How might the UK's university admissions system be redesigned?

Ensuring university admissions are both fair and efficient is a challenge for policy-makers, particularly following two summers of disrupted exams. One possible solution could be to adopt a post-qualification admissions system that includes a matching mechanism.

This summer, for the second year in a row, A-level examinations did not take place and grades were instead determined by teacher assessments. The results – released earlier in August – showed a record number of students achieved A or A* grades. This has had a knock-on effect on university admissions, as more students than expected met their offers, meaning that some courses are oversubscribed.

This has boosted the argument to change the current system of higher education admissions and move to post-qualification admissions (PQA). Adopting a system based on PQA would mean that students would receive and accept university offers after they have received their A-levels (or Level 3 equivalent) grades. This differs to the current system in which students apply up to a year before starting higher education and offers are made on the basis of predicted grades.

While the intention behind such proposals is to remove the potential unfairness of offer decisions based on predicted grades, the specific design of a new system will be critical in its ability to deliver this promise.

Problematic issues with the existing system are not limited to its significant reliance on predicted grades. For example, universities are currently not able to coordinate offers across the whole system effectively. As a result, the system suffers from congestion: universities do not know which of their offers will result in recruitment and there is not enough time after results day for offers to be made, accepted, or rejected effectively.

Many students receive offers they won’t eventually accept, while others miss out on offers which they would deserve and accept in a well-functioning system. A PQA timeline would substantially narrow the window of communication between universities and students, which could intensify existing congestion. As a result, an effective matching mechanism to coordinate offers and students’ responses is needed.

A matchmaking mechanism can assign students to courses fairly, efficiently, and quickly. To do so, each student would privately submit to the matchmaker their preference ranking of the courses they have applied to. Universities and Colleges Admissions Service (UCAS) would be a natural institution to play the role of the matchmaker in this case.

Universities would similarly report to the matchmaker how many students they aim to recruit in each course, and how they rank their applicants from first-to-admit to last. With this information alone, the matchmaker could identify a match which guarantees for every student their most preferred choice for which they can qualify.

Such a system would:

allow students to express their preferences over their applications;
coordinate universities’ offers to ensure students receive offers only from their best achievable courses (reducing congestion);
ensure no student misses out on an application at the expense of a less-qualified applicant;
guarantee that it is in every student’s best interest to reveal their preference ranking honestly; and
ensure universities meet their target student numbers with certainty, and therefore minimise the need for a clearing mechanism and remove any temptation to circumvent the system.

What is the nature of congestion in UK university admissions?

While there is currently a centralised framework through which the students submit their university applications, namely UCAS, universities’ offers are determined in a completely decentralised way. Universities receive applications, evaluate them on their suitability for the intended courses and decide which of those applicants will be granted offers.

Offer decisions are made without knowing what other offers their applicants might be holding. As a result, the universities' task of deciding whom to make offers to while controlling their student intake numbers is a complicated problem. It is strategic in the sense that the outcome of the process (who will study where, how many students will be in each course, etc) depends on the complex interaction of offer decisions made by all universities and choices made by all students (including those with multiple offers).

The difficulty of reliably predicting which of their offer holders will gain a place leaves the universities in a complicated guessing game. The current admissions system in the UK aims to mitigate universities’ difficulties in accurately predicting and managing student numbers at the cost of restricting student choice.

Upon receiving offers (which are typically conditional), students must choose two final places: a firm and an insurance choice. This means that even though the students might have a competitive chance to meet their conditions on other offers, they are not able to pursue them at all.

This policy might help universities in their admissions process, but recent evidence shows that it does not provide security. Many universities want a lot more certainty. To achieve this, they are increasingly resorting to ‘conditional-unconditional’ offers, the scope of which has recently been documented by UCAS.

Such offers require the recipient student to commit to a single university at the expense of discovering whether their applications to other universities might be successful at the end of the admission cycle. This further shifts the burden of strategic guesswork and its numerous adverse consequences on to students.

Without effective coordination across the sector, allowing students to pursue their ambitious applications without risking safer choices is complicated. In the absence of a matchmaker, it takes repeated negotiation between students and universities to fully discover for all students what their best feasible choices are.

New York City high school match is an example where students used to receive offers from multiple schools and the market suffered from congestion, until the system was redesigned to incorporate a matchmaking mechanism.

How would matchmaking work?

