
How Likely Is Someone Accused of Assault by Multiple People to Be Innocent? - svtrent
http://obsessionwithregression.blogspot.com/2014/12/how-likely-is-someone-accused-of.html
======
pekk
Some centuries ago, there were periods when many people would get accused of
consorting with the devil, and multiple witnesses would be brought forward to
substantiate this, and many people were burned as a result.

That's not just a problem of ancient superstition; as recently as the 90s, a
number of people were convicted of Satanic Ritual Abuse, with multiple
witnesses, and some of the real victims (often women working in places like
daycare centers) have been in jail for decades on the basis of clearly
unbelievable and coached testimony.

Whenever one of these periods occurs, it's not a one-off act by some
individual, nor even a matter of any specific religion. It's a clear
indication that the justice system has been fundamentally compromised in the
way it treats evidence and renders a final judgement.

This article might have good intentions, but its method could be applied to
witchcraft or Satanic Ritual Abuse, and obtain the same kinds of conclusions:
If you're accused of witchcraft by multiple people, you're probably guilty.
This is still mostly true if we don't believe that witches are a separate kind
of people. Increasing our certainty that witches are witches is even good for
the people who are accused of being witches.

Counting up the number of accusations is clearly a wrong standard for
determining that someone is guilty. The available evidence in each case
matters, and accusations are not necessarily independent. The general
presumption of innocence until proven guilty is still necessary and still
applies to rape as to other crimes.

~~~
philwelch
The difference being that witchcraft and satanism were moral panics that never
actually happened to anyone, and rape is something that actually happens to
real people fairly often.

~~~
s_q_b
It is a mistake to believe that moral panics regarding sexual assault never
occur. That's precisely what the satanic (sexual) ritual abuse trials were.

Because the Department of Justice says that a female is one third more likely
to be raped not attending college than on a college campus I'd say it is at
least possible we're in the midst of a moral panic over sexual assaults on
college campuses.

The lack of reliable data, which places the number of campus sexual assaults
somewhere in the wildly varying range of .08% to 20% of the population, the
pseudo-religious "with-us-or-against-us" mentality, the desire to see justice
done extralegally rather than in a court, and the vitriolic shaming of
dissenting voices all have the flavor of a moral panic.

The mob-based tribal thinking that "if he's been accused more than once, he
must be guilty" is an inherent flaw in human reasoning, of which this program
is simply a mathematical model.

Mathematically, the fatal flaw of the model is that it assumes all accusations
are supported by evidence of an arbitrary positive weight, and that all
accusations are independent. This is never the almost never the case in real
accusations. Perhaps before dropping out of school he should read up on other
misuses of statistics that have manipulated juries and ruined lives, like the
famous "Prosecutor's Fallacy."
[http://en.wikipedia.org/wiki/Prosecutor%27s_fallacy](http://en.wikipedia.org/wiki/Prosecutor%27s_fallacy),
which quite literally lead to the death of British Solicitor Sally Clark.

What saddens me most is that some casual readers are now walking around with
the incredibly mistaken assumption that it is mathematically sound to assume a
person accused thrice is virtually certain to be guilty.

I don't say any of this to diminish the very real problem of sexual assault,
but merely to point out that people are surrendering their rights and their
reason to mob mentality.

That mentality is precisely what two thousand years of legal scholarship
evolved to fight. And whether executed by silicon or scythe, mob mentality is
wrong. And quite frankly it is frightening to watch.

~~~
philwelch
I will agree that multiple accusations of sexual assault are unlikely to be
independent. One of the biggest reasons victims come forward is when they
realize that their rapist has raped other people in the past and will continue
to rape other people in the future. Is there any such reason for _false_ rape
accusations to be joined?

Moral panics very rarely involve people coming forward and accusing an
individual person of attacking them. It's possible for one or two deranged nut
jobs to go around saying that (eg) Bill Clinton raped them. Over a dozen
people accusing someone like Bill Cosby who isn't widely hated the way Clinton
was, and recounting their individual experiences? Is there any precedent for
something like that happening?

~~~
s_q_b
Yes, many. See e.g. The McMartin Preschool Trial.
[http://en.wikipedia.org/wiki/McMartin_preschool_trial](http://en.wikipedia.org/wiki/McMartin_preschool_trial)

>"By spring of 1984, it was claimed that 360 children had been abused."

