Deferred acceptance theory has been used in many noble causes … as well as speed dating

What do speed dating, applying to a state secondary school and undergoing a potentially life saving transplant from an organ donor have in common?

It might take an economist to notice that all three can be seen as markets – but ones where no money changes hands.

Alvin Roth and Lloyd Shapley have won the Nobel prize for their work on how these difficult choices can be made without using prices as a mechanism.

Shapley first dared in 1962 to tackle the question asked by women's magazines through the years – how to find a suitable match.

The specific question he sought to answer was: how could individuals in a group be paired up when they all had different views on who would be their best match? Along with economist David Gale, Shapley developed a method to match 10 women and 10 men, so that no two people would prefer each other over their current partners. The so-called 'deferred acceptance' theory has since been used in many noble causes, as well as speed dating.

Their deceptively simple formula involved either the men or the women choosing the partner they liked the best. Each man was given a list of the women who chose him, and he would then select his top choice from the list. Those women left without a match after the first round would have a second round to choose from the men they initially rejected. Shapley and Gale proved mathematically that this process led to a stable match, where no couple sees any gain in swapping partners. However, the sex that initially gets to choose gets a better outcome than the one being chosen.

No marriages were actually arranged through the algorithm, though it later found a very modern application in speed dating evenings. Almost 30 years after the initial paper Roth applied it to the problem of assigning student doctors to hospitals. The idea was that an employer and employee trying to find the best match is similar to a hypothetical husband and wife.

His theory has gone on to be used to allocate prospective pupils to secondary schools. In London, for example, parents put their six top choices in order of preference. The schools are not told their ranking but apply their admissions criteria to all the students that applied. Where a student gains a place in a higher ranked school, any other places are discarded and the schools are required to offer more places.

Researchers are now looking to apply the algorithm developed by Gale and Shapley to the challenge of matching up kidney donors and those who need a transplant.