How many accusers need to come forward before you believe the accused is guilty?

[laughing dog]

LD asked for a thought experiment, not about the courts, perhaps to examine people's impressions prior to even getting into a jury, or to examine the impressions of the populace in consideration of voting.

Imagine there is a 50% chance each accuser is telling the truth and a 50% chance they are lying. Assume they are independent. What is the probability that all N are lying?
N Probability all are lying
1 50%
2 25%
3 12.5%
4 6.25%
5 3.125%
...and so on...

How confident do you as a person need to be to "believe" something? 51% confident? 80% confident? 90% confident? If you need to be 51% confident, then 2 people would be enough on average and with certain assumptions. If you feel you need to be 95% confident to believe something, then maybe that is 5 people for you to believe it.

As for me, I may end up believing something sometimes at less than a 90% confidence. However, I try to practice my life in a way where I suspend belief because it is a complicated thing based on intuitions and super-fast brain processes in some advanced algorithm that can be wrong. I would want to confirm my beliefs using evidence and arguments or suspend them in some cases when the outcomes have large risk for quick, rash decisions.

Also, importantly, the assumption of independence of accusers can be wrong. If we're talking about a particular accused person, like a rich or charismatic person, there may be multiple persons who all want to accuse them for the same reason. Or accusers could all be Republican operatives lying about an atheist, etc.

And the assumption of 50% telling the truth versus lying can be wrong and may be context based. So, for example, back in Salem in the 1600s, people lying about witches may have been common. Today, ladies lying about sex assault is rare.

Suppose we were talking about Salem witches then. Suppose accusations were independent [they often were not] and that this was about practice of witchcraft, not actually being a real magical witch. So, if you collected herbs and tried to poison someone, you may have been practicing but nothing magical about it. Now, suppose there was a 90% chance that accuser was lying. So we'd have:
N Probability all the accusers are lying
1 90%
2 81%
3 72.9%
4 65.6%
5 59%

So maybe you'd need 20 people telling you someone was a witch to believe they did some kind of Wiccan thing, like dancing in the forest or collecting herbs...but of course the magical claims would be 100% false at all times.

Now, suppose we are talking about women being sexually assaulted. Suppose accusations are independent [in cases of famous accused, they might not be]. Estimates range from 2% to 10% about women lying about such things. So, let's take the bigger number. Suppose there is a 90% chance that accuser is telling the truth. So we'd have:
N Probability all the accusers are lying
1 10%
2 1%
3 0.1%
4 0.01%
5 0.001%

That answer addresses the OP without any of the unnecessary assumptions about a trial or credability of a particular witness.

 

[ronburgundy]

LD asked for a thought experiment, not about the courts, perhaps to examine people's impressions prior to even getting into a jury, or to examine the impressions of the populace in consideration of voting.

Imagine there is a 50% chance each accuser is telling the truth and a 50% chance they are lying. Assume they are independent. What is the probability that all N are lying?
N Probability all are lying
1 50%
2 25%
3 12.5%
4 6.25%
5 3.125%
...and so on...

How confident do you as a person need to be to "believe" something? 51% confident? 80% confident? 90% confident? If you need to be 51% confident, then 2 people would be enough on average and with certain assumptions. If you feel you need to be 95% confident to believe something, then maybe that is 5 people for you to believe it.

As for me, I may end up believing something sometimes at less than a 90% confidence. However, I try to practice my life in a way where I suspend belief because it is a complicated thing based on intuitions and super-fast brain processes in some advanced algorithm that can be wrong. I would want to confirm my beliefs using evidence and arguments or suspend them in some cases when the outcomes have large risk for quick, rash decisions.

Also, importantly, the assumption of independence of accusers can be wrong. If we're talking about a particular accused person, like a rich or charismatic person, there may be multiple persons who all want to accuse them for the same reason. Or accusers could all be Republican operatives lying about an atheist, etc.

And the assumption of 50% telling the truth versus lying can be wrong and may be context based. So, for example, back in Salem in the 1600s, people lying about witches may have been common. Today, ladies lying about sex assault is rare.

