Published on March 3, 2025 4:10 PM GMT
Our oldest is finishing up 5th grade, at the only school in our citythat doesn't continue past 5th. The 39 5th graders will be split upamong six schools, and we recently went though the process ofindicating our preferences and seeing where we ended up. The processisn't terrible, but it could be modified to stop giving an advantageto parents who carefully game it out while better matching kids topreferred schools.
First, what is the current process? You put in 1st, 2nd, and 3rdchoice rankings, which are interpreted in three rounds. Kids areassigned to 1st choice schools, then the ones who didn't get in areassigned among 2nd choices, and finally 3rd choices. Ties are brokenby sibling priority, proximity priority, and then by lottery number.
For sibling priority, if you have a sibling who will be in the schoolnext year you have priority over students who don't. In practice thismeans if you list a sibling priority school as your first choice youget it.
For proximity priority, each family has a proximity school. This maynot be the closest one to their house, and for us it isn't, but its atleast reasonably close. It's the same as siblings: you have priorityover any non-proximity students. Listing your proximity school firstwon't always get you in, since some schools (ex: ours) have many moreproximity students than open spots.
The open spots this year are:
| School | Sibling | Proximity | Available seats |
|---|---|---|---|
| A | 0 | 3 | 2 |
| B | 0 | 3 | 0 |
| C | 0 | 3 | 10 |
| D | 2 | 11 | 23 |
| E | 1 | 16 | 4 |
| F | 0 | 0 | 4 |
Under the current system, what did it make sense for us to put for ourtop three choices? Ignoring B, which has no available spots, ourpreference order is D > E > A > C > F. We could put thatdown directly (D, E, A) but how do proximity and limited spaces affectour decision?
Our proximity school is E, with 4 available seats. It was very likelythat the family with sibling priority would put it first, so really 3available seats. If we put it first and so did all other familieswith proximity, we'd have a 3/15 chance of getting a spot there. Ithink this means our best chances would be putting first D, then C,and then it doesn't matter much:
While we have proximity at E, since there are so many moreE-proximal students than spots, even if it was our top choice I'd onlyput it first if we thought "E vs everything else" was the key question.But since we prefer D, and since I expect enough proximity studentswill put E first that it will go in the first round, we shouldn'tlist it at all: that would waste our 2nd or 3rd pick.
Similarly, I expect A to go entirely to students withproximity, so no point listing it.
Putting our 1st choice on D makes sense to me: it's our actualfirst choice, and even after accounting for sibling and proximitystudents it still has ten open spots.
Then we should put C next, since we prefer it to F.
For simplicity, lets assume everyone has the same preferences we wouldhave if we lived where they did. That means people prefer whicheveris closest of A, E, or D. Then on the first round, of the 39rising 6th graders:
- Two or three list A with priority, two get it and zero or one miss outZero list BZero list CThirteen list D with priority, and fifteen to twenty, includingus, list without priorityFour to ~eight list E with priority, four get it, and zero to fourmiss out.Zero list F
So our odds of getting D would be somewhere between 10/20 and 10/15.
But the real world looks a bit better than this:
Some kids are probably moving out of district, though they maywait until after they know their school assignment to decide.
Not every family has the same preferences.
Some families don't game this out carefully. I especiallythink it's likely that too many families who are close to indifferentbetween D and E put E first on the basis of it being their proximityschool.
When we put in our preferences I guessed our likely outcomes were 62%D, 35% C, 2% other. Several weeks later we learned that our lotterynumber was 19/39, we got C and were placed first on the waitlist forD. Since there are ~70 rising sixth graders for D I think it's verylikely that at least one of them will move away and we'll get in.
This felt a bit like playing a board game because that's the mainplace I work through rules in a zero-sum context, but here the resultsmatter. I really don't like that us getting a school we preferessentially has to come at the expense of other families getting whatthey'd prefer.
While the zero-sum nature is unavoidable, we could at least rework thesystem to no longer require families to be strategic. This isactually a very well-known problem,and we can apply the Gale–Shapleyalgorithm, which is used in medical residency matching:
Instead of listing just your top three choices, you list all of them.Because there's no benefit to misreportingyour preferences this is relatively easy. Once you haveeveryone's preferences you assign lottery numbers as before, and thenrun multiple rounds of an algorithm.
In the first round, every student "applies" to their top choice. Theschool ranks students by sibling status, then proximity status, thenlottery number, and provisionally accepts students up to capacity. Inthe next round unassigned students "apply" to their next rankedschools, with schools provisionally accepting anyone they rank higherthan their previously provisionally accepted students and bumpingstudents as needed. This continues until everyone has a place, andwhich point provisional acceptances become real acceptances andstudents are notified.
I especially like that with this algorithm families don't need toconsider what other families are likely to do. If they prefer E to D,they can just put E first, without worrying that they are wasting achoice. While as someone who does think through strategy I expectthis change would make our family mildly worse off, a system wherepeople have the best chances of getting into their preferred schoolsif they accurately report their preferences seems clearly betteroverall.
Discuss
