# The Probability Of Being Accused Of The Hate Crime Of Disparate Impact Approaches 1

You’re an employer who has to hire 100 employees to get your Meme Factory running. You’ll hire the first 100 who come in the door.

Given this information (and what you learned in Class), what is the probability the government will roast you for the hate crime of “disparate impact”?

“Briggs, all hate crimes are political crimes.”

Yes, I know. But what about the chance of you been pilloried for this political crime?

“You haven’t given us enough information.”

Ah, you’re right. In order to fulfill the conditions of the hate crime of “disparate impact” you also need an Oppressor and a Victim.

“Disparate impacts” occur when, and only when, an Oppressor does not hire at least as many Victims as exist proportionally in the population.

Suppose your Victims are 13% of the population. Then, if you are an Oppressor, you have committed a hate crime if you do not hire at least 13 Victims.

“What if I hire more?”

If you achieve Diversity, that noble state where all 100 of your employees are Victims, this is not a crime. Indeed, this will likely win you an award.

“But if there are 13% Victims, that means there are 87% Oppressors. Don’t I have to hire 87 Oppressors to maintain balance?”

No. You do not need to hire any Oppressors. The hate crime only occurs if you do not hire sufficient Victims. And only if you are an Oppressor owner.

“You mean if I’m a Victim myself, I can hire as many Oppressors as I want?”

You can, as long as you are voluble in your declaration of your own Victim status. If you’re quiet about it, you run the risk of being treated as an honorary Oppressor.

Anyway, enough stalling. I’ve given you all the information you need to answer the question. What are the chances you’ll be nabbed for a hate crime if you hire the first 100 who walk in the door?

“I’m not sure. Thirteen percent?”

Not even close. Here’s how to get the right answer. Given our information, there’s a 13% chance any person walking into the door is a Victim. So you want the chance that you hire no Victims, or just 1 Victim, or just 2, or and so on, up to just 12 Victims. Hiring any number less than 13 can land you into hate crime territory. Hire 13 or more and you are safe.

“Oh, I get it. That’s easy. That’s a binomial. That gives about a 46% chance of hiring 12 or fewer out of 100.”

That’s right. There is a 46% chance you will hire insufficient Victims and run the possibility of being charged with the hate crime of “disparate impact”, even when, as here, you are wholly innocent of any crime.

About half of companies which are not discriminating, at all, will be guilty of hate crimes.

It also turns out, for boring technical reasons (look up the expected value of a binomial) the answer is about a 50% chance of a hate crime no matter how many employees you must hire.

I don’t know about you, but 50% is an awfully large chance to be charged with the hate crime of “disparate impact.” How would you solve that problem?

“Wait. In our culture there is more than one Victim group, though, isn’t there? Don’t they all have to be hired for proportional representation? Doesn’t that make it harder to escape being charged with a hate crime?”

Yes.

It turns out about half the Oppressors are actually Victims themselves. And that the original Victims themselves can be split into two groups, each about equally sized. That can be confusing, so here’s the breakdown:

Oppressors: 43.5%; Victim group 1: 43.5%, Victim Group 2: 6.5%; Victim Group 3: 6.5%.

We now want the chance that we hire 43 or fewer Victim Group 1s or 6 or fewer Victim Group 2s or 6 or fewer Victim Groups 3s. The number of Oppressors don’t matter, as before.

I know you don’t know the answer to this, so I’ll just tell you. It involves the multinomial distribution. We want 1 – Pr(Oppressors >= 0 & VG1 > 43 & VG2 > 6 & VG3 > 6 | all that information). This turns out to be about 94%. That is, with no discrimination at all, you stand a 94% chance of being accused of a hate crime.

We also have to be more careful about the number of employees. The fewer you hire, the more likely you can be charged with a hate crime. But once you hire about 1,000 or more, the chance settles down to about 93%.

“Dude, that means—”

Wait, I’m not done yet. For we have more than just these three Victim groups. There’s another, now exceedingly famous Victim group, that is about 3% of the population. We have to add that, too (and adjust the others lower). That gives about a 96% chance, or higher, that you can be charged with the hate crime of “disparate impact” even when you are not discriminating.

“And if we add more Victims the chance only grows?”

You got it.

“But it’s already almost certain you’ll be guilty even when you’re innocent!”

That’s right. So again I’ll ask: how do you handle this?

“I guess I’d have to have HR institute hard quotas, to make sure I hire at least as many Victims as I need, to ensure I don’t run afoul of the law.”

But that’s discriminating by Victim status, isn’t it? And isn’t discriminating by Victim status against the law? Not the hate crime law, but that Civil Rights law.

“You’re right. It is.”

So no matter what, you will almost certainly be guilty of crime. Even when you are entirely innocent.

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