Suppose we were talking about Salem witches then. Suppose accusations were independent [they often were not] and that this was about practice of witchcraft, not actually being a real magical witch. So, if you collected herbs and tried to poison someone, you may have been practicing but nothing magical about it. Now, suppose there was a 90% chance that accuser was lying. So we'd have:
N Probability all the accusers are lying
1 90%
2 81%
3 72.9%
4 65.6%
5 59%

So maybe you'd need 20 people telling you someone was a witch to believe they did some kind of Wiccan thing, like dancing in the forest or collecting herbs...but of course the magical claims would be 100% false at all times.

Now, suppose we are talking about women being sexually assaulted. Suppose accusations are independent [in cases of famous accused, they might not be]. Estimates range from 2% to 10% about women lying about such things. So, let's take the bigger number. Suppose there is a 90% chance that accuser is telling the truth. So we'd have:
N Probability all the accusers are lying
1 10%
2 1%
3 0.1%
4 0.01%
5 0.001%

That answer addresses the OP without any of the unnecessary assumptions about a trial or credability of a particular witness.

That answer highlights how the OP cannot be answered rationally, without extensive caveats and clarifications. You asked about some vague, variable, context-dependent state of "believe", which has no reliable relationship to probability estimates. Where exactly does the decrease in probability of all accusers lying = a change in "believe"?

Then, even by substituting probability estimates for "believe", Don's post has zero application to any real world situation, because it makes a logically impossible assumption that all accusations against a given person are independent. The "Independence" logically required by Don's method of computed combined probabilities doesn't just mean the accusers do not know each other, it means there is nothing that connects them in any way and no shared causal factors that impact the probability of each event. Thus, it is logically impossible for 2 accusers of the same person to ever be independent. Unlike coin flips, accusations (true and false) against a person are not random events. Who the accused is and many things about them has a causal impact on their probability of being accused, both falsely and truthfully. Which means those same factors impact the probability of each accusation against them, making each accusation against them non-independent from each other, by definition. Plus, countless things, such as how the accused is known to the accusers (e.g., are they famous and known to most people) impacts the degree of non-independence. The amount of non-independence inversely reduces the amount that the second accusation impacts the net probability. Since the amount of non-independence is always non-zero but its degree varies wildly by context, the hypothetical where total independence is assumed does not apply to any situation.

The only answer to the OP that has any applicability to actual world is something vague and qualified enough to actually be relevant to most situations, for example "In general, as the number of accusers increase there will tend to be some variable amount of increase in the probability of the accusations being true."

Note that even there, "tend to" is a required caveat because it is possible for an added accusation to have no impact or even to decrease the probability of the accusation being true. Since the accusations against the same person are not independent, what is true of one accusation increases the probability that the same is true of other accusations. For example, physical evidence that the second accusation is true also increases the probability that the first accusation is true. Likewise, information that suggests that the second accusation is false decreases the probability that the first accusation is true. If two people make accuse a person and one of the accusations has direct evidence that it is false, then the probability that the other accusation is true is actually lower than if it was the only accusation made.

 

[Elixir]

What tips my opinion to "he did it" is the fact that his (BK's) supporters had a whitewash performed by the FBI.
With all their harping on transparency, the rethuglicans have demonstrated a curiously strong aversion to getting to the truth of the matter. Almost as if they already KNOW what would have happened if Trump had allowed the FBI to interview the people who came forward and asked to be interviewed...

 

[Jarhyn]

LD asked for a thought experiment, not about the courts, perhaps to examine people's impressions prior to even getting into a jury, or to examine the impressions of the populace in consideration of voting.

Imagine there is a 50% chance each accuser is telling the truth and a 50% chance they are lying. Assume they are independent. What is the probability that all N are lying?
N Probability all are lying
1 50%
2 25%
3 12.5%
4 6.25%
5 3.125%
...and so on...

How confident do you as a person need to be to "believe" something? 51% confident? 80% confident? 90% confident? If you need to be 51% confident, then 2 people would be enough on average and with certain assumptions. If you feel you need to be 95% confident to believe something, then maybe that is 5 people for you to believe it.

