The Sure Thing
DSA ADS Course - 2021
The Sure-Thing Principle, Causal Reasoning, Data-Driven Decision-Making, Algorithm Decision Making, Applied Probability, Nonlinear Utility Scale, Simpson’s Paradox, Blyth’s Game
Discuss applied probability, causal reasoning and types of decision making processes. Apply to both traditional algorithms and machine learning algorithms in decision making processes.
See also: The Sure-Thing Principle
The Sure Thing - 2021
If we prefer action a to b both under an event and under its complement, then we should just prefer a to b. This is Savage’s sure-thing principle. In spite of its intuitive- and simple-looking nature, for which it gets almost immediate acceptance, the sure thing is not a logical principle. So where does it get its support from? In fact, the sure thing may actually fail. This is related to a variety of deep and foundational concepts in causality, decision theory, and probability, as well as to Simpsons’ paradox and Blyth’s game. In this paper we try to systematically clarify such a network of relations. Then we propose a general desirability theory for nonlinear utility scales. We use that to show that the sure thing is primitive to many of the previous concepts: In non-causal settings, the sure thing follows from considerations of temporal coherence and coincides with conglomerability; it can be understood as a rationality axiom to enable well-behaved conditioning in logic. In causal settings, it can be derived using only coherence and a causal independence condition.