The surprising math of racial hate crimes

I've been studying the FBI's data on racial hate crimes.  One thing I noticed quickly is that blacks are much more-likely (16.5x) to be victims of racial hate crimes than whites, and more-likely (2.5x) to commit racial hate crimes than whites.

This surprised me.  So I thought about it, and realized it's what we should expect.

A racial hate crime is not like casual racism.  A casual racist might treat every person of the race he doesn't like poorly.  But racial hate crime is where some racists get together and say, "Let's go get us an X tonight."  The difference is that a racist doesn't have time to commit racial hate crimes against every X he meets; he has to choose one.

Now say we have a population of 1 black and 1 white.  Also say that blacks and whites are equally likely to be racist.  Say 1/100 is racist enough to go out looking for an X.

Then the black has a 1/100 chance of being the victim of a hate crime, and so does the white.

Now say there's 1 black and 6 whites--about the ratio in the US.  The expected number of times that the black will be a victim of a racial hate crime is 6 times 1/100.  Each white has a 1/100 chance of committing such a crime; and if they do, we know whom the victim will be.

The expected number of times that any one of the whites will be a victim is the chance that the one black commits a hate crime, divided by 6, because there are 6 whites.  So the expected number of racial hate crimes that a white will experience is 1/600.

6/100 divided by 1/600 is 6 x 600 / 100 = 36.  That means that, if blacks and whites are equally racist against each other, a black has 36 times as great a chance of being the victim of a racial hate crime as a white does.

It's reasonable to suppose that being the victim of racial hate crimes can make a person racist.  So the blacks, responding to more racism than the whites experience, should become more racist, and be more likely to commit a racial hate crime.

Perhaps a more-important conclusion is that this probably means we can never have equality in all ways in such a situation.  For for the one black to experience the same amount of hate crime as one white, we need the probabilities p_w that a white commits a hate crime, and p_b that a black commits a hate crime, to give us

6p_w = p_b/6

p_b = 36p_w

That is, we need each black to be 36 times as racist as each white.

The data shows that blacks are only 2.5 times as likely to commit a racial hate crime, and only 16.5 times as likely to be the victim of a hate crime. This is probably the equilibrium reached, from which we could compute how much an increase in victimization causes an increase in inclination to victimize others, if we had the time. My point is only that the equilibrium does not achieve equal victimhood. So to reach equality in that, we would need to give race-based incentives, probably by making the penalty for racial hate crime worse for whites than for blacks.

The best we can do then is reach a trade-off, which would punish whites a little more, and expose blacks to a little more hate crime. There doesn't appear to be any way to create equality in victimhood without creating inequality somewhere else.

(There is of course equality when there are zero hate crimes all around. But that won't happen until humans have all been rendered identical in every respect, or have been replaced with AIs.)

Comments

[Herald of Opera]

Whites have an unfair advantage in experiencing fewer hate crimes, while blacks have an unfair advantage in being punished less for the same crime. That's the best we can do.

Of course, because nearly all of the judges are white, what actually happens is that only the blacks are punished at all. Sometimes without even being guilty.

(Explaining is not condoning)

[Bad Horse]

5814333
Right; I meant whites would have a harsher penalty. Actually I just erased that paragraph, because it was confusing even me. However, the idea that only blacks are punished for hate crimes is empirically untrue.

[mishun]

Then the black has a 1/100 chance of being the victim of a hate crime, and so does the white.

If there's one crime per racist

6p_w = p_b/6

p_b = 36p_w

6 p_{w} = \frac{p_{b}}{6}

p_{b} = 36 p_{w}

[mathblock]
6 p_{w} = \frac{p_{b}}{6}
[/mathblock]
[mathblock]
p_{b} = 36 p_{w}
[/mathblock]

[Bad Horse]

5814430

6 p_{w} = \frac{p_{b}}{6}

Classy!

[Calipony]

Do you know the old Star Trek episode called ‘Let that be your last battlefield’?

[Herald of Opera]

Speaking of unexpected things that make perfect sense once you actually analyze them, just the other day I was thinking about peacocks. Shen from Kung Fu Panda 2, as a vicious warmonger, completely goes against the usual stereotypes of the animal... yet anyone who knows how nature works would quickly realize it was the only possible way that particular animal could function. Its ridiculous tail means it can't run or hide, so its only choice to deal with predators is violence.

[Bad Horse]

5814626
Wait, are peacocks violent? I've only met a few, and they were shy. The showy part of the tail isn't visible unless they display it on purpose.

[Bad Horse]

5814550
Sure. Haven't seen it in 40 or 50 years, but I remember it.

[GaPJaxie]

You are a fascinating psychological case study.

[Heavy Mole]

This is a kind of classical reductio against social engineering. Race crimes will always be disproportionate between minorities and a primary demographic, even if both parties are acting in good faith (i.e. a-historically, as race-motivated violence is more complex than being the victim of race crime, oneself). Therefore, to create an equality of victimhood--or shall we say, an equal racial 'experience' in a given country, we must resort to absurd measures of correction.

It goes without saying that this argument can be applied to any statistically quantifiable discrepancy between an identified minority and majority group. To provide an equality of education, we must lower standards for Group A, and raise them for Group B.

The theory is that such measures are temporary. Fundamentally, they are intended to address problems of cultural cohesion, rather than those of technical achievement (i.e. meritocracy). The difference between blacks and whites in the United States is, of course, not merely a matter of numbers. The trouble is that these goals can be harder to define--and even when they are defined, difficult to asses.

[Bad Horse]

5815223

It goes without saying that this argument can be applied to any statistically quantifiable discrepancy between an identified minority and majority group. To provide an equality of education, we must lower standards for Group A, and raise them for Group B.

The specific case of hate crimes is different, because the only necessary statistical discrepancy to create different personal experiences is a difference in the numbers of each group, not any difference between the people in the two groups. The math I showed produces inequality from nothing other than the number of people in each group. That math doesn't apply to education.

[Heavy Mole]

5815298
If we assume that both groups are equal, and we ascribe some quantifier to 'education' (e.g. the number of graduates per hundred), we will arrive at the same dilemma. We would simply say (for instance) that a member of A is 36 times more likely to be a graduate than a member of B within the system.

[Bad Horse]

5815741 Why would that happen?

[Heavy Mole]

5815806
It would seem to be ineluctable, from our interpretation.

[Truth_Seeker]

Exercises like this make my empty brain wonder what the Tulsa Massacre or your average pogrom look like as an FBI statistic.

Not that I'm gonna take the time or energy to find out, mind you. Busy worrying about the price of eggs over here.