The Sure Thing

Marco Zaffalon, Enrique Miranda
Proceedings of the Twelveth International Symposium on Imprecise Probability: Theories and Applications, PMLR 147:342-351, 2021.

Abstract

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.

Cite this Paper

BibTeX
@InProceedings{pmlr-v147-zaffalon21a, title = {The Sure Thing}, author = {Zaffalon, Marco and Miranda, Enrique}, booktitle = {Proceedings of the Twelveth International Symposium on Imprecise Probability: Theories and Applications}, pages = {342--351}, year = {2021}, editor = {Cano, Andrés and De Bock, Jasper and Miranda, Enrique and Moral, Serafı́n}, volume = {147}, series = {Proceedings of Machine Learning Research}, month = {06--09 Jul}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v147/zaffalon21a/zaffalon21a.pdf}, url = {https://proceedings.mlr.press/v147/zaffalon21a.html}, abstract = {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.} }
Endnote
%0 Conference Paper %T The Sure Thing %A Marco Zaffalon %A Enrique Miranda %B Proceedings of the Twelveth International Symposium on Imprecise Probability: Theories and Applications %C Proceedings of Machine Learning Research %D 2021 %E Andrés Cano %E Jasper De Bock %E Enrique Miranda %E Serafı́n Moral %F pmlr-v147-zaffalon21a %I PMLR %P 342--351 %U https://proceedings.mlr.press/v147/zaffalon21a.html %V 147 %X 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.
APA
Zaffalon, M. & Miranda, E.. (2021). The Sure Thing. Proceedings of the Twelveth International Symposium on Imprecise Probability: Theories and Applications, in Proceedings of Machine Learning Research 147:342-351 Available from https://proceedings.mlr.press/v147/zaffalon21a.html.

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