Sure-thing principle

In decision theory, the sure-thing principle denotes that outcomes which occur regardless of which actions are chosen, sure things, should not affect one’s preferences.

The principle was coined by L.J. Savage:^[1]

A businessman contemplates buying a certain piece of property. He considers the outcome of the next presidential election relevant. So, to clarify the matter to himself, he asks whether he would buy if he knew that the Democratic candidate were going to win, and decides that he would. Similarly, he considers whether he would buy if he knew that the Republican candidate were going to win, and again finds that he would. Seeing that he would buy in either event, he decides that he should buy, even though he does not know which event obtains, or will obtain, as we would ordinarily say. It is all too seldom that a decision can be arrived at on the basis of this principle, but except possibly for the assumption of simple ordering, I know of no other extralogical principle governing decisions that finds such ready acceptance.

He formulated the principle as a dominance principle, but it can also be framed probabilistically.^[2]

The principle is closely related to independence of irrelevant alternatives, and equivalent under the axiom of truth (everything the agent knows is true).^[3] It is similarly targeted by the Ellsberg and Allais paradoxes, in which actual people's choices seem to violate this principle.^[2] Furthermore, Simpson's paradox relates to cases where a naive attempt to apply the sure-thing principle would give the wrong answer.

References