The aim is to find a fair and efficient way of pairing students with university courses. To do so, the matchmaker will collect students’ preferences for the courses they have applied to. Similarly, for each course, the matchmaker will solicit from the universities a target intake number and a ranking of applicants from best-qualified to least-qualified.

With this information, the matchmaker could then operate the following simple procedure on behalf of all participants:

In round one, each student applies to their top choice. Each course keeps all the applicants who were given early offers, and in addition keeps the best ones among the remaining applicants up to its target intake number. All other applicants are rejected.
In round two, all rejected applicants apply to their next favourite course. Each course considers its applicants kept from the previous round together with the new applicants, keeps all who were given early offers and the best ones among the remaining up to its target intake number. All others are rejected.
These rounds are repeated until no student is rejected (which must eventually happen because no student applies twice to any course).

This process uses a deferred acceptance (DA) algorithm (Gale and Shapley, 1962). In theory, deferred acceptance always yields the unique ‘student-optimal fair matching’. Fair because no student misses out on any application at the expense of a less-qualified applicant. Student-optimal because every applicant receives their best possible match subject to this fairness criterion.

This system has been successful in the design of the centralised clearing house for junior doctors in the United States, the redesign of school admissions systems in New York City, Boston, and many UK cities, and in university admission systems in countries such as Germany, Hungary, and Turkey.

How might a PQA model for UK admissions be structured?

Over the past year, UCAS, Universities UK (UUK), and University and College Union (UCU) all published their alternative PQA models. These propose to change the admissions timeline to delay university offer making (in the case of UCAS and UUK models) or both applications and offers (in the UCU model).

But they maintain the decentralised nature of offer making, which can lead to inefficient and unfair matching. Incorporating a matchmaking mechanism creates a system that privately collects and effectively processes the right information to find a fair and efficient matching of students to courses.

One way to envision such a PQA model is as follows:

Student applications: By mid-January, for September entry of that year.

Preliminary assessment: Based on all available information (possibly including predicted grades), universities can assess applicants. This means universities can:

make early offers to applicants with special needs (e.g. from overseas), and
form preliminary course admission scores (which they will later update upon the release of A-level results in August).

Critically, having preliminary admissions scores will allow universities to be ready to assess candidates quickly in August without ignoring all the other factors that might matter for a holistic assessment (such as interviews, reference letters, contextual factors, or teacher predictions).

Early offers: Those who have previously completed their A-levels (or equivalent), have special needs, or are overseas applicants may receive early offers. They are not obliged to decide on these offers until they participate in the main matching round.

A-level results: Released in early August.

Main matching round: Mid-August

Those university courses that are willing to accept late applications announce this possibility and applicants make additional applications if they wish to.
Students privately submit to the matchmaker their preference rankings of all courses they applied to.
Incorporating the released A-level results, universities finalise their course admission rankings to list their applicants for each course from first-to-admit to last. They privately submit to the matchmaker their target course capacities and their course admission rankings.
Using the submitted information, the matchmaker runs the deferred acceptance algorithm.

How does this compare with the existing system?

This system differs from the current one as:

Students do not need to sacrifice any of their applications and can pursue the outcome of all their applications all the way to the end of the admissions cycle.
Instead of trying to manage recruitment numbers, universities can focus on assessing students (considering whatever they think is relevant including contextual assessment and access targets) and report their assessment rankings to UCAS.
The Department for Education (DfE) or UCAS need not monitor or discipline universities for uncompetitive offer making, because the mechanism deters circumventing the system.
Based on students’ full preferences and achieved qualifications, the mechanism operates transparently and quickly.
It ensures fairness: no student misses out on a course at the expense of a less-qualified applicant.

It is important to note that for this proposal to work, it will be necessary to build the right ecosystem to support students of all backgrounds and universities with wide-ranging services and goals. Especially important is transparency regarding what it takes for an applicant to make realistically ambitious choices when deciding which courses to apply to.

While the PQA system will better inform universities about their applicants’ suitability, more accurate and standardised information about courses and their entry requirements must be easily accessible. Such information will not only help widen participation in the system but also enable all students to make informed decisions when choosing and ranking their applications.

Where can I find out more?

A Modern Design for University Admissions in the UK: Paper containing more information on this proposal, including consultation with policy-makers and other stakeholders.
The reviews of university admissions: House of Commons Briefing Paper 8358
PQA: Reforming University Admissions: Sutton Trust Research Brief (October 2020)

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