# Compound lottery preference implies simple lottery preference

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.

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