A math problem about racism
Dec. 11th, 2006 10:57 am![[personal profile]](https://www.dreamwidth.org/img/silk/identity/user.png){kind=small}
xiphiasI 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.)
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.)
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Date: 2006-12-11 05:25 pm (UTC)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.