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Among the many joining the rally in response to the recent fatal police shooting in Toronto were those carrying signs emblazoned with the word "Murder". The urge to label this tragedy so definitively – while the formal investigation has scarcely begun – emerges from a natural flow of grief and anger. Any compassionate person, whether they're pro- or anti-police, should recognize that these emotions play a key role in the social catharsis, learning and healing that everyone hopes will follow on the heels of such tragedies.

Less easy to recognize is the fact that science has an equally important role to play in this emotional circle. The use of lethal force by law enforcement is a much-studied phenomenon. There is a rich body of scientific literature available to police officers and those who instruct them. Science reveals truths about use of force that are radically different from what we see in movies and on TV. If you judge real police use of force by the standards of mass entertainment, your judgment will be compromised.

Among those well-versed in the science of use of force the following examples will not be surprising, but they are not usually appreciated by the public at large:

1. Knives can be more dangerous than guns;

2. Even when an officer has a gun drawn, if a knife wielding assailant gets closer than 21 feet, the officer faces a serious risk of death, because the assailant can inflict fatal injuries before being stopped by gunfire;

3. Shooting a knife out of an assailant's hand is the stuff of Hollywood myth that no responsible police agency teaches its cadets;

4. In live situations, handgun accuracy plummets to as little as 30 per cent of target range accuracy rates;

5. Depending on a host of variables, humans can inflict lethal wounds on others even after receiving multiple gunshot wounds. Accordingly, if it is necessary to use lethal force, multiple gunshots are not at all unusual.

Do these principles necessarily lead us to any particular conclusion in any given case? No. But these principles do teach us that passing judgment on use of lethal force by police officers is a complex, multi-dimensional science-based task. It is neither intuitive or performed in haste. Sound judgments surrounding use of force demands that a fully informed, detached decision maker conduct a thorough review and analysis of all available evidence, from every possible source.

The immediacy and power of emotionally driven conclusions about police shootings (like Tuesday's protest) conflict mightily with the crucial need for a thorough investigation. Each type of conclusion reached – the emotional and the rational – originates from an important place in our social psyche. So how are we as a society to reconcile these warring perspectives on the same event? How we answer that question helps define us as a society. I suggest the following, three-part answer:

First, to be appropriately compassionate, we should give full and respectful reign to the immediate and forceful expression of emotions like grief and anger. Second, because we value knowledgeable, defensible decision making, we must hold investigative agencies and, if necessary, courts who pass judgment on these tragedies, to the highest standards of investigative rigour, detachment and scientifically informed analysis. Third, and most importantly, we must recognize boundaries between emotional and analytical responses to police shootings.

Detached, science-based analysis of police shootings does not in any way invalidate the intense emotional reactions to such tragedies. But neither can emotional reactions, however deeply held, compromise detached analysis or influence investigators or courts when passing judgment on behalf of us all.

David Butt is a criminal lawyer based in Toronto. He has defended both civilians and police officers