 _All_ of these linked allegations later turned out to be complete
fabrications, creations by the investigators invented out of whole cloth, and
targeted against the same specific individuals.

In fact false accusations from multiple individuals are a common police
tactic. Perhaps the individual has slept with several others, and the
encounters ended non-violently but non-amicably. Suddenly consensual
encounters retroactively become remembered as non-consensual after questioning
by investigators, the very purpose of which is to elicit accusations. As a
representative at these hearings, and student advisor, I've witnessed this
happen to students many times.

See also the DSK trial, where a French author from years before brought
charges that were similarly dismissed. The bandwagoning effect occurs
regardless of whether the allegations are true or false. People want money,
power, special treatment, and attention, and sadly, false allegations are
often an easy mechanism used to get them.

So yes, both false allegations and true allegations are unlikely to be made
independently. Not to mention the truly crazy people who are completely
uninvolved and will jump in for no discernible reason whatsoever, or in
criminal cases CIs who are transformed into additional "victims" to secure
convictions.

This isn't a story of math to the rescue. It's a store of bad statistics and
not paying enough attention in class, where they usually teach some variant of
the prosecutor's fallacy, since this type of falsity comes up often enough to
warrant consistent reinforcement that statistics aren't magic, and they can
ruin people's lives.

~~~
philwelch
Well children in specific are far easier to manipulate. As for DSK, I conceded
the possibility of "one or two deranged nut jobs", which is pretty much all
that happened in his case.

Agreed that the statistics don't tie out.

~~~
s_q_b
Yeah, I'm debating off the top of my head. I've seen it happen enough, I'm
sure there's a good exemplar case involving adults, but bandwagoning of false
allegations is a very real phenomenon.

~~~
s_q_b
If you don't believe in the correlation of false accusations, perhaps a Bloom
Filter could give us some help. Thinking through the details, but check this
weekend for a github implementation. Reply or PM if interested in helping out.

------
jeffdavis
This article is reckless. The author throws out a mathematical model regarding
a very sensitive subject with no evidence that the model reflects reality.

In effect, it just gives a mathematical veneer to the author's guesses.
Similar to how wearing a lab coat while stating your opinion makes it seem
scientific.

(The most obvious issue is non-independence, but there are plenty of other
problems.)

~~~
skj
Exactly correct. It was more or less, "Given this model, my assumptions are
correct!", completely missing the point that the model was the assumption
itself.

------
jeffdavis
"the rate of false accusations is low"

I didn't read the study, but how could anyone know this? I suppose you could
assume that a conviction means that the accusation is true, and that
exoneration means that accusation is false, but there are a lot of cases where
it's not known one way or another. I would be surprised if 90%+ of accusations
result in a conviction, so the study must be assuming that any accusation is
true if the accused is not exonerated.

There are also other, like if one party believes an assault took place and the
other does not, or if the accusation is true but the perpetrator is
misidentified.

Please correct me if I'm wrong, but my guess is that the statement above
(alone, out of context) is not well supported by evidence.

~~~
glenra
You're correct, the rate of false accusations might be quite high. The "2-8%"
stat given in OP really should be "2-10%" \- advocates somehow tend to lose
track of a couple studies that came out on the high end - but even that number
range is only the percentage of rape accusations _that were brought to the
police_ which were deemed _demonstrably_ false. For instance: the alleged
victim reported it to the cops but later recanted or changed their story so
much that it couldn't be trusted, or the facts on the ground made the story as
stated impossible.

Advocates are correct to note that this "2-10%" includes some mistakes - true
rape victims might be very confused in their testimony or might recant because
they get frustrated with the justice system - but it still should probably be
regarded as a _lower bound_ on the actual number of false accusations, as it's
a subset of the full total.

False accusations that wouldn't show up in this measurable "2-10%" include (a)
those in which the accusation is plausible, consistent and the accuser does
_not_ recant, (b) false accusations that _aren 't_ ever brought to the police.

~~~
clay_to_n
Are you sure this can be considered a "lower bound"?

