May 05, 2008

Stable Marriage and Information Failure in the Social Marketplace

Standing around at a bar last Friday night, sipping a dirty martini and semi-engaged in a lackluster conversation with some random woman I had met approximately ninety seconds earlier, I felt my thoughts drift almost involuntarily from trying to figure out whether she was attractive or I was hallucinating, to the Stable Marriage Algorithm and pervasive information failures in day-to-day existence. This is only one of the many reasons why I do not have a girlfriend.

The Stable Marriage Algorithm, a Primer

At the outset, it is probably necessary to explain the Stable Marriage Algorithm¹ to those who do not have the great privilege of holding a degree in computer science—nor the concomitant life marked by unchecked awkwardness, universal mockery, and paralyzing sexual frustration. Wikipedia describes it as an algorithm which solves the following problem:

Given n men and n women, where each person has ranked all members of the opposite sex with a unique number between 1 and n in order of preference, marry the men and women off such that there are no two people of opposite sex who would both rather have each other than their current partners. If there are no such people, all the marriages are stable.

Perhaps that still does not make sense (it barely does for me). But the intuition should be clear, I hope: if everyone in a particular group ranks at a particular level of desirability vis-à-vis everyone else, the algorithm purportedly will assign you to the highest-ranked person on your list who cannot get anyone that ranks better than you on their list. In essence, the point is to make everyone settle for the least-bad person that they can get because, theoretically, if either partner in a couple could get someone better, they would do so, and thus, break the marriage. In that way, the problem tracks so-called real life very well. What is marriage² if not settling for the least-bad person you can get given your own inevitable worthlessness. In fact, that's the best case scenario; many people settle for much worse than the least-bad they could have gotten (e.g., the foolish person I trick into marrying me).

Information Failures

Now, onto the real question: why did my thoughts drift to Stable Marriage when I should have been staring unabashedly at the woman who had made the grievous error of initiating conversation with me (and coming up with something inadvertently offensive to say that would promptly end any chance I may have had)? The answer is rather simple: interactions in bars, clubs, and the like tend to be extremely inefficient, and could be drastically improved by better application of the principles which underlie the Stable Marriage Algorithm.

To be clear, the problem is not that we do not implement stable marriage in the aforementioned social settings, only that we do a piss poor job of it. The fundamental cause of our inefficient implementation is information failure. In deciding to approach (or not approach) an acquisition target in such a setting, an individual has very little to work with to make a rational decision. In the worst case scenario, i.e., the stranger case, all that one has is physical appearance—both the individual's and the target's—which unfortunately does not comport with individual desirability ratings at any level of meaningful granularity outside of Los Angeles and South Beach (where all that matters is how hot you are). However, if there was a mechanism for disseminating even slightly better information, many inefficient transactions could be avoided.

Friday Night's Failed Transaction

An example should clarify what I mean. Returning to the bar, ninety seconds earlier, I had been paying for a round of shots when the woman in question approached. Unlike my woeful failures in the past, I was not confused as to why this approach had occurred. The conversation began with a discussion of what the shot was, what was in the shot, and how she and her friend were here to celebrate the latter's birthday. In short, the proposed transaction was a $10 drink in exchange for five minutes maximum of a moderately uninteresting conversation with a moderately attractive woman, whereupon she would thank me for the drink and excuse herself. Talk about no-value-add.

Sadly, this occurrence is one I am altogether too familiar with from my days as a corporate douche. I was not inclined to accept the entirely worthless transaction then, and I certainly was not going to do so now, when I had no steady income and an ever-increasing debt. Nevertheless, I had to expend resources, namely time, in avoiding the overture:

Moderately Attractive, Moderately Uninteresting Woman: Wow, that's a lot of shots!
Rohit: (looking up) Yeah, well, it's been a long day.
MAMUW: (laughs) What are they shots of?
R: Liquid cocaine.
MAMUW: What's that?
R: (already bored) Bacardi® 151, Goldschlager® and Jager(meister)®
MAMUW: Must have been a real long day.
R: Most days are when you hate your life as much as I do.
MAMUW: (laughing) Oh, it can't be that bad.
R: (straight faced) You have no idea.
MAMUW: (laughs again and briefly places her hand on my arm) You're funny. So, who are all these shots for?
R: (pointing vaguely to law school comrades) My friends over there.
MAMUW: Oh, I see. Yeah, I've never had a liquid cocaine shot before. I don't know if I could handle it. Are they good? I don't do that well with shots. My friend's been trying to make me take them all night. It's her birthday. She's coming over here right now. She's really hot, isn't she?
R: (handing shots to said comrades) You should buy her one. It's a good shot. Cheers!

At that point, I took the shot with my friends, and walked away. Perhaps some of you think I was a bit harsh. Then again, perhaps the same some of you are idiots. Such nonsense conversations already have a negative value; why anyone would pay to engage in them is beyond me. The larger point is that this was a lose-lose interaction. She did not get her drink, and I'll never have those two minutes of my life back. Moreover, had there not been a colossal information failure, she might have indeed met a person more amenable to paying $10 for a negligible chance at a phone number.

The information failure here was simple: this particular woman's thinly-veiled attempts to score a free drink for herself, and possibly her friend, did not comport with fundamental notions of dual income and brand management which form the basis for my ranking system; indeed, her actions flew directly in the face of the sacred criterion of dual income. So, while her mistaken belief that I was an individual willing to buy her a drink may have upped me in her ranking system for the purpose of that transaction, my steadfast commitment to not engaging freeloaders resulted in her receiving a very low rating on my list for the same transaction. Had there been a way for her to know ex ante (yes, I went there) about my commitment to dual income, this failed transaction would never have occurred, and both of us would be better off.

Then, the $64,000 question: how can we disseminate information better in the social marketplace to avoid such patently inefficient expenditures of resources? Certainly, the advent of dating websites has significantly reduced information failure in the social marketplace as a whole, but such technology has done little to address the problems faced in casual interactions. Technology may still be the answer, however. I'm thinking software running on Bluetooth-enabled smartphones that could assess basic compatibility with those individuals of the proper gender in your general vicinity, and let you know which ones are (1) compatible, and (2) available. In fact, if stable marriage could be implemented in a distributed manner, we might even be able to achieve the optimal result (the Holy Grail in both economics and engineering) for any given venue at any given time. Think of the possibilities!

Don't even think of jacking my idea! Patent pending!

^ ¹ Long time (really long time) readers may recognize the Stable Marriage Algorithm. In fact, more than four years ago, I implemented this algorithm in a web application for a dating game I ran as a Resident Assistant at Unit 3 for Valentine's Day, 2004. The application assigned each resident who partook in the program with his or her most compatible mate based on answers to a survey. It was rather awesome.
^ ² Though the algorithm name says marriage, it can be used in any instance where matching is involved. So, for instance, even if you are only looking to get paired up with someone only for the night, the algorithm, and thus, this article, would still apply to you.