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Strict Dominance and Symmetry

Pruss, Alexander R. (2022) Strict Dominance and Symmetry. [Preprint]

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The Strict Dominance Principle that a wager always paying
better than another is rationally preferable is one of the least contro-
versial principles in decision theory. I shall show that (given the Axiom
of Choice) there is a contradiction between Strict Dominance and plau-
sible isomorphism or symmetry conditions, by showing how in several
natural cases one can construct isomorphic wagers one of which strictly
dominates the other.
In particular, I will show that there is a pair
of wagers on the outcomes of a uniform spinner which differ simply in
where the zero degrees point of the spinner is defined to be but where
one wager dominates the other. I shall also argue that someone who ac-
cepts Williamson’s famous argument that the probability of an infinite
sequence of heads is zero should accept the symmetry conditions, and
thus has reason to weaken the Strict Dominance Principle, and I shall
propose a restriction of the Principle to “implementable” wagers. Our
main result also has implications for social choice principles.

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Item Type: Preprint
Pruss, Alexander R.
Subjects: Specific Sciences > Probability/Statistics
Depositing User: Dr Alexander Pruss
Date Deposited: 15 Dec 2022 18:30
Last Modified: 15 Dec 2022 18:30
Item ID: 21560
Subjects: Specific Sciences > Probability/Statistics
Date: November 2022

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