A Model For The Probability Of Guilt In The Age Of #MeToo

The case of journalist-turned-government minister MJ Akbar in India got me thinking about the probability of guilt when a man is independently accused of sexual harassment by a number of different women. At last count, 16 different women have come forward as part of the #MeToo wave sweeping India, to accuse Akbar of various kinds of sexual misconduct.

At the time of writing, Akbar has chosen to brazen it out by filing a criminal defamation suit against the first woman who made her accusation public.

This case has since become a cause célèbre in India, with commentators taking various positions on it.

I personally believe that the weight of credibility is on the side of Akbar's accusers, but I was wondering whether there was a way to approach such a situation more objectively, even quantitatively. After all, each individual accusation could be dismissed as a case of "He said, she said", but put together, the accusations build up a more compelling argument.

How compelling?

Let's start with the simplest case. A man is accused of misbehaviour by a woman. He denies it. Neither of them has any evidence, or any witness, to back up their claim. Prima facie, both of them seem equally credible. What should an objective observer think?

With no further input and with no biases, an objective person would have to conclude that there is a 50% probability that the woman is telling the truth, and therefore a 50% probability that the man is guilty. The corollary is that there is a 50% probability that he is innocent.

Now, this obviously contradicts the legal principle that an accused person is 100% innocent until proven guilty, but this is not a court of law, where evidence is required beyond the shadow of a doubt before an accused can be convicted of a crime. This is a thought experiment. We are trying to compute what we can adopt as a working hypothesis, based on the balance of probabilities.

In graphical terms, this is what the picture looks like when a man is accused by just one woman:

Now let's make this more interesting. Let's say a second woman steps forward to make a similar accusation, based on an independent incident. And let's say he denies this accusation too.

Does our view of the man's guilt change? Do we still think it's just his word against his accusers', and therefore that he's no more guilty than we thought before? Or do we start to doubt him a little more now? If so, by how much?

My model is that each subsequent accusation halves the probability of his innocence. And so, this is what the picture should look like:

It's important to note that we are not treating the three claims as completely independent, and assigning a 33.33% probability to each. That's because the claims of the two women, while independent, nevertheless reinforce each other. The accusation of the second woman halves the probability of innocence that we granted him after the first accusation. So we assign a probability of only 25% to his innocence now, not 33.33%.

What happens when a third woman steps forward? It's easy to follow the logic now:

With three independent accusers, the man's probability of innocence reduces to 12.5%, notwithstanding his protestations.

Stated in mathematical terms, the probability of a man's guilt when independently accused by 'N' women is given by

P_g = 1 - (½)^N

When N = 1, P_g = 0.5, or 50%
When N = 2, P_g = 0.75, or 75%
When N = 3, P_g = 0.875, or 87.5%

Let's apply this model of guilt to the MJ Akbar case. The number of his accusers now stands at 16:

1. Priya Ramani
2. Ruth David
3. Majlie de Puy Kamp
4. Saba Naqvi
5. Ghazala Wahab
6. Shutapa Paul
7. Shuma Raha
8. Kanika Gahlaut
9. Suparna Sharma
10. Prerna Bindra
11. Harinder Baweja
12. Anju Bharti
13. Malini Bhupta
14. Kadambari Wade
15. Swati Gautam
16. Tushita Patel

What's the probability that Akbar is guilty?

P_g = 1 - (½)¹⁶ = 0.999984741210938, or 99.998%

In non-mathematical language, he's toast.

#TimesUp

Update 17/10/2018: MJ Akbar has resigned as Minister of State for External Affairs, after 20 women expressed their desire to testify in court against him. Three of them were from the original list (Tushita Patel, Kanika Gahlaut and Suparna Sharma), but the other 17 were all new, bringing the total number of his accusers to 33.

17. Meenal Baghel
18. Manisha Pande
19. Ramola Talwar Badam
20. Kaniza Gazari
21. Malavika Banerjee
22. A.T. Jayanthi
23. Hamida Parkar
24. Jonali Buragohain
25. Sanjari Chatterjee
26. Meenakshi Kumar
27. Sujata Dutta Sachdeva
28. Hoihnu Hauzel
29. Reshmi Chakraborty
30. Kushalrani Gulab
31. Aisha Khan
32. Kiran Manral
33. Christina Francis

Don't even bother calculating the probability of his guilt now.
(If you're curious, it's 99.99999999%.)

