Suppose we have the following four lotteries:
$L_{1}=[(1,\$1)]$
$L_{2}=[(0.01,\$0),(0.89,\$1),(0.1,\$5)]$
$L_{3}=[(0.9,\$0),(0.1,\$5)]$
$L_{4}=[(0.89,\$0),(0.11,\$1)]$
If our agent says that he prefers $L_{1}$ to $L_{2}$ and prefers $L_{3}$ to $L_{4}$, then he is not following the expected utility assumption of independence (also known as substitutability).
Anyone know how to explain this?