Prosecutor’s fallacy in the war on drugs

QUoting from oxford reference, Prosecutor’s fallacy is a misstatement of a probability as result of misunderstanding of conditional probability. sally Clark was a British who gave birth to her first son Christopher in 1996. three months after, Christopher died in his sleep. A year after, Clark gave birth to a second son, Harry, who also died in infancy. in applying conditional probability, pediatrician sir Professor roy Meadow testified that the probability of two infants dying in the same family is 1 in 73 million. the jurors convinced that this could not have been coincidence, Clark was convicted and sentenced to life.

The statistic that Sir Professor Meadow used is the probability of having two infant deaths among all innocent families. However, the statistic that should have been used is the probability of being innocent among all families who suffered two infant deaths. In the first, the numerator is the number of families with two infant deaths and the denominator is the number of all innocent families. This commits the Prosecutor’s fallacy. In the second, the numerator is the number of innocent families who suffer from two infant deaths, and the denominator is the number of all families (innocent and guilty) who suffer from two infant deaths. After several appeals and protests from many imminent statisticians, Clark was released in 2003.

The Prosecutor’s fallacy is relatable if explained in the war on drugs. On March 21, 2018 police killed 13 suspected drug dealers in dozens of anti-narcotics operations in Bulacan and Cavite. Citing a Reuters article published on March 22, 2018, “These operations are part of our stepped-up campaign against drugs and all other forms of criminality in the province,” Bulacan police chief Romeo Caramat said in a statement. “Unfortunately, 13 of the suspects were killed when our officers fired in self-defense shortly after the suspects who were armed with concealed guns sensed they were being entrapped and started firing.” What the reasoning implied basically is that there is a very small probability that an innocent suspect will fire back at police or nanlaban. Therefore, the suspect must have been guilty of drug trafficking. Therefore, the police were justified to kill the suspect.

However, there is a bigger probability that a suspect who shoots back is innocent. Therefore, police should have been more judicious and should not have killed on merit of self defense. In statistical parlance, police looked at P (nanlaban | innocent) when it should have looked at

P (innocent | nanlaban). The first is the

“nanlaban” among the innocents, and the second is the innocent among the

“nanlaban.”

Consider the following stylized figures. It is conceivable that there is close to 0 percent chance that an innocent suspect will fire back. That is, the number of innocent suspects firing back over the number of all innocent suspects (nanlaban or otherwise). If a suspect is innocent, s/he will probably not fight back. However, it is conceivable that there is significantly greater, say 5-10 percent, chance that a suspect firing back is innocent. That is the number of suspects firing back over the number of suspects (guilty or innocent) firing back. If a suspect shoots back, s/he might have a reason.

The suspect shooting back might be reacting irrationally, for example, due to panic or by psychological disorder. The suspect might be acting based on knee jerk reaction. S/he might be defending himself or herself from the police’s abuse of power. Maybe s/he is just framed and is officially reported as one shooting back. For clarification, a vast majority of police are good and hardworking people, but the reality is that there are some corrupt police. If there is a big chance that the suspect is innocent, it is not without unreasonable doubt that the suspect is guilty. The suspect should not have merited death on merit of police’s self defense.

Statistics aside, one should not downplay that the cause of deaths in the war on drugs as mere reaction to the Prosecutor’s fallacy. According to Human Rights Watch, the war on drugs has caused 12,000 deaths, with about 2,500 attributed to the Philippine National Police. Anger has taken over reason, and this is the root of the killings. It is also wrong to resist arrest whether innocent or guilty. As stated, a vast majority of police are good and hardworking people. Thus, the best course of action against police’s abuse of power is to report the minority evils to the majority good.

Also, one should not downplay the drug problem. Drug users are mostly sick but innocent; most of them are victims, not assailants. Drug dealers must be put to justice. And in the administration of justice, there will be collateral damage.

Still, the Prosecutor’s fallacy has been used to justify the killings of those who shoot back. If people become aware that a significant proportion of people who shoot back are innocent, then people will become more aware that shooting back in itself does not justify the killing of suspects.