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Perception is everything

I recently received an article about hate crimes from one of the many email groups I read. It purported reporting is one sided and made a number of interesting statements. One that cannot be denied is that acts of violence of one person against another simply because of “what” rather than “who” they are is about as nondiscriminatory an occupation as one can find: everyone bashes everyone else with approximately equal fervour. This was most humourously stated several decades ago by Tom Lehrer in his song “National Brotherhood Week”.

The gist of the posting was that when whites trash blacks it is reported; but when blacks do similarly awful things it is not. It noted the absolute numbers of hate crimes committed by whites against blacks was larger, but statistically the rate of such crimes by blacks against whites was higher. As I have somewhat of a mathematical inclination this got me thinking. There was just something wrong with the reasoning and it wasn’t until much later over a pint at the local the flaw finally made itself clear to me.

It’s the perceived risk.

Let’s say there is an imaginary and mostly happy land of VRB in which a mix of A’s and B’s live. The vast majority of A’s and B’s are extremely decent folk, but unfortunately there is a rare genetic disorder that strikes 1 out of 10 newborns. They are born throwbacks to a primitive type of A or B. On the average these pitiful genetically-challenged pre-A’s and pre-B’s commit one act of violence against a member of the other type per year.

Now it happens that the VRB’s population is 100. There are 85 A’s and 15 B’s. So there are roughly 8 pre-A’s and 1 pre-B’s. That means that 8 B’s and 1 A get the shite kicked out of them each year. That is to say, over 50% of B’s are assaulted in a given year and 1% of the A’s.

Needless to say, the perception of B’s will be all A’s are out to get them. The average A will feel virtually un-threatened. They may not even know any of the violent pre-A’s who attack the B’s and wouldn’t associate with that sort anyway. The average A would likely only have heard pub rumours of an A getting beat on.

The second year, the pre-B’s will have some of the more fearful B’s beside them for “self-defense” and the percentage of violent B’s will go up. If just 2 more join the pre-B, they will triple the rate of violence of B’s against A’s. However the difference between a 1% and 3% chance of getting clobbered will not modify A’s risk perceptions at all.

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