P(Guilty|Innocent) = ?

different if he hadn’t bluffed his way to victory in a poker tournament. A lot of powerful characters are depicted to be good at poker: Harvey Specter in Suits, James Bond in Casino Royale, Henry Gondorff in The Sting, Rusty Ryan in Ocean’s Eleven, and so on. Deception is the sine qua non of poker. In chess, it all comes down to a battle of wits, again. Every move is interpreted by two human minds, each with its idiosyncrasies. When you play against someone you begin to form a sense of their beliefs and preferences, which may not always be objective. You prey on the beliefs of your opponent and present them with the opportunity to deceive themselves. World Champion Emanuel Lasker has shown legendary prowess at this technique.

“If winning isn’t everything, why do they keep score?’’ But there is more to winning than just satiating your dopamine appetite. Shooting for the stars keeps you going, it gives you purpose to be the best version of yourself. So you could choose to bluff your way through life or call out other people’s bluffs, but you got to know when to hold ‘em, know when to fold ‘em.

WRITTEN BY ILLUSTRATED BY

Tanmay Dadhania Tanishka Sonavane

Comps 3rd year ECE 2nd Year

Vishvesh Trivedi

Comps 2nd year

An unusual bustle was present outside the Chester Crown court on the 28th of October 1999. A crestfallen 35-year-old solicitor, Sally Clark, who had recently lost both of her infant children to the mysterious Sudden Infant Death Syndrome (SIDS) was facing charges of allegedly murdering them. And what followed is perhaps regarded as one of the biggest blunders of employing statistics in courts. The prosecutors had roped in statisticians to quantify the chances of two SIDS deaths from the same womb. One-in-seventy-three million was the number presented to the jury of the chances of Sally being innocent. The statisticians considered each infant’s death as an independent event thereby multiplying the probabilities to itself, resulting in an oddly slim figure which spoke against the defendant. Genetic factors, biological reasons, and scientific intricacies of SIDS were completely overlooked during the trial. Consequently, Sally Clark was declared guilty and awarded a non-bailable life sentence based on this highly dubious mathematical ratio. Apart from being reviled by the media for being a child-killer, she spent nearly four years behind closed bars. Later on, she was released on additional findings in the case, but the damage was done. The trauma of the deaths and the trial took a huge toll on her mental health eventually prompting her to commit suicide, four years later.

In the same year when Sally was freed, another woman from Australia was charged along the same lines. Convicted of murdering her three children and manslaughtering one. Astoundingly, the same obsolete theory of using seemingly improbable events in determining guilt was used. Perhaps, the courtrooms across continents were still plagued by misconstrued probabilities.

All of these mishaps arise from the misunderstanding of a concept well-known to our crowds, Bayes’ Theorem. Aptly dubbed the “Prosecutor’s Fallacy”, the error assumes that the P(A|B) == P(B|A), the probability of A given B has occurred is the same as the probability of B given A has occurred. By design,

statistics is a complicated discipline that is difficult to execute and comprehend accurately by untrained minds. Sometimes even experts have a hard time wrapping their heads around certain problems. Case in point, The Monty Hall Problem. The problem itself isn’t important in this context, what’s important to highlight is the reaction of the academic world to the problem itself. Thousands of Ph.D. holders and prolific mathematicians like Paul Erdős were stumped by the problem and even had to be shown computer simulations for them to be convinced. But that doesn’t mean that statistics shouldn’t be used in a courtroom.

Courts around the globe often claim to live by the principle of the innocent until proven guilty beyond a reasonable doubt; this principle originates from Blackstone’s formulation that “It is better that ten guilty men escape than that one innocent suffer“. But in many cases, the hunger to find a name to attach to a villain consumes the desire to uphold our principles.

The SIDS cases were classic examples of a case being solely decided based on ‘a priori’ arguments. Contrary to ‘a posteriori’ based evidence where knowledge is obtained from an experiential basis, ‘a priori’ is when knowledge is obtained independent of any experience. The verdict in these cases was decided after calculating statistical probabilities and an assertion made by a British Pediatrician, Dr. Roy Meadow that stated - ‘one sudden infant death is a tragedy, two is suspicious and three is murder, until proved otherwise.’ No evidence was presented of the women actually committing the murders instead, the probability of their innocence was wrongly ascertained and the hapless women were imprisoned.

Another reason why Blackstone’s formulation should be held to the highest degree is the government. By its nature, the government is the only organization legally authorized to use violence. Its power and resources are incomparable to the individual, thus putting the individual in a compromised situation when faced with a criminal trial. This is why it’s important to place as many checks and balances as possible to level the playing field for the individual. After all, the lifespan of humans is relatively very short. Confining an innocent man robs him of ever experiencing those years again. No amount of money can ever make up for lost time. But if you ever find yourself on either end of a criminal trial always remember the great words of the British economist Ronald Harry Coase, “If you torture the data long enough, it will confess to anything”.