EDIT: Just so people don’t get the wrong idea, I’ll mention that I’m not suggesting this because of some personally traumatic experience I’ve had with job searching; in fact, the last difficult career decision I made was when I was 18. I just think it’s an idea worth considering, and one worth hearing other people’s input on. END EDIT.
As I’ve read more about the medical resident match, I’ve recently become a lot more convinced that a match for mathematics jobs makes a lot of sense. Fundamentally, the point of a match world be that schools and candidates wouldn’t ever have to play mind games with each other. Everyone would just make a list, and the computer would make sense of them.
I feel the benefits of such a scheme are obvious. What about the objections?
- How random is it? In practice, not very. While one can come up with pairs of preference lists with lots of very different stable matchings, these seem to be very unrealistic. Roth and Peranson did an analysis of the medical resident match, and found that roughly 1 in a 1000 residents had different matches that were stably possible.
- What about couples? Luckily, the medical resident match has already dealt with this problem. They use a modified match algorithm which allows couples to rank pairs of positions, including “unmatched.” One could imagine having this with collaborators, as well as romantic partners.
- What about negotiating salaries? This is one can of worms that the medical resident program has stayed out of is the question of differential salaries; each resident program has a single salary and benefit package which they publish beforehand. But I don’t think this is strictly necessary. Schools could publish the possible different combinations of salary they would consider and people could rank those, so you could decide
school X at $70,000 a year > school Y at $70,000 a year > school X at $65,000 a year
and so on. Schools would simply have separate preference lists for the 65K and 70K positions. Similarly, I don’t think it would damage the algorithm much for a school to say “we would hire 3 people if they were all on this list, but only 2 otherwise.” This would just involve replacing a 3 opening job with 3 different jobs, one of which has a shorter preference list.
- Won’t it be extremely difficult for schools and candidates to rank that much stuff? Yeah, you got me there. That wouldn’t be fun. On the other hand, each choice would be much lower stakes. Hopefully it would be easier to do interdepartmental horse trading when the question is “how many spots do we move so-and-so up” rather than being offered a binary choice “do we give a offer to X or Y?” In fact, one could imagine simply having a departmental vote using STV.
- Wouldn’t university bureaucracies be completely resistant to such an idea? Oh, Boldface, why must you burst my bubble?