In romantic comedies, each man and woman marries their own true love. In real life, some people settle for second-best, which can lead to lots of trouble. If John and Mary love each other but are married to other people, they will be tempted to leave their current partner and marry each other. But if John loves Mary, while Mary loves her husband more than John, both will stay put.
Mr Gale and Mr Shapley devised an algorithm for matching an equal number of men and women that would guarantee this second, more stable outcome. Each man and woman ranks their preferred partners. Each man proposes to his highest-ranked woman. Each woman rejects all the proposals she gets except the highest-ranked among them. But she does not accept the proposal, in case a man she prefers even more proposes next time. The algorithm is rerun until all women have a satisfactory proposal.
(Free exchange, Economist)
Call me slow on the uptake (I haven’t actively followed econs stuff in like two years, even if you count lazily cramming for H2 econs with a three-month side dish of surprisingly delectable game theory) but this seemed like great fun to me. As with most other econs stuff it’s elegantly efficient in theory even if there’re a million doubts in practice, some quite serious-sounding and some just plain trivial. Here I list just some, and counteracting male- and female-side policies that governments across the globe would do well to implement.
1) Imperfect information for the males. Bob’s never going to end up happy if he only knows three girls in his entire life, especially if two of those support rival football clubs and the last one reveals that she’s more interested in other girls. Even accounting for the fact that many of the girls he’s never going to meet are almost consequently girls he’d never consider anyway due to distance or cultural differences (and opinions on those differ from person to person anyway) – we need to set up Bob with as many girls as we/he can so he can find the perfect Mrs Bob. Governments need to set up speed dates, online or off – government mandated Chatroulette, anyone?
2) One-itis. What’s going to stop Bob from dwelling on Bobbina, the very first and only girlfriend he’s ever had? (who dumped him 12 years ago in fifth grade but is still very much The One) Bob’s not alone, so we don’t want throngs of men quitting the auction after just one failed bid, or bidding for the same girl repeatedly in a desperate abandonment of dignity. Policies mentioned in point 1 go some way toward mitigating this, but for a more targeted approach, the media needs to step in with lurid and offensive items about how quantity trumps quality any day – music videos of Justin Bieber slowly grinding ten black rappers while yammering about “layin’ on all the hoes, don’t matter who” would be especially effective and poignant.
3) Asymmetry. It’s obvious from the onset that this system greatly empowers the women who can sit on a decision indefinitely – why should Bobette choose hapless ol’ Bob if she thinks Bobbytonelli might be taking a swing in ten years? The asymmetry of power between the sexes leads inevitably to fickleness on one hand, unresolved pining on the other, and in the long run a lot of dissipated affection and virility. Let’s just assume that the asymmetry’s going to have to stay: we don’t want a system where some but not all women get to bid for their favoured men, because that’s controversial on so many levels. What we can do is mandate the strapping of large and noisy timepieces on every single woman that blare “tick tock” in an annoyingly nasal voice every second of the day. These patented Biological Clocks™ will cause great distress to every female and make her more decisive on marital matters. They will also open the market for neo-Elvises wanting to croon about “love terrorists” and, uh, stimulate the economy.