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It is not the case that A non-transitive value ordering cannot form the basis of a satisfactory answer to what one ought to choose
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Reasons For
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Reason for
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1.
Coupled with the standard formulation of consequentialism, a non-transitive ordering yields the counterintuitive result that no action is right in the mere addition paradox
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2.
Consequentialism holds that an action is right if and only if its outcome is at least as good as the outcomes of all alternative actions
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Reasons Against
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Reason against 1 of 2
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1.
A choice procedure that licenses cyclic preferences over outcomes permits money-pump exploitation, undermining rational agency entirely.
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2.
Sen's work on social choice demonstrates that non-transitive orderings generate systematic indeterminacy across all multi-option choice sets.
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3.
An agent facing A>B>C>A cannot identify a stopping point, making deliberation infinite and practical reason impossible.
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Reason against 2 of 2
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1.
Broome's formalism shows that any coherent betterness relation must satisfy transitivity to generate well-defined rankings across populations.
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2.
Without transitivity, aggregative comparisons in population ethics lose their mathematical grounding in real-valued utility functions.
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