The amount of people who were raped and never went to the police could be much
higher than the amount of people who lied to the police about being raped.

~~~
glenra
> _Are you sure this can be considered a "lower bound"?_

Pretty sure. my guess is that the true number is at least 15%, based largely
on the sort of accounting found here:

[http://slatestarcodex.com/2014/02/17/lies-damned-lies-and-
so...](http://slatestarcodex.com/2014/02/17/lies-damned-lies-and-social-media-
part-5-of-%E2%88%9E/)

(The lower bound is 2-10%; the upper bound is 20-40%)

> _The amount of people who were raped and never went to the police could be
> much higher than the amount of people who lied to the police about being
> raped._

This is true, but here is a factor you are overlooking:

"While rape victims have some incentives to report their cases to the police –
a desire for justice, a desire for safety, the belief that the evidence will
support them – false accusers have very strong incentives not to – too much
work, easier revenge through other means, knowledge that the evidence is
unlikely to support them, fear of getting in trouble for perjury if their
deception gets out. So I consider it a very conservative estimate to say that
the ratio of unreported to reported false accusations is 4:1 – the same as it
is with rapes. A more realistic estimate might be as high as double or triple
that."

~~~
philwelch
Rape victims have many more reasons not to go to the police than to go to the
police. The experience of being raped very commonly causes PTSD, and all of
the steps involved in going to the police--having a rape kit done (i.e. being
touched and examined in the very intimate parts that were just violated),
recounting your experience, seeing the suspect--would all cause a PTSD
sufferer to essentially relive the traumatic experience.

------
dahart
> But how can we combine multiple accusations of assault, given that survivors
> are usually unaware of each other and often reluctant to come forward?

I see the other comments pointing at this potential problem as well, but I'll
phrase it as a question - since the article opens with a reference to Bill
Cosby, is it even valid to combine multiple accusations of assault when the
accusers are aware of each other, possibly through media exposure, and may
have come forward as a result?

And while there is a (perhaps unsurprising?) correlation between independent
accusations and probability of guilt, how can this statistical approach be
responsibly used, and should it, and what for?

Assault is awful and I'm sure the majority of assaults with even one accuser
is (or should be) straightforward), but it seems like there are other
uncontrolled possibilities here besides the independence of accusations, like
whether the accuser and accused know each other.

~~~
kaitai
One way to deal with this is discussed in the article -- if details of reports
are not widely publicized (often the case), then details of
reports/allegations can be compared. In many cases, as noted in the post,
methods are consistent. You could use some Bayesian analysis to figure out the
probability that independent reports would come up with the same details.

------
crazypyro
Is there any consideration taken for the fact that public figures, like
celebrities, present a larger target, based on their wealth and fame?

I'd imagine that would make a difference when compared with a regular person
who is not in the public spotlight or doesn't have a large estate.

Does this "intuitive thought" actually represent real world events?

~~~
kaitai
Take a look at actual accusations of celebrities. Because of their wealth and
fame, they are really good at sweeping these accusations under the rug. The
first really public allegation against Cosby, for instance, was made public in
2002. Since it took until 2014 for anyone to care, it seems doubtful that the
wealth and fame of celebs makes them "better" targets.

It would be really interesting for someone to actually pull lists of famous
celebrities from the last few decades (from mentions in media, for instance),
look at rape accusations, and classify results. I don't know how you could
compare to "regular" guys as most non-famous people don't make the news even
if accused of rape, but a comparison of conviction rates could be
illuminating.

------
Alex3917
> The intuition that, “if you are accused of assault by multiple people,
> you’re probably guilty” is often accurate. Importantly, even if you were to
> choose settings where someone who has been accused once is more likely than
> not to be innocent, the probability of innocence often drops dramatically if
> they have been accused twice.

This doesn't account for whether or not the accusations are independent of one
another, which in this case most were not.

~~~
statistician409
(I'm the author of the post) the fact that accusations may not be independent
is of course important (although I'd question the aptness of the above
commenter's comparison to witch trials); I'd welcome your suggestions for
incorporating correlations into the model. This is one of the reasons the tool
discussed in the NYT's article could be powerful -- because it allows us to be
more confident that accusations were levied independently, since people submit
to the tool without knowing about other accusers.

~~~
logicallee
The comparison with witch trials is simple. People can be totally independent,
and not know each other, and independently conclude that you're a witch. Why
would they do this? Obviously due to some factor about you. The mistake you
make is using Occam's razor to conclude that that factor is "being a witch".
The other poster used the example of witches because we all know there is no
such thing.

