# Sure-thing principle

In decision theory, the sure-thing principle states that a decision maker who would take a certain action if he knew that event E has occurred, and also if he knew that the negation of E has occurred, should also take that same action if he knows nothing about E.

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.

— p. 21

He formulated the principle as a dominance principle, but it can also be framed probabilistically.[2] Jeffrey[2] and later Pearl[3] showed that Savage's principle is only valid when the probability of the event considered (e.g., the winner of the election) is unaffected by the action (buying the property). Under such conditions, the sure-thing principle is a theorem in the do-calculus[3] (see Bayes networks). Blyth[4] constructed a counterexample to the sure-thing principle using sequential sampling in the context of Simpson's paradox, but this example violates the required action-independence provision.[5]

The principle is closely related to independence of irrelevant alternatives, and equivalent under the axiom of truth (everything the agent knows is true).[6] It is similarly targeted by the Ellsberg and Allais paradoxes, in which actual people's choices seem to violate this principle.[2]

## References

1. ^ Savage, L. J. (1954), The foundations of statistics. John Wiley & Sons Inc., New York.
2. ^ a b c Jeffrey, Richard (1982). "The Sure Thing Principle". Proceedings of the Biennial Meeting of the Philosophy of Science Association. 2: 719–730. JSTOR 192456.
3. ^ a b Pearl, Judea (2009). Causality: Models, Reasoning, and Inference (2nd ed.). New York: Cambridge University Press.
4. ^ Blyth, C. (1972). "On Simpson's paradox and the sure-thing principle". Journal of the American Statistical Association. 67: 364–366. doi:10.2307/2284382.
5. ^ Pearl, Judea (December 2015). "The sure-thing principle" (PDF). UCLA Cognitive Systems Laboratory, Technical Report R-466.
6. ^