The Intern Hiring Conundrum

When I say "STEM is for Everyone," I mean it.  STEM is not just for people who do STEM - problems that come up in our daily lives can be solved with the techniques we learn by studying STEM.  When you hear "economics," don't think "price of wheat in a drought," think "hiring interns."

Here's why.  A friend came to me with a problem her organization is having hiring interns. There are 7 divisions in her organization, and it used to be that each division handled intern hiring independently.  Too often multiple divisions would end up giving offers to the same candidates, which confused the candidates and made it harder for the divisions to predict yield (that is, the percentage of candidates that will accept offers).

So a couple of years ago they switched to a coordinated hiring process, where each of the divisions would select their preferred candidates and representatives from each of the 7 divisions would sit in a room to resolve any conflicts.  But these meetings could get very heated and led to inter-divisional conflicts.  So they want to take emotions out of the process and develop a fair system allocate candidates between the divisions.

Economists will recognize this as a matching problem.  Matching is a very complex problem - indeed, a matching algorithm was one of the accomplishments that led to the 2012 Nobel Prize in Economic Science for Lloyd Shapley and Alvin Roth.  For various reasons, the organization is not going to use candidate preferences in making division assignments, which helps simplify the system to a more traditional resource allocation problem.  Drafts, lotteries, and auctions are all mechanisms for allocating scarce resources.  Picking the right system will help you get the right interns to the right groups.  To figure out which is the right system, you need to understand your objectives and constraints, and how each system handles your situation.  After the jump, I go through some of the possible intern assignment systems and their pros and cons.

I should point out that I have not studied either economics or game theory extensively - I find these issues fascinating, but true experts would have a lot more to say about this.


Case Study: Coordinated Intern Hiring

The first thing to look at are some of the features of the problem and characteristics of a good solution.  This is how we define our "objective function":

1. Each division needs a different number of interns - one division might want 15 interns and another might only want 3.  The system needs to provide all divisions with an opportunity to get their preferred candidates, however many they need.
2. Each division tends to prefer interns with superior academic backgrounds, but as each division does different work, a candidate might be better suited to one division than another.  Preferences may vary between divisions - the system should allocate candidates to the division that wants the candidate the most.
3. Intensity of interest can vary.  For example, suppose two divisions are interested in candidates A and B, and both prefer A to B.  Division 1 likes A and B about the same, with a slight preference for A. Division 2 would take B in a pinch, but really wants A.  In this situation, the system should place candidate A with division 2 and candidate B with division 1.
4. Everyone in the organization must be satisfied with the fairness of the system.

While it's important to consider what happens when certain participants act strategically - such as overstating the number of interns desired to get an advantage - the fact that the participants are all part of a larger organization work counter to this effect.  Also, this is a "repeated game" - that is, the divisions will go through this process every year, so it is possible to accommodate for bad outcomes one year with an advantage in a future year.

So let's see how some of the allocation systems work against these factors?

Draft: Each division takes turns picking their favorite candidate.  This is commonly used in sports leagues, where each team has similar priorities and needs the same number of players.  Also, in sports leagues it is often used to help equalize teams by giving teams that performed worst in the previous season first pick of the best players this season.  In this case, draft order could be set randomly or based on organizational priorities.  It is a very simple system, but in this case it does not handle the factors very well.  If division A wants to hire 15 candidates and division B wants to hire 3, it is difficult to design a fair draft.  If you do 1 candidate per division per round, then division B gets to hire all of its candidates before division A has the opportunity to offer 80% of its slots.  If you let division A pick 5 times for every time division B picks a candidate, then division B feels that it loses out on its opportunity to pick high quality candidates.  Either way, one of the divisions feels the system is unfair.  It also does nothing to address intensity of interest.

Lottery: Each division gets one lottery ticket for each slot they have to hire, and when a division is called, it gets to pick.  This is a lot like the draft, but with added randomness. This randomness may make it seem more fair, or may lead to more resentment - unfortunately you won't know which until the lottery has occurred.  In a draft, a poor draft position seals your fate, but in a lottery, each pick is a new chance to be a winner.  However, a fair lottery might let 6 of the division pick several times each before the 7th picks once.  If this happens, it will feel unfair to the 7th division. Whether or not the outcome feels fair, it still does not accommodate for intensity of interest. 

Preference Ranking: Each division ranks candidates in order of preference.  The system attempts to place as many 1st choice candidates as possible, then as many 2nd choice candidates as possible, and so on.  This system takes less time than a draft because the divisions set their preferences ahead of time and the results are calculated immediately.  This has the same issues as a draft with respect to handling different division sizes.  A system for handling conflicts if 2 or more divisions select the same candidate in a given round would be necessary - either a coin-toss or some kind of rotating priority.  Despite similarities between this and a draft, it is likely to yield significantly different assignments.  An interesting experiment would be to simulate how the outcomes differ between a draft and preference ranking and see how those match up to the objectives.

Live Auction: Each division is assigned bidding credits based on how many slots the division has.  Once credits are spent, they can no longer be used for bidding for further candidates.  One problem is that a division that needs 15 candidates will have 5 times as many credits as a division that needs 5, and thus can outbid every other division for their preferred candidate(s).  This gives the large divisions effectively first choice for candidates (at the expense of ending up with several less-competitive candidates toward the end).  You can address this by putting a cap on the maximum bid, but since there is no cost to bidding to the loser, most divisions will be willing to bid all the way to the cap on candidates they are interested in - so you're left with a conflict almost as much as before there was a system in place at all.

Single-Round Sealed-Bid Silent Auction: Each division is assigned bidding credits based on how many slots the division has.  The division can choose how many credits it wants to allocate to any given candidate.  In this way it can account for intensity of interest.  In the situation described in point 3 above, division 1 might assign 15 points to candidate A and 5 points to candidate B.  Division 2 might assign 11 points to candidate A and 9 points to candidate B.  The sealed bid feature changes the dynamic with respect to large  divisions over-bidding on their top choice candidates because all bids need to be made before it is known if any are accepted.  There is a potential for ties in a sealed-bid auction, but the ties should only happen if there is genuinely equal interest among the divisions so the system is equally served by either outcome.  A draw back of this system, though, is that it is a lot more complex for the participants than the other systems - figuring out how to allocate points across the entire pool of candidates is a daunting and complex process.

There may be no one best answer (or the best answer may be the consensus-driven process they are currently using), but by applying concepts from economics, the divisions can explore which system works best to handle their hiring conundrum.  You can probably write an entire thesis analyzing the options, coming up with new options, and identifying pros and cons and pitfalls that I have neglected.  But the bottom line is that, economics and game theory are useful, even if you never practice either professionally.