As for me, I may end up believing something sometimes at less than a 90% confidence. However, I try to practice my life in a way where I suspend belief because it is a complicated thing based on intuitions and super-fast brain processes in some advanced algorithm that can be wrong. I would want to confirm my beliefs using evidence and arguments or suspend them in some cases when the outcomes have large risk for quick, rash decisions.

Also, importantly, the assumption of independence of accusers can be wrong. If we're talking about a particular accused person, like a rich or charismatic person, there may be multiple persons who all want to accuse them for the same reason. Or accusers could all be Republican operatives lying about an atheist, etc.

And the assumption of 50% telling the truth versus lying can be wrong and may be context based. So, for example, back in Salem in the 1600s, people lying about witches may have been common. Today, ladies lying about sex assault is rare.

Suppose we were talking about Salem witches then. Suppose accusations were independent [they often were not] and that this was about practice of witchcraft, not actually being a real magical witch. So, if you collected herbs and tried to poison someone, you may have been practicing but nothing magical about it. Now, suppose there was a 90% chance that accuser was lying. So we'd have:
N Probability all the accusers are lying
1 90%
2 81%
3 72.9%
4 65.6%
5 59%

So maybe you'd need 20 people telling you someone was a witch to believe they did some kind of Wiccan thing, like dancing in the forest or collecting herbs...but of course the magical claims would be 100% false at all times.

Now, suppose we are talking about women being sexually assaulted. Suppose accusations are independent [in cases of famous accused, they might not be]. Estimates range from 2% to 10% about women lying about such things. So, let's take the bigger number. Suppose there is a 90% chance that accuser is telling the truth. So we'd have:
N Probability all the accusers are lying
1 10%
2 1%
3 0.1%
4 0.01%
5 0.001%

That answer addresses the OP without any of the unnecessary assumptions about a trial or credability of a particular witness.

That answer highlights how the OP cannot be answered rationally, without extensive caveats and clarifications. You asked about some vague, variable, context-dependent state of "believe", which has no reliable relationship to probability estimates. Where exactly does the decrease in probability of all accusers lying = a change in "believe"?

Then, even by substituting probability estimates for "believe", Don's post has zero application to any real world situation, because it makes a logically impossible assumption that all accusations against a given person are independent. The "Independence" logically required by Don's method of computed combined probabilities doesn't just mean the accusers do not know each other, it means there is nothing that connects them in any way and no shared causal factors that impact the probability of each event. Thus, it is logically impossible for 2 accusers of the same person to ever be independent. Unlike coin flips, accusations (true and false) against a person are not random events. Who the accused is and many things about them has a causal impact on their probability of being accused, both falsely and truthfully. Which means those same factors impact the probability of each accusation against them, making each accusation against them non-independent from each other, by definition. Plus, countless things, such as how the accused is known to the accusers (e.g., are they famous and known to most people) impacts the degree of non-independence. The amount of non-independence inversely reduces the amount that the second accusation impacts the net probability. Since the amount of non-independence is always non-zero but its degree varies wildly by context, the hypothetical where total independence is assumed does not apply to any situation.

The only answer to the OP that has any applicability to actual world is something vague and qualified enough to actually be relevant to most situations, for example "In general, as the number of accusers increase there will tend to be some variable amount of increase in the probability of the accusations being true."

Note that even there, "tend to" is a required caveat because it is possible for an added accusation to have no impact or even to decrease the probability of the accusation being true. Since the accusations against the same person are not independent, what is true of one accusation increases the probability that the same is true of other accusations. For example, physical evidence that the second accusation is true also increases the probability that the first accusation is true. Likewise, information that suggests that the second accusation is false decreases the probability that the first accusation is true. If two people make accuse a person and one of the accusations has direct evidence that it is false, then the probability that the other accusation is true is actually lower than if it was the only accusation made.

All I see here is an attempt to impugn a dispassionate discussion because the person making it used language too honest and technical for you to wrap your head around it. Just because you don't understand how de/fuzzification works, doesn't mean it's wrong.

If I pull one raspberry out of a container and it has mold, I throw it away. If I find a second, I throw it away too. If I find a third, I dump out the package. This is a real-life intuitive application: one raspberry means a 25% chance the basket is gross. A second means that there is a much higher chance the basket is gross. A third means that the basket is almost definitely gross. Not hard to understand. It's merely a formal description of a natural concept.

