Pearl’s Causal Sure-Thing Principle

Judea Pearl The Sure-Thing Principle TECHNICAL REPORT R-466 February 2016, University of California, Los Angeles (UCLA) Computer Science Department

This discusses Savage’s sure-thing example:

“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.”

Jeffreys noted that this is much less reasonable if the businessman’s decision could affect the outcome of the election. Pearl thus opines:

Definition 2 (The Causal Sure-Thing Principle (CSTP))

Let f and g be two acts, and B any event that is equally probable under f and under g, that is, P(B|do(f)) =P(B|do(g)) .(1)
If a person prefers f to g, either knowing that the event B obtained, or knowing that the event not-B obtained, then he ought to prefer f to g even if he knows nothing about B.

But suppose that f is to buy the property, g to not buy, and that the property would be highly desirable to either party, but that the president will only buy from someone who supported their candidacy., and the property would otherwise be a great loss. Definition 2 The above CST Principle says that if the purchase of the property does not affect the outcome of the election then if the business has not declared support for either candidate, he could buy the property, declare support for the candidate who he knows will win, then sell at a profit. but if he does not know who will win buying the property would be a gamble, so he could reasonably not buy.

The difficulty here is that the event B implies an action (declaring support for the winning candidate) that is not possible when the event is certain. One might try to fix the CST Perinciple by requiring that no other actions are possible until the result of B is known. But this would be of very restricted applicability.

Dave Marsay

 

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