David Gale: 2 ideas and puzzles worth knowing

2 ideas and puzzles from David Gale, each explained in a minute and credited to the original work. Free on Savvy.

Match everyone up so no one wants to swap partners
Ten men and ten women each privately rank everyone of the opposite sex from most to least preferred. You have to pair all twenty of them off into couples. Is it always possible to …
— David Gale and Lloyd Shapley, College Admissions and the Stability of Marriage
An algorithm from 1962 still matches doctors to hospitals nationwide
In 1962 David Gale and Lloyd Shapley proved that a simple round-by-round proposal process always produces a 'stable' matching, where no pair would rather ditch their assigned partn…
— David Gale and Lloyd Shapley, College Admissions and the Stability of Marriage

Five ideas worth knowing, every week