The problem here, that we have with High N in terms of accusers, is that lying is unlikely, and more independent accusation is exactly indicative of exponentially greater likelihood o truth. Your quibbles about his formality don't erode this concept at all.

 

[starwater]

Ummm....humans are not raspberries.

 

[laughing dog]

That answer highlights how the OP cannot be answered rationally, without extensive caveats and clarifications.......

Wrong. I asked a subjective question. This is not some scientific study nor a problem in the application of Bayesian analysis. At some point, people do tend to come to a conclusion about believing someone is guilty or not. Sometimes, it is based on the number of accusations. I was interested in a general idea.

 

[Jarhyn]

Ummm....humans are not raspberries.

Talk about non-sequitur. We're talking about probabilistics. In the example, the humanness or raspberryness of the thing doesn't matter. It is the fact of probability that matters, especially in the Bayesian context. Probabilities get higher with additional independent factors indicating said event, whether it's a bad batch of raspberries indicating a gross pint, or a bunch of angry women indicating a gross judge.

 

[Trausti]

The number of accusers is a bit of a red herring; what matters is the strength of the evidence. Is there corroboration? Certainly there have been instances where there is no accuser - the victim was murdered, but there is physical evidence of sexual assault. As is oft stated, claims made without evidence can be dismissed without evidence. To leave it just to the accusation, without more, is to return to witch trials.

 

[Elixir]

As is oft stated, claims made without evidence can be dismissed without evidence.

Rethuglicans - Trump in particular - were very proficient at making sure there was no evidence (presented).
I admit though - just seeing the juxtaposition of an obviously traumatized woman apparently telling the truth to the best of her ability, vs. an accused man exhibiting the textbook behavior of a guilty (or insane) person, was enough to make me 90% sure he was guilty. The enthusiastic obstruction of justice by Trump and his enablers pushed it up to around 99%.

 

[Jarhyn]

The number of accusers is a bit of a red herring; what matters is the strength of the evidence. Is there corroboration? Certainly there have been instances where there is no accuser - the victim was murdered, but there is physical evidence of sexual assault. As is oft stated, claims made without evidence can be dismissed without evidence. To leave it just to the accusation, without more, is to return to witch trials.

The whole point is that you are dead wrong. A single credible accuser is weak evidence, but additional credible accusers is strong evidence, and ignoring that won't make the probabilistics go away. At any rate, if you want to see witch trial, just give it a few years, and we'll be back into the full swing of the McCarthy era reborn. Not that you or the senate were interested in finding evidence, since they didn't even LOOK for corroboration, which they could have found if they looked into Tobin's house; if it has or had at the time a "narrow staircase" and a "bathroom across from a bedroom", or even done a house lineup for Ford, all that would have been easy to corroborate. But those weren't even questions the FBI was allowed to ask. At least for BK. At any rate, we aren't asking anyone to be sent to jail or burned at the stake. We are asking for claims to believed enough to be honestly investigated

We are asking for the trust that we then follow with verification. You're position seems to be "I will trust only after verification" alongside "I will only attempt verification if I trust", leading to neither trust nor verification.

 

[Elixir]

We are asking for claims to believed enough to be honestly investigated.

Obviously the claims were believed enough for the 'thugs to want to suppress evidence...
But what I would ask, is that qualification for a seat on the highest court in the land should rise above "innocent until proven guilty", hopefully to at least the level that I would exact from an entry level production worker in my Company. Certainly wouldn't hire someone who lied under oath as Kavanaugh did... but Trump and his trumpsuckers have a lower, more compassionate standard for hiring his stooges.

 

[starwater]

Ummm....humans are not raspberries.

Talk about non-sequitur. We're talking about probabilistics. In the example, the humanness or raspberryness of the thing doesn't matter. It is the fact of probability that matters, especially in the Bayesian context. Probabilities get higher with additional independent factors indicating said event, whether it's a bad batch of raspberries indicating a gross pint, or a bunch of angry women indicating a gross judge.

