means nothing if the ‘me’ in it is exclusive of EACH ‘me’ in the world, including those being accused of something. Is the measure of how trustworthy someone is to be measured by how WE personally would or would not accuse another about something heinous? You can’t measure the actual trust of another based on your own capacity to trust (or distrust). It’s begging.

You also have to question how society places virtue in trusting mere appearances. Why anyone would even trust the words of a GOOD ACTOR/ACTRESS is beyond me (thinking of the accusations about the entertainment professions, for instance. Their primary skill is lying.)

I DON’T like many of the people being accused of sexual harassment often because they are the ones that people continuously FAVOR FOR their general aptitudes for being that way but by people who want vengeance AFTER the fact they’ve been burned personally, not because they would actually prefer nicer people. It’s a wink-wink kind of attitude. “Nice” only works if you first APPEAR “bad” but are expected to ACTUALLY be ‘nice’ in some hidden and personal way to those who want you to prove you are ‘worthy’ of being treated with exception.

This is all irrelevant. It is POLITICS that this guy is being counter-harassed for ONLY. And if you opt to decide differently, you are only proving you accept LYING to yourself as a justified rationale to measure others by.

I’m just assuming that for the sake of argument.  A kind of middle ground that something happened but he didn’t attempt to rape her.  Even by her own description- it didn’t sound like he was attempting to do that.  The brass tacks is that even if you assume something happened- it’s not enough.  All the extra crap about “boofing” and drinking is nonsense.  Kavanagh HAD to lie.  You can’t sit there and admit to being an idiot in your past - not in this interview.

 
mapadofu
 
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07 October 2018 19:48
 

He /had/ to lie?  Under oath?  And still be an officer of the court?

 
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07 October 2018 21:13
 
mapadofu - 07 October 2018 07:48 PM

He /had/ to lie?  Under oath?  And still be an officer of the court?

Yes.  I mean what is he supposed to do?  “It says here in your high school yearbook that you were looking to boof.  What is boofing?”
“Yes senator that refers to anal sex.”

Who gives a shit about this?  This was 35 years ago, he was probably looking to be funny.  Ask some questions on his judicial career if you want straight answers.  If you want someone with nothing embarrassing in their past pray for the second coming.  Maybe something happened between him and Ford and he did remember but saw it a totally different way.  He can’t defend himself by saying ANYTHING - or he is out.

 
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08 October 2018 02:45
 
mapadofu - 06 October 2018 04:48 PM

Here’s are more fleshed out version of the model I’m working from:

Variables:
- T: with boolean states, true -> the witness truthfully and accurately reports the number of accomplices
- A: the configuration of attack, with a special “no attack” state a_null, and then states for a_0 for 0 accomplices, a_1 for 1 accomplices, a_2 for 2 accomplices and so on
- R: the number of accomplices reported: r_null = no event reported at all,  r_0 = event but no accomplices reported, r_1 for reporting the event occurred with one accomplice etc.

The joint distribution P(T,A,R) can be factored into P(R|T,A)P(T,A).
My assumed properties for P(R| T,A) are:
- p(r_x | T=true, a_y) = 1 if x==y and 0 otherwise; this is the perfect reporting model
- p(r_x | T=false, a_null) = let’s just say it is a geometric distribution with a mean value 0<mean<1 for r_0, r_1… and 0 for r_null. I tend to think that the probability distribution needs to be monitonically decreasing.  This is the distribution for the number of accomplices reported in false accusations.
- p(r_x | T=false, a_y) = 0 if x==y (if the victim mis-represents the count,  he/she can’t report the true number).  Other than this, I don’t have any intuitions about how this distribution would look; however it doesn’t matter.

Again, my interpretation of Sam’s prose is that he’s just talking about specific features of the of the conditional relationship, specifically p(r_1 | true, a_1) and p(r_1 | false, a_null), and how they play into the posterior for the relative likelihood between the two hypotheses (true, a_1), (false, a_null).  This is pretty straightforward Bayesian hypothesis testing stuff.

I appreciate you taking the time to flesh out the model, but as far as I can tell it only shows, rigorously, that you are distorting Bayesian hypothesis testing and making a fundamentally meaningless comparison.  Again, I don’t mean this to be harsh or judgmental, as you are clearly working in good faith.  But again, I think, in error.

Like I’ve already indicated, what you are doing is comparing all alternative likelihoods to a “null” likelihood stipulated at 1, which means by definition all alternatives will be less probable; therefore the model tests nothing.  It merely tautologically reiterates the proposition that when people tell the truth, their statements are true with a probability of 1, compared to when they lie, they could tell one of many lies, therefore the probability of a given lie is less than one; therefore truth telling is more likely than lying.  And like I said, this may co-opt one aspect of the form of Bayesian reasoning (what you claim is “pretty straightforward Bayesian hypothesis testing stuff”), but it abuses—if not outright violates—its substance by computing a fundamentally meaningless likelihood.

What we want to know is who of two people are accurately reporting an event, the nature of which we do not know.  We have two sources of information on this event, and thus two “hypotheses”: Ford is telling the truth and Kavanaugh is telling the truth—or alternatively and equivalently, Ford is lying and Kavanagh is lying.  From their testimony we have data (x), and we use the probability of this data given the truth of their testimony to update the prior probability (P(H)) that either testimony is true (for tractability, we’ll just assume the probability of their information as such—the denominator in Bayes’ formula, (P(x))—is 1).  Given what we already know about sexual assaults and lying, Ford’s prior of being truthful is likely higher than Kavanaugh’s, but either way, in assessing each hypothesis individually for comparison, we estimate the probability of a specific piece of information given telling the truth (P(x|H)), then multiply that by their prior (P(H)) to get the posterior probability (P(H|x)).  One does not stipulate a “perfect reporting model” (P(x|H)= 1) and test alternative false reports against that in a “likelihood ratio” (what you do).  Instead, to ‘compare the hypotheses,’ as it were, one would iteratively update the prior for each piece of relevant information from their respective testimonies, then compare the final posterior probabilities to see which of the two is greater.  From there, one would “decide” which one is telling the truth.

What I describe is essentially what Harris is doing verbally, just with making the error (I think) that Judge is a witness that “improves” Ford’s posterior instead of an accomplice that either leaves it unchanged (for asking the FBI to interview a hostile accomplice tells says nothing about whether one is lying) or even, really, lowers it (two men in a sexual assault being less probable than a single assailant, as most assaults are by single assailants). 

That, I think, is the “pretty straightforward Bayesian” reasoning that should be applied to this case.  What you model is pseudo-Bayesian hypothesis testing that shouldn’t be applied to any case because it’s a tautologically uninformative ‘test’ that will always produce the same result, to wit—alternatives to telling the truth will always be rejected because true statements in truth telling are always more probable than a specific lie in lying.

 

[ Edited: 08 October 2018 03:40 by TheAnal_lyticPhilosopher]
 
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08 October 2018 04:30
 

Degeneration,
He was supposed to tell the truth (the whole truth and nothing but the truth).  You are right, adolescent braggadocio isn’t disqualifying.  Committing perjury is, or at least should be.

 
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