Policy Market Blog

O.J. Simpson, Alan Dershowitz, Bret Kavanaugh, Bill DeBlasio, and Statistics

Martin Kennedy - Wednesday, September 26, 2018

Alan Dershowitz, during the O.J. Simpson trial, noted that fewer than one in 1000 women who are abused by their husbands are later killed by them.  The juror considers.. 'what is the probability that a man who has abused his wife went on to murder her?'  One in one thousand.  Not a frequent course of events.  

Unfortunately, the prosecutors did not challenge Dershowitz’s crude use of statistics.

The fact was that Nicole Brown Simpson had been killed.  Something was known. That makes it a conditional probability.  The appropriate question? 

Given that a woman has been killed, what is the probability that the husband, ex, or boyfriend who abused her did the killing? 

Answer: More than 80% of the time.  It’s a conditional probability.  

Nevertheless, pundits have asked why would a woman come forward (if it weren’t true).’  Of course they didn't really ask, rather it was a rhetorical question, posed repeatedly.  It was frequently followed by noting that few, between 2 and 10%, of sexual assault accusations are false.  

It's similar, though not identical, to the conditional probability.  The implication of the rhetorical question is that normal people don't make false accusations of sexual assault.  That's true enough as far as it goes.  A tiny percentage of women make false accusations.  But, we know something, namely that an accusation was made.  Considering whether it might be false, given that it was made, is not the same thing as pondering why any given woman would come forward.

Therefore, given that an accusation was made, why might it be false?

A fundamental assumption in economics is that people respond to incentives.  People do unseemly, and even horrific, things for money, power, and attention.  Occam’s Razor suggests a false allegation in this case might be motivated by ideological opposition.  Is it unreasonable to consider?  Of course not.  

Ideology stirs passion.  Some, not many, have bombed abortion clinics.  They risked not just a media circus and disapprobation but jail and a homicide conviction.  Others have become eco-terrorists.  An Alabama football fan killed a beautiful tree at Auburn.  Questioning motives is fraught but that doesn't suggest it isn't justified or advisable.  


As for the data, that between 2% and 10% of accusations are false, it is low but includes only those cases where the accusation is demonstrably false.


There is a much higher rate of unsubstantiated accusations – those that are not supported or proven by evidence.  Some portion of those are false (and others true) but indeterminate after an investigation.  It is reasonable, if not probable, to conclude that the true rate of false accusations is well north of the reported data. 


Since any false allegation should be assumed to be motivated by something, it follows that motive and the probability of a false accusation are not distinct.  We don't expect a false accusation to be made for no reason at all. 


The rate of sexual violence is notoriously difficult to quantify.  Methodologies vary and the range -- from rape and attempted rape to levels of harassment -- is broad. The Bureau of Justice provides estimates of unreported auto theft (31%) and aggravated assault (42%).  They report that accusations of rape lead to arrest 18% of the time (26% for robbery and 40% for (non-sexual) assault).  Convictions, across the board, are rarer still.   


Most reports of sexual assault involve someone who is or was intimate with the victim, an ex-husband or boyfriend for example (33%), or an acquaintance (39%).    

The rate of unsubstantiated accusations of sexual assault vary between jurisdictions. At the extreme, NYC’s Dept of Education has substantiated just seven of 471 sexual harassment complaints since 2013 (about 1.5%). 

Why so low?  Here's NYC Mayor, Bill De Blasio via the New York Daily News, April 25, 2018

There has been a history, it's pretty well-known inside the education world, of some people bringing complaints of one type or another for reasons that may not have to do with the specific issue — and this is not just about sexual harassment it's about a whole host of potential infractions.

He went on to say... 

...that the city takes very seriously "any sincere reporting" of problems, from sexual harassment to cheating on tests, but insisted DOE employees toss around fake accusations at one another.

The headline of the story?

De Blasio blames the DOE’s high number of unsubstantiated harassment complaints on fake accusations

An application:

If you have no good idea about the population of Philadelphia but are asked to speculate, you construct something like the following in your mind… 



Less than one million


Between one and two million


More than two million



Now, suppose you are told that Philadelphia was the fifth largest city in the country in 1990 and that the sixth largest city at that time was San Diego with a population of 1.1 million. 

You still don’t know what the population of Philadelphia is but you have more information.  You speculate given a condition, the factoid you'd been provided.  You update your table…



Less than one million


Between one and two million


More than two million


In other words, citing the infrequency of false accusations of sexual assault in general is of dubious value in a particular case.  Rather, what we know about the given condition(s) should be considered first.  The condition influences the probability.   


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