Stable marriage problemIn mathematics, economics, and computer science, the stable marriage problem (also stable matching problem or SMP) is the problem of finding a stable matching between two equally sized sets of elements given an ordering of preferences for each element. A matching is a bijection from the elements of one set to the elements of the other set. A matching is not stable if: In other words, a matching is stable when there does not exist any pair (A, B) which both prefer each other to their current partner under the matching.
Gale–Shapley algorithmIn mathematics, economics, and computer science, the Gale–Shapley algorithm (also known as the deferred acceptance algorithm or propose-and-reject algorithm) is an algorithm for finding a solution to the stable matching problem, named for David Gale and Lloyd Shapley. It takes polynomial time, and the time is linear in the size of the input to the algorithm. It is a truthful mechanism from the point of view of the proposing participants, for whom the solution will always be optimal.
Sorting algorithmIn computer science, a sorting algorithm is an algorithm that puts elements of a list into an order. The most frequently used orders are numerical order and lexicographical order, and either ascending or descending. Efficient sorting is important for optimizing the efficiency of other algorithms (such as search and merge algorithms) that require input data to be in sorted lists. Sorting is also often useful for canonicalizing data and for producing human-readable output.
Stable distributionIn probability theory, a distribution is said to be stable if a linear combination of two independent random variables with this distribution has the same distribution, up to location and scale parameters. A random variable is said to be stable if its distribution is stable. The stable distribution family is also sometimes referred to as the Lévy alpha-stable distribution, after Paul Lévy, the first mathematician to have studied it. Of the four parameters defining the family, most attention has been focused on the stability parameter, (see panel).
General willIn political philosophy, the general will (volonté générale) is the will of the people as a whole. The term was made famous by 18th-century Genevan philosopher Jean-Jacques Rousseau. The phrase "general will", as Rousseau used it, occurs in Article Six of the Declaration of the Rights of Man and of the Citizen (French: Déclaration des droits de l'Homme et du citoyen), composed in 1789 during the French Revolution:The law is the expression of the general will.