There is 0% chance of someone being a witch, whom nobody has ever so much as
suspected of being a witch. But there is also 0% of someone being a witch,
about whom dozens of totally independent people, in different locations,
throughout the person's life and career, have independently come to the firm
and undeniable conclusion that they are a witch.

This is why this was the example that was used.

~~~
darkhorn
Everyone says that [put some religion here] is true. All these people can't be
wrong, can they be? Therefore this religion is true. Applies not only to
religion but also to heating home, sickness, astrology, cutting penices of
children etc.

~~~
logicallee
Not bad :) Author should post "How likely is someone to be the son of God
based on number of disciples?" and we can see where 12 fits in.

------
upside
The author starts off with a Bill Cosby example, front and center, then
continues to develop a stat model while acknowledging an inability to account
for incidentals, while never mentioning that Bill Cosby is more than likely to
have a significant number of incidentals.... Like, tonnes of money and hangin'
out at playboy mansions where shady-ness pervades. Back in the day, pre-
blogging, when journalism was actually a profession, journalists were taught
to avoid this kind of set up. Now it's everywhere and I can't help but be
unimpressed.

------
pcthrowaway
While interesting, this also completely fails to take into account motivations
for targeting people with false accusations.

For example, while Michael Jackson was accused of assault on two occasions, I
think it's fair to also consider that the prospect of a financial payoff could
be a motivation to press charges against him. In the first such case, he
eventually settled for $15 million towards a trust fund for the accuser,
despite no evidence and a strong case that the accusations were only levied as
a money grab (the accuser was seeking a monetary settlement instead of
criminal charges from the very beginning)

In the second public accusation (years later), Michael was found innocent.
Additionally, given the way things went in the first case, it is entirely
believable that someone could see accusing Jackson of child molestation as a
means to an easy payoff.

I'm not saying Michael Jackson is innocent beyond all doubt, but the court
clearly determined it was impossible to make a case that he was guilty beyond
all doubt. I do think it's important to consider other factors in situations
where assault (sexual or otherwise) is accused though.

For what it's worth, I think it's very likely Bill Cosby is guilty of most of
the allegations he is currently party to.

------
grandalf
What about the probability of someone who has been accused multiple times to
also draw false accusations? True ones?

What about the substantially different personal cost of making an immediate
accusation vs a delayed one? The same applies to someone like Snowden who
could have waited until he was in his 70s before blowing the whistle.

------
Xcelerate
My issue is more with smear campaigns. Leave the concern of guilt or innocence
to the justice system. For every 100 people that are "probably" guilty on the
basis of hearsay, how many innocent ones have had their reputation
irreversibly ruined by widespread internet witch-hunts? If these people would
focus their time and energy on actually coming up with solutions to the
problems they're complaining about in their generality rather than targeting
specific individuals (for instance, solving the problem of performance
enhancing drugs in cycling vs creating a media sensation about Lance
Armstrong), I think society would be much better off.

------
aratinga
Why do I get the strange feeling that most of these comments were posted by
males, I wonder?

Leaving college aside, there has been a lot of discussion of rape in the
military. Apparently there are a number of repeat predators, in an environment
where bringing an accusation can result in the accuser's being thrown out of
the military, shunned, or assaulted. (Male victims abound, by the way.) I
would love to see this simulation with numbers based on the military
experience. Meanwhile the military are reluctant to allow outside interference
in their complicity with rape. The missing item in the reporting is how many
of those accused were accused more than once.
[http://www.militarytimes.com/story/military/pentagon/2014/12...](http://www.militarytimes.com/story/military/pentagon/2014/12/04/pentagon-
rand-sexual-assault-reports/19883155/)

------
casebash
"probability a non-DA will assault someone in a given encounter" \- so
according to this model, if someone has enough sexual encounters there is a
near 100% chance that they will assault someone. That's kind of dodgy.

------
casebash
"probability a non-DA will assault someone in a given encounter" \- So this
assumes that if someone has enough encounters that they will eventually have
near 100% chance of committing assault.

------
nosespray
Until the effect of media bombardment and other 'incidentals' can be given a
weight, the whole thing is an exercise in futility.

------
mpweiher
This is horribly wrong on so many levels.

