Past exam of the mathematics course of the University of Cambridge / 2012 / iii / Paper 44 / 1 / a / Solution Created 2026-10-03 Updated 2026-10-07
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An affine function preserves mixtures, so
(1)
Therefore
(2)
The positive mixture weight preserves the strict sign; the common component cancels. This is the independence axiom for lottery preferences for the affine utility on probability measures.
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