When Good Sense Seasons Justice - The Justice Verma Committee's Report

After weeks of hearing nothing but the most mediaeval claptrap emerging from the mouths of India's public figures, it was a pleasant shock to read page after page of sweet reason in the long-awaited report of the Justice JS Verma Committee. The report, modestly titled "Amendments to Criminal Law", can be thought of as the thinking man's (or woman's) reasoned response to the brutal gang rape in Delhi in December last year. I would recommend that people at least download the document and skim through it, because it's almost a mini-degree in liberal arts for the aspiring cultural sophisticate.

The references in this report to the Indian constitution reminded me of the mental model that I have of the Indian justice system, without which I find it an infuriatingly contradictory mess. When one understands the Indian system of law as comprising three different layers that represent three completely different world-views, the madness becomes partially understandable.

A simple explanation of India's legal schizophrenia (click to expand)

[Of course, this is a gross oversimplification, and can be faulted on several levels. Still, I believe it represents a fairly good working model that explains the often puzzling contradictions between the various voices that are heard in Indian forums.]

Justice (Retd) JS Verma, a former Chief Justice of the Supreme Court, flanked by Justice (Retd) Leila Seth, former Chief Justice of the Himachal Pradesh High Court and former Solicitor General Gopal Subramanium

I especially like the following aspects of the JS Verma Committee report:

1. It recognises the multi-faceted nature of the problem and does not come up with facile and simplistic solutions. It blames lacunae in the law, lax enforcement, an unsympathetic officialdom and a pervasive culture of patriarchy, and then follows them up with recommendations in all these areas.

2. It recognises the concept of "marital rape", which should come as a welcome cultural shock to Indian society.

3. It unwraps the national flag from around the armed forces, explicitly recommending that soldiers be held accountable for crimes against women in disturbed areas under the control of the military. Any criticism of the military has been considered unpatriotic, and armed forces personnel have operated with impunity for far too long under the protection of the AFSPA (Armed Forces Special Powers Act). A similarly uncowed treatment of police misbehaviour occupies a full section.

4. It resists the pressure of the mob baying for blood by ruling out death and castration for rape. The maximum recommended sentence for rape is life imprisonment with no chance of parole. We are reminded that we are talking about justice here, not revenge or retribution. India cannot and must not be a Saudi Arabia.

5. It excoriates traditional "morality" with many examples, such as the misplaced notion of "honour" and the outrageous idea that rape victims ought to marry their offenders for the problem to be "solved". It also quotes from Sohaila Abdulali's famous autobiographical article on why rape is horrible (hint: it has nothing to do with the loss of "honour" or "virtue").

6. It highlights the need to recognise the rights of citizens with different gender identities and sexual orientations, such as gay and transgender people.

7. It guides Indian law towards greater compliance with UN resolutions and international treaties. No country is an island; there is a web of shared values that needs to tie human civilisation together. It demolishes the stereotypes of Indian women versus Western women that have characterised even some Supreme Court judgements.

8. It comprehensively addresses the issue of sexual harassment and has a number of recommendations not just for the government but also for independent tribunals and for employers of all kinds.

9. It does not neglect various other forms of violence and injustice, such as acid attacks, domestic violence, human trafficking (with very moving testimony from victims), dowry-related harassment, child sexual abuse, the notorious Khap Panchayats, etc.

10. It addresses the need to improve public safety for women and provide better amenities. It also lays out a very comprehensive code of practice for the medical and legal examination of sexual assault victims.

11. It doesn't shy away from raising the issue of electoral reforms, given that so many MPs have rape and molestation charges against them.

12. It talks about educational reform and social engineering to improve perceptions.

In short, this is an amazing document. In much the same way that Thomas Huxley was "Darwin's Bulldog", the Justice Verma Committee's report is the Indian constitution's bulldog. It can shock awake the conscience of those who read it.

Refreshingly, the report does not artificially curtail its content in the interests of conciseness. It is 630 pages long. It recognises that certain things need to be said, and that this is the most opportune time in Indian history to say them, a time that President Obama would call a "teachable moment". It is a comprehensive critique of everything that is wrong with Indian society and Indian systems where the treatment of women, children and the "different" are concerned. And it only took 30 days to produce!

Much has been made of India as a civilisation, and the scriptures that are deemed the spiritual foundation of that civilisation. But if India as a nation is ever to be thought of as truly civilised in the modern sense of the term, this document could well be the moral foundation on which such a civilised society is based.