I disagree. Raspberries are not sentient, nor can they move. If they could move they would get away from the molder ones.

 

[Jarhyn]

Ummm....humans are not raspberries.

Talk about non-sequitur. We're talking about probabilistics. In the example, the humanness or raspberryness of the thing doesn't matter. It is the fact of probability that matters, especially in the Bayesian context. Probabilities get higher with additional independent factors indicating said event, whether it's a bad batch of raspberries indicating a gross pint, or a bunch of angry women indicating a gross judge.

I disagree. Raspberries are not sentient, nor can they move. If they could move they would get away from the molder ones.

Can anyone comment on whether this kind of garbage is normal to this person's discourse and thus worth just putting him on ignore? I tend to hate doing that to people, unless I know pretty confidently that they are entirely vacuous.

 

[Jarhyn]

We are asking for claims to believed enough to be honestly investigated.

Obviously the claims were believed enough for the 'thugs to want to suppress evidence...
But what I would ask, is that qualification for a seat on the highest court in the land should rise above "innocent until proven guilty", hopefully to at least the level that I would exact from an entry level production worker in my Company. Certainly wouldn't hire someone who lied under oath as Kavanaugh did... but Trump and his trumpsuckers have a lower, more compassionate standard for hiring his stooges.

I actually started a thread about that that mostly went nowhere about the reasonable symmetry that guilt should be certain in indictment as much as worthiness must be certain in elevation: if you cannot be certain someone didn't rape, you shouldn't put them in a position to judge on laws about women or consent, just as much as if you cannot be certain someone DID rape, they don't really belong in jail. I fin this symmetry to be the starting point for these standards. Or in other terms, a change of position vertically requires certainty, much like all acceleration requires force.

Either way, trust but verify is pretty much the basis for all rational inquiry. Always start out believing, but throw your belief through the wringer.

Honestly, I believe her. Doesn't mean I'm not going to verify her story honestly and dispassionately. But I DON'T believe him; he lied early and often.

 

[starwater]

I disagree. Raspberries are not sentient, nor can they move. If they could move they would get away from the molder ones.

Can anyone comment on whether this kind of garbage is normal to this person's discourse and thus worth just putting him on ignore? I tend to hate doing that to people, unless I know pretty confidently that they are entirely vacuous.

 

[Elixir]

We are asking for claims to believed enough to be honestly investigated.

Obviously the claims were believed enough for the 'thugs to want to suppress evidence...
But what I would ask, is that qualification for a seat on the highest court in the land should rise above "innocent until proven guilty", hopefully to at least the level that I would exact from an entry level production worker in my Company. Certainly wouldn't hire someone who lied under oath as Kavanaugh did... but Trump and his trumpsuckers have a lower, more compassionate standard for hiring his stooges.

I actually started a thread about that that mostly went nowhere about the reasonable symmetry that guilt should be certain in indictment as much as worthiness must be certain in elevation: if you cannot be certain someone didn't rape, you shouldn't put them in a position to judge on laws about women or consent, just as much as if you cannot be certain someone DID rape, they don't really belong in jail. I fin this symmetry to be the starting point for these standards. Or in other terms, a change of position vertically requires certainty, much like all acceleration requires force.

I did see that thread - not sure, but don't think I replied. It did iirc elicit an impressive bunch of dissembling from our few Kavanuts. I have been angered (probably to an unhealthy degree) by hearing all those 'thugs bandy "beyond a reasonable doubt" around, as if we were talking about a criminal conviction. They're fucking legislators, trying to pretend they don't know any better...
One more reason I will vote straight blue this fall even if I have Republican friends running at the local level. That party has gone full-on batshit crazy with power, and will certainly turn this country into something far(ther) from a representative democracy if allowed to do so.

 

[Jarhyn]

I actually started a thread about that that mostly went nowhere about the reasonable symmetry that guilt should be certain in indictment as much as worthiness must be certain in elevation: if you cannot be certain someone didn't rape, you shouldn't put them in a position to judge on laws about women or consent, just as much as if you cannot be certain someone DID rape, they don't really belong in jail. I fin this symmetry to be the starting point for these standards. Or in other terms, a change of position vertically requires certainty, much like all acceleration requires force.

