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Suppose $\alpha>\beta$ and for two lotteries $L, L'$

$\alpha L + (1 - \alpha)L' \succ \beta L + (1- \beta) L'$

where $\succ$ implies preference. If the independence theorem holds, how do you prove that this implies that $L \succ L'$.

Thanks.

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  • 2
    $\begingroup$ What have you tried? Do you have a more specific doubt other than how to prove it all together? This is pretty straightfoward $\endgroup$ – user20105 May 19 at 15:21

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