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Matchings

November 6, 2012

I recently have been searching for jobs, and the process seems extremely annoying and inefficient.  Students have a separate, long interviewing process for each company, in which over half the time is spent on things that aren’t company-specific.  (And I suspect most interviews are terrible screens anyways).  Companies impose short deadlines in order to gain leverage, despite the fact that everyone graduates in seasons.  Negotiation has a huge amount of social friction.  Because things happen asynchronously, the resulting matching isn’t necessarily even any good.

It seems like you can potentially kill all these birds all with one well-aimed stone, simply by having someone who just does scouting and recruiting for everyone.  Personally, I would consider using a service where the process looked something like this:

  1. Companies and potential employees sign up with the service
  2. Potential employees indicate their interests and skill set, including some preliminary rankings of companies
  3. The service interviews the potential employees many times, surveying their skill set
  4. Companies reach out to potential employees and engage in completely non-technical talk.  This is purely to gauge everything but ability.
  5. Companies and employees submit preferences.  It is assumed that companies offer a fixed starting salary to all employees (vying for the same position).
  6. An algorithm is ran, and a good matching is output!

My response to some obvious objections:

  • Why should companies offer a fixed starting salary?  I think that although this is a valid question, it’s true that many companies do offer a fixed starting salary in practice.  Bargaining is hard, and letting the company choose the split is not a terrible solution, especially if they have a rough gauge for how much the employee is worth.  Also, companies get to control future raises anyways.
  • This puts a lot of weight on a single set of interviews.  Of course, there would be many more interviews than a single company normally sees, but some applicants may do poorly under the pressure of each one.  This is like the sort of argument against standardized testing.  But I think it’s less strong an argument here, because the alternative is to let companies subject themselves to the variance of just a couple interviews, only to be let down afterwards by regression to the mean.

Unfortunately, there are many other issues with a business like this, many of which I have probably not thought of.  That being said, it still seems likely to me that something like this is a good idea.

Now, at the core of this business, there is a matching algorithm.  Where did this algorithm come from, and what sort of matching does it output?  Luckily, lots of smart people have been thinking about matching problems for a long time.  50 years ago, Lloyd Shapley and David Gale proposed an algorithm for the stable (monogamous) marriage problem.  This is a super simple and elegant algorithm, and it’s easy to imagine how algorithms like this might be applied to something like speed-dating.

For the case of companies and employees, we’re interested in solving a many-to-one matching problem.  Though this makes things a little harder, it’s even more applicable and much research has been done.  One prominent use case is the putting of medical students in residency programs; you can read about a simplified version of the algorithm here.  In fact, MIT’s externship program runs some sort of matching algorithm to pair students up with externships, as well.  Thus I am tempted to say that the problem is algorithmically in reach.

It’s only fitting that Shapley and Alvin Roth won the 2012 Nobel Prize in economics, for “the theory of stable allocations and the practice of market design.”  Roth, besides contributing to the medical residency algorithm, has done work on romantic match-making, public school enrollment, and kidney exchanges.  And I suspect Gale would have shared the prize as well, were he still alive.  Although I know pretty much nothing about most economics research, I can still say – Congratulations to those folks, and hooray algorithms!  And boo this job search!

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