mathbabe

I’ve been thinking a lot recently about mathematical models and how to explain them to people who aren’t mathematicians or statisticians. I consider this increasingly important as more and more models are controlling our lives, such as:

• employment models, which help large employers screen through applications,
• political ad models, which allow political groups to personalize their ads,
• credit scoring models, which allow consumer product companies and loan companies to screen applicants, and,
• if you’re a teacher, the Value-Added Model.
• See more models here and here.

It’s a big job, to explain these, because the truth is they are complicated – sometimes overly so, sometimes by construction.

The truth is, though, you don’t really need to be a mathematician to know what a model is, because everyone uses internal models all the time to make decisions.

For example, you intuitively model everyone’s appetite when you cook a meal for your family. You know that one person loves chicken (but hates hamburgers), while someone else will only eat the pasta (with extra cheese). You even take into account that people’s appetites vary from day to day, so you can’t be totally precise in preparing something – there’s a standard error involved.

To explain modeling at this level, then, you just need to imagine that you’ve built a machine that knows all the facts that you do and knows how to assemble them together to make a meal that will approximately feed your family. If you think about it, you’ll realize that you know a shit ton of information about the likes and dislikes of all of your family members, because you have so many memories of them grabbing seconds of the asparagus or avoiding the string beans.

In other words, it would be actually incredibly hard to give a machine enough information about all the food preferences for all your family members, and yourself, along with the constraints of having not too much junky food, but making sure everyone had something they liked, etc. etc.

So what would you do instead? You’d probably give the machine broad categories of likes and dislikes: this one likes meat, this one likes bread and pasta, this one always drinks lots of milk and puts nutella on everything in sight. You’d dumb it down for the sake of time, in other words. The end product, the meal, may not be perfect but it’s better than no guidance at all.

That’s getting closer to what real-world modeling for people is like. And the conclusion is right too- you aren’t expecting your model to do a perfect job, because you only have a broad outline of the true underlying facts of the situation.

Plus, when you’re modeling people, you have to a priori choose the questions to ask, which will probably come in the form of “does he/she like meat?” instead of “does he/she put nutella on everything in sight?”; in other words, the important but idiosyncratic rules won’t even be seen by a generic one-size-fits-everything model.

Finally, those generic models are hugely scaled- sometimes there’s really only one out there, being used everywhere, and its flaws are compounded that many times over because of its reach.

So, say you’ve got a CV with a spelling error. You’re trying to get a job, but the software that screens for applicants automatically rejects you because of this spelling error. Moreover, the same screening model is used everywhere, and you therefore don’t get any interviews because of this one spelling error, in spite of the fact that you’re otherwise qualified.

I’m not saying this would happen – I don’t know how those models actually work, although I do expect points against you for spelling errors. My point is there’s some real danger in using such models on a very large scale that we know are simplified versions of reality.

One last thing. The model fails in the example above, because the qualified person doesn’t get a job. But it fails invisibly; nobody knows exactly how it failed or even that it failed. Moreover, it only really fails for the applicant who doesn’t get any interviews. For the employer, as long as some qualified applicants survive the model, they don’t see failure at all.