sure-thing principle

{{Short description|Decision principle}}

In decision theory, the sure-thing principle states that a decision maker who decided they would take a certain action in the case that event E has occurred, as well as in the case that the negation of E has occurred, should also take that same action if they know nothing about E.

The principle was coined by L.J. Savage:Savage, L. J. (1954), The foundations of statistics. John Wiley & Sons Inc., New York.

{{quote|text=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.|source=p. 21}}

Savage formulated the principle as a dominance principle, but it can also be framed probabilistically.{{cite journal |first=Richard |last=Jeffrey |jstor=192456 |title=The Sure Thing Principle |journal=Proceedings of the Biennial Meeting of the Philosophy of Science Association |volume=1982 |year=1982 |issue=2 |pages=719–730|doi=10.1086/psaprocbienmeetp.1982.2.192456 |s2cid=124506828 }} Richard Jeffrey and later Judea Pearl{{cite book|last1=Pearl|first1=Judea|title=Causality: Models, Reasoning, and Inference|date=2009|publisher=Cambridge University Press|location=New York|edition=2nd}} 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 (see Bayes networks). Blyth constructed a counterexample to the sure-thing principle using sequential sampling in the context of Simpson's paradox,{{cite journal|last1=Blyth|first1=C.|title=On Simpson's paradox and the sure-thing principle|journal=Journal of the American Statistical Association|date=1972|volume=67|issue=338|pages=364–366|doi=10.2307/2284382|jstor=2284382}} but this example violates the required action-independence provision.{{cite web|last1=Pearl|first1=Judea|title=The sure-thing principle|url=http://ftp.cs.ucla.edu/pub/stat_ser/r466.pdf|website=UCLA Cognitive Systems Laboratory, Technical Report R-466|date=December 2015}}

In the above cited paragraph, Savage illustrated the principle in terms of knowledge. However the formal definition of the principle, known as P2, does not involve knowledge because, in Savage's words, "it would introduce

new undefined technical terms referring to knowledge and possibility that would render it mathematically useless without still more

postulates governing these terms." Samet{{cite journal|last1=Samet|first1=Dov|title=The impossibility of agreeing to disagree: An extension of the sure-thing principle|journal=Games and Economic Behavior|date=2022|issue=338|pages=390-399|doi=10.1016/j.geb.2022.01.016}} provided a formal definition of the principle in terms of knowledge and showed that the impossibility to agree to disagree is a generalization of the sure-thing principle.

It is similarly targeted by the Ellsberg and Allais paradoxes, in which actual people's choices seem to violate this principle.