Irrevocable decision
Named by 4 essays across one field — each of them below, with the objects they name alongside it.
Also named here as optimal stopping, threshold rule — the same set of essays touches all of them, so they are one junction rather than several.
When to stop looking
Candidates arrive one at a time in a random order. Each must be accepted or rejected on the spot, with no going back and no way to know what is still to come. The best possible rule is to look at about a third of them and then take the first one that beats everything seen — and it works about a third of the time, however many there are.
When the numbers are shown
The secretary rule wins a third of the time and cannot do better, because it is told only who is ahead. Show the actual values and say where they came from, and the same problem is won three times in five — by a standard that falls as the end approaches.
Giving up on the best
The secretary rule treats landing the second-best exactly as badly as landing the worst, which is a strange thing to want. Ask instead for the smallest average rank and the answer is about the fourth-best candidate — whatever the size of the field, and whether it is ten or ten million.
Half of what an oracle takes
Compare an online rule not against the best it could have done but against a rule that has seen every value in advance. One fixed threshold secures half of what the oracle collects, whatever the distributions are — and there is an example on which half is all there is.
Named alongside it
The objects these essays reach for when they reach for this one.
Conditional probabilityDecision procedureExpectationOptimal stoppingThreshold ruleBackward inductionCounting argumente, the numberBoundCompetitive ratioHarmonic seriesPermutation