Dear Economist,

Traditionally, women have to wait for men to propose marriage - or, indeed, a date. Isn’t this out of date and unfair, too?

Fiona O’Callaghan, Dublin

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Dear Fiona,

It has been out of date since 1962, when David Gale and Lloyd Shapley published a paper on the problem of who marries whom, to work out whether there is a way of pairing up men and women so that no potential adulterers would rather marry each other. There may be loveless singletons around, but as long as nobody wants to marry them, the situation is said to be a “stable assignment”.

Gale and Shapley suggested an algorithm guaranteed to produce a stable assignment. Each man proposed to his preferred partner; each woman then rejected all the less attractive offers and kept the remaining fellow on tenterhooks in case someone better came along. The rejects would then propose marriage to someone closer to their league, each woman would reject all but the best so far, and the humiliating process would continue.

The algorithm eventually produces a stable assignment, where nobody prefers a willing partner to the one they have. It also produces a billion broken hearts; presumably the assignment is stable because nobody wants to go through the whole thing again.

The algorithm works equally well if the women do the proposing and the men do the rejecting. Intuitively it’s not clear which you should prefer, but the mathematics are unambiguous: out of all the stable assignments that exist, the one where men propose is the very worst for women and the very best for men. Nearly five decades after this revelation, a change in tradition is probably overdue.

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