False reports/accusations of crime in general tend to be low, in the 2-8%
range reported here. By this logic, we can dispense with this whole silly and
expensive criminal justice system and just convict _everyone_ based on simple
accusation. We used to call this sort of thing "lynching", and it is generally
considered a good thing that it's become rare.

"It is better that ten guilty persons escape than that one innocent suffer"[1]

Also note that the "low rate" for false accusations is for cases were the
false accusation is _proven_ :

"The determination that a report of sexual assault is false can be made only
if the evidence establishes that no crime was committed or attempted. This
determination can be made only after a thorough investigation. This should not
be confused with an investigation that fails to prove a sexual assault
occurred. In that case the investigation would be labeled unsubstantiated. The
determination that a report is false must be supported by evidence that the
assault did not happen."[2][3]

By this standard, cases of rape that are actually proven are also low,
depending on where you look in the 7% range of reported[3]. So the "we just
don't know" figure is very, very high, we simply do not have strong evidence
either way[4]. Other studies have found false report rates much higher [5][6].

The Air Force study[6] is interesting in that admissions of false accusations
increased dramatically when it became known that a Polygraph would be
administered (though AFAIK, the Polygraph information itself was not used as
indication of a false report, only an actual admission). The raw data of
admitted false cases was then combined with other characteristics of those
cases to develop a model for "likely" false accusations (things like "does the
rape cause problems or solve problems for the accuser", "does the report
follow widely assumed patterns of rape vs. real patterns", "do the injuries
show patterns that are typical of self-infliction" etc.) With that model,
applied conservatively, the false report rate was above 50%.

There is also an interesting investigation showing that the 2% figure that
pops up in many "studies" books and papers on the subject can all be traced to
a single off-the-cuff, non-researched remark.[7]

So the reference figures are at best flawed and way too uncertain to base a
model on.

Additionally, the statistics are incorrectly applied to a single event ("How
likely is _someone_ ..."). The statistics only work for a sufficiently large
population.

Finally, as many others have pointed out, the events are not uncorrelated, and
the assumption that they are and that "lots of reports must mean there is
something there" is a well-documented fallacy of human cognition. The McMartin
case is an obvious one, but there is also the famous case of the French city
of Orleans, where an entire city was convinced that girls were being drugged
and abducted in fashion stores, which turned out to be completely
unfounded.[8][9][10]

So please pack up this model, or let's all just abandon our legal system, due
process and meet for a happy lynching.

[1]
[http://en.wikipedia.org/wiki/Blackstone's_formulation](http://en.wikipedia.org/wiki/Blackstone's_formulation)

[2] [http://yesmeansyesblog.wordpress.com/2010/09/09/false-
rape-a...](http://yesmeansyesblog.wordpress.com/2010/09/09/false-rape-
allegations-are-rare/)

[3] [https://rainn.org/get-information/statistics/reporting-
rates](https://rainn.org/get-information/statistics/reporting-rates)

[4]
[http://lawprofessors.typepad.com/crimprof_blog/2004/12/2_fal...](http://lawprofessors.typepad.com/crimprof_blog/2004/12/2_false_rape_st.html)

[5]
[http://www.informationisbeautiful.net/visualizations/rape-a-...](http://www.informationisbeautiful.net/visualizations/rape-
a-lack-of-conviction/)

[6]
[http://www.fathersmanifesto.net/mcdowell.htm](http://www.fathersmanifesto.net/mcdowell.htm)

[7]
[http://digitalcommons.lmu.edu/cgi/viewcontent.cgi?article=22...](http://digitalcommons.lmu.edu/cgi/viewcontent.cgi?article=2216&context=llr)

[8] [https://www.kirkusreviews.com/book-reviews/edgar-
morin/the-r...](https://www.kirkusreviews.com/book-reviews/edgar-morin/the-
rumor-in-orleans/)

[9]
[http://de.wikipedia.org/wiki/Gerücht_von_Orléans](http://de.wikipedia.org/wiki/Gerücht_von_Orléans)

[10]
[http://fr.wikipedia.org/wiki/Rumeur_d'Orléans](http://fr.wikipedia.org/wiki/Rumeur_d'Orléans)

------
peterwwillis
First OP says they want to find the likelihood, then they try to find the
probability? Already I am skeptical of the methodology.