I did see that thread - not sure, but don't think I replied. It did iirc elicit an impressive bunch of dissembling from our few Kavanuts. I have been angered (probably to an unhealthy degree) by hearing all those 'thugs bandy "beyond a reasonable doubt" around, as if we were talking about a criminal conviction. They're fucking legislators, trying to pretend they don't know any better...
One more reason I will vote straight blue this fall even if I have Republican friends running at the local level. That party has gone full-on batshit crazy with power, and will certainly turn this country into something far(ther) from a representative democracy if allowed to do so.

See, my biggest problem with things o that kind are that people don't hold them to questions. They say something that has a corollary they disagree to? Nobody presses them on the defense of the corollary. Someone asks them questions about their actual positions about things? They disappear or don't answer the question. I happen to think that we need to start hammering questions rather than letting them squeak away and change the subject. But that kind of cooperation isn't to be expected in a place like this, I guess.

I count it a pretty significant victory that I actually got one of them to admit that they would not accept a rapist on the SCOTUS... even if they fail to understand that a lack of physical evidence does not mean innocence, and that the standard for elevation should be innocence beyond a reasonable doubt. But no, they are too much of cowards to, at least at this point in time, agree that the standard of evidence has a symmetry around direction of promotion.

 

[Elixir]

I actually started a thread about that that mostly went nowhere about the reasonable symmetry that guilt should be certain in indictment as much as worthiness must be certain in elevation: if you cannot be certain someone didn't rape, you shouldn't put them in a position to judge on laws about women or consent, just as much as if you cannot be certain someone DID rape, they don't really belong in jail. I fin this symmetry to be the starting point for these standards. Or in other terms, a change of position vertically requires certainty, much like all acceleration requires force.

I did see that thread - not sure, but don't think I replied. It did iirc elicit an impressive bunch of dissembling from our few Kavanuts. I have been angered (probably to an unhealthy degree) by hearing all those 'thugs bandy "beyond a reasonable doubt" around, as if we were talking about a criminal conviction. They're fucking legislators, trying to pretend they don't know any better...
One more reason I will vote straight blue this fall even if I have Republican friends running at the local level. That party has gone full-on batshit crazy with power, and will certainly turn this country into something far(ther) from a representative democracy if allowed to do so.

See, my biggest problem with things o that kind are that people don't hold them to questions. They say something that has a corollary they disagree to? Nobody presses them on the defense of the corollary. Someone asks them questions about their actual positions about things? They disappear or don't answer the question. I happen to think that we need to start hammering questions rather than letting them squeak away and change the subject. But that kind of cooperation isn't to be expected in a place like this, I guess.

...or in the Senate judiciary committee.

I count it a pretty significant victory that I actually got one of them to admit that they would not accept a rapist on the SCOTUS... even if they fail to understand that a lack of physical evidence does not mean innocence, and that the standard for elevation should be innocence beyond a reasonable doubt. But no, they are too much of cowards to, at least at this point in time, agree that the standard of evidence has a symmetry around direction of promotion.

Yup. And yup again. It's shameless behavior, unless one is willing to ascribe to them the intelligence of a parakeet.

 

[Loren Pechtel]

That answer addresses the OP without any of the unnecessary assumptions about a trial or credability of a particular witness.

The problem is the OP is making the assumption the claims are independent.

Once the women know of other reports it ceases to become independent--it could be someone with an axe to grind jumping on the bandwagon.

That's why in a situation like this credibility matters a lot more than numbers.

Ford was credible, Kavanaugh's response made him look very guilty, Ford's supplying a bunch of details that have since been verified goes a long way towards proving this isn't just revenge about some unknown slight. Something highly memorable happened at that party and an assault is by far the likeliest answer as to what.

 

[laughing dog]

That answer addresses the OP without any of the unnecessary assumptions about a trial or credability of a particular witness.

The problem is the OP is making the assumption the claims are independent.

No it doesn't.

Once the women know of other reports it ceases to become independent--it could be someone with an axe to grind jumping on the bandwagon.

Or it could be someone who is making a valid accusation.