The Stable Marriage Problem

Nope, this post isn't about my home life. :)

There's a problem in computer science called the "Stable Marriage" problem. It's about how to match one set of people other people, based on asking each of the groups what they prefer the most.

It's best known as the system used by Medical school programs to match students with programs they like. For medical school, each applicant presents a ranked list of schools they would like to attend, and each school does the same. "The Match" picks the a good global solution to satisfy all these wishes. Not perfectly, but well enough that it "maximizes happiness"...or at least the computers think so.

I've been thinking about the comparisons with housing. And rather than having academic credentials like prospective med students, buyers have money, in varying amounts.

Recently, buyers have had a multiplier on their money: the amount of risk they were willing to tolerate in toxic loans (or they were otherwise convinced they could "afford"). If you were willing to accept a negative-am loan at a variable rate, or maybe a little appraisal fraud with cash back at closing, you could afford "twice as much" house for the same monthly payment. And as we know, home prices in some areas increased by 180% from 2000 prices.

So let's follow this argument to its painful conclusion: if the MCAT administrators were to say, "As of 2004, we're doubling all the test scores! It should make everyone so much more pleased with their results! With twice the score you'll get into a much better school!" Across the board, a rising tide lifts all boats, right?

Of course, because this is a contrived example, you know that nothing at all would change except for the MCAT scores. The Match would proceed identically to the year before, with everybody ranking schools in the same order and vice-versa.

And in areas like the one I live, where almost no new housing was created in 2004-2006, this is exactly what happened.

The loan amounts doubled. For just a bit, people got a little more house than they would before--they "matched" a little higher. But after awhile, they got the same house, or a little smaller one, for twice or three times the money.

I suppose all I'm saying is that the "housing market" just does something that most people don't readily assume: prices reflect demand, not value. After you get over that, price is just a number based on what everyone else can afford.

Of course, occasionally some value was added: Los Angeles County alone kept the Viking corporation in business. But upgrades to existing structures? 5% increase in value for a 100% increase in price. Not value, demand.

I usually get out my moral indignation hat and put it on at this point in the story. It makes sense that new construction of the highest quality could cost some money. But it seriously doesn't make sense for a house that cost $15,000 when it was purchased to now cost 100x as much.

But this is apparently how markets work, and I suppose that we'll see how they work on the other side of the housing bubble as well.

1 comment:

  1. Here in Texas, if I understand things correctly, this effect has definitely knocked the wind out of the "low end" of the market (i.e., houses under $400K), while higher-end houses have been largely unchanged or even growing in value. That tends to imply that the low end of the market experienced some amount of crazy borrowing, while the high-end didn't.

    In California, "creative financing" appeared to have become the norm, and definitely inflated people's buying power and thus property prices. The flip side of that should definitely take hold.

    People without equity who were planning to just refinance later on to avoid ballooning payments... they're going to be forced to sell. This has already been a huge force in the central valley. The big question is when it's going to impact more urban areas.