 _" While it can be difficult to determine guilt in a single case, my
intuition is that a person independently accused of assault by multiple people
is quite unlikely to be innocent."_

Just so we're clear here: intuition is a heuristic, which is incredibly flawed
and only intended to be used as a potential risk indicator for split-second
decisions. Any time you hear of something risky you are more inclined to
believe it because to _not_ believe it would potentially open yourself up to
risk. The only way to mitigate it is to have additional information or motive
that overrides the unknown risk.

Back to the model: they cite one study on sexual assault. Do you know how many
actual studies there have been on sexual assault? Not many. Do you know how
many of them had widely varying results? Most of them. Do you know how many
had different methodologies which changed the nature of the model? All of
them. So I guess let's ignore that someone could probably pick a different
study that would change the results.

So what does this particular study say? The study involved asking 2,000 men at
one college in one state about their sex lives. (Random sampling? Who needs
that?) Of those men, about six percent admitted to sex that fell under the
legal definition of rape without consent of the woman, which includes force or
alcohol.

Consider for a moment that the legal guidelines basically say that if you have
a bottle of wine with your girlfriend and you end up in bed together, it's
rape if there wasn't a consent agreement. In this case they're only asking the
men and making a judgement based on the legal framework, and not asking the
women about their relationship or if there was consent, which could _possibly_
change the results. But anyway,

 _" I think the UVA episode illustrates precisely why statistics are so
important -- because anything can happen in a single story, making it a risky
thing to hang a cause on."_

So why would you create a model based on a single limited study, and not at
the very least recreate your model based on the data from other studies?

 _" Regardless of what really happened at UVA, the broader trend is clear: the
rate of campus sexual assaults is high (20%, says CDC, although better data
should be collected); the rate of false accusations is low (this review cites
6 studies which all yield estimates between 2% and 8%, lower than the rate of
false reports for car theft)."_

Another study said the campus assaults were 90%. The CSA final report put it
at 13.7%. And (all) the false accusation studies were collected and analyzed
by Philip N.S. Rumney and determined that due to the unreliable research
methodologies used, along with unreliable judgements by law enforcement, it
was impossible to give a plausible statistic.

I've always found that people rely on statistics when they want a nice simple
number to sum up their opinions, and don't want to deal with the fact that
there is no simple, clean way to summarize complicated, wide-ranging
circumstances, events and behaviors.

~~~
kaitai
The study is not so easy to slag off; this is 6 percent of guys saying that
their encounters fit the definition of rape and that they do it over and over
again. It is remarkable that I've talked to a number of guys who wouldn't have
sex with a girlfriend so drunk she can't consent, but these special guys
manage to do it on average 5.8 times each and are fine admitting it. If you
just happen to keep getting your "girlfriends" so drunk they can't consent and
then having sex with them -- a new one every few months -- don't you think
there's something wrong with your relationship patterns? Why defend that?

~~~
peterwwillis
I have not and do not defend anyone for their actions, whatever they are,
consensual or not. I am responding to a flawed statistical model. You're free
to judge whomever you want, though, including people who respond to flawed
statistical models. You're also free to essentially accuse me of defending
quasi-rapists just because I find a statistical model flawed. It's a free
country, after all.

"Can't consent" is different than "lack of consent", which is different than
"consenting", etc. Consent is a highly varied and complex subject. There's
explicit consent, implicit consent, informed consent, implied consent, non-
consent, consent agreement violation, consensual non-consent, re-established
consent, etc etc. Legally speaking (Note that I am not a lawyer) in America,
there's very few laws that determine what is consensual or not. Usually it has
to be determined by a jury when it goes to trial. It's because of this that,
legally speaking, having alcohol does not alone remove the ability to consent
in all cases.

Non-legally-speaking, I think you missed my original point. Nowhere in my
commentary, nor in the study, does it say that anyone was actually intoxicated
past the point of being able to consent. It merely says that _within the legal
framework_ someone could have been held liable for non-consensual sex. All
this requires is that the person was intoxicated (about .08 BAC, or 1 beer, in
the US).

If you feel like condemning people for this, so be it. All i'm saying is a
study that generalizes based on guidelines like this is flawed, amongst other
things.

------
darkhorn
[http://m.liveleak.com/view?i=db6_1370665965&comments=1](http://m.liveleak.com/view?i=db6_1370665965&comments=1)

