A math problem about racism

[xiphias]

I just had a math problem pop into my head, which, as I think about it, may explain something about racial profiling, prejudice, and that sort of thing.

Or it may not; I dunno.

Let's say that you have a city which is populated by two kinds of people -- polka-dotted people and plaid people. The plaid people are generally economically disadvantaged, and are a poor minority population, and are distrusted by the majority.

The plaids are only 10% of the population. But they have VASTLY more criminal behavior in their community.

In fact, 80% of Plaid people engage in criminal activity.

Only 20% of Polka-dotted people do.

So, a liquor store is robbed.

Knowing absolutely nothing else but this information, is it statistically more likely that a Polka-dotted person or a Plaid person did it? What are the odds either way?

If you pick up a random Plaid person off the street nearby, what are the odds that you can get SOME kind of dirt on them, whether or not they actually committed THIS crime? What if you pick up a random Polka-dotted person?

(Note that all percentages have been made up and the numbers are not intended to reflect any kind of actual reality -- the numbers are chosen just to make the math easy. In real life, the percentages between different populations are a lot closer, and closer still if our criminal justice system treated white-collar crime the same as "blue-collar-crime." But there are, nonetheless, statistical differences which can be examined.)

Comments

[mabfan.livejournal.com]

For some reason, I want to say that it is about twice as more likely that the criminal who robbed the store was polka-dotted.

(By the way, picking plaid and polka-dotted as the two subgroups makes the problem a little more confusing, since the two words have similar letters in them. It might have been better to go with something else.)

[madcaptenor.livejournal.com]

You're right. The odds are actually nine to four. 8% of people are plaid criminals; 18% of people are polka-dotted criminals.

[mabfan.livejournal.com]

That's what my calculations told me.

And to go further...

If we pick a random plaid person off the street, the chance that the person is a criminal is 80%. The chance a random polka-dotted person is a criminal is only 20%. Which is why people might be more ready to consider a plaid person the criminal for any random crime, even though the chances are better for any random crime that a polka-dotted person did it.

[chanaleh.livejournal.com]

But that's just the problem. If you divide the world up differently, based on izzycat's math above, 26% of all people are criminals and 74% are not. Your law-abiding population is 97% polkadot (72/74) and 3% plaid (2/74). But even your pool of criminals is 69% polkadot (18/26) and 31% plaid (8/26). -- Do you suppose those numbers are accurately reflected in the conviction rates of this theoretical society? :-}

[metahacker.livejournal.com]

I've found the real problem comes when a figure like "80% of Plaid people engage in criminal activity" for one neighborhood, where, say, there are five plaid people and four of them run together, and then it is read by someone who lives in a community which is 50% plaid. Given earlier observations about the nearly 100:1 ratio in the proportion of blacks in various states of the USA (Maine: 0.5%; Mississippi: 35%), this is not an unrealistic nor unusual situation.

[jerrymurray.livejournal.com]

Interesting choice of wording though. If 80% of a minority is engaged in criminal actvity, and if the police "profiled" said minority...would it truly be racist? Or would it be "going with the numbers?"

In Baltimore City, whites are the minority. Yet the overwhelmingly numbers of crimes comitted, either murder, drug related robbery etc are by blacks. Is it racist to state that in Baltimore city blacks commit more of the crimes?

Personally, I am sick of the race card being played out. We read it every day in the paper and see it on the news.

Thats just my opinion.

[xiphias.livejournal.com]

I didn't say whether profiling was a good or a bad thing. I just threw out some numbers to see in what circumstances it might make sense. Or not.

[jerrymurray.livejournal.com]

gotcha

[browngirl.livejournal.com]

What about the innocent 20%? Or is it just their fault for having chosen to be plaid?

Edited for clarity

[rubynye.livejournal.com]

When I was in college, I and my roommate, who are of different races, used to joke that we should go to a department store; one of us would be followed around by the salespeople and the other one would steal stuff. Of course we never did, but considering the difference in scrutiny afforded two similar girls whose main differing variable was race, the joke was bitterly apropos.

Personally, I'm sick of people assuming they know how I'm going to act based on how other people of my skin color act. What race do I identify as, based on that statement?

[bradhicks.livejournal.com]

And the percentages are even closer, according to the annual Substance Abuse and Mental Health phone survey, if you count drug crime as blue collar crime. And that's relevant, considering how many people, especially plaid people, are in jail for drugs. A point I've belabored before.

The drug issue is relevant though, because there's a class of math problems related to it that also applies to your example: the false-positive problem. Using the same numbers, assume that your criminal justice system is 95% accurate. 20 random plaid people on the (as you've demonstrated, false) assumption that since 80% of the plaid people are criminals the liquor store was probably held up by a plaid person, odds are you're going to put at least 1 innocent person in jail.

[browngirl.livejournal.com]

This is the sort of thing that makes you such a good teacher.