Expected utility theory (Lottery notation) A wheel of fortune has outcomes $S=\left \{ 1000,100,50,20,0 \right \}$ as money prices. A consumer has the preferences
$$20\sim \left ( \frac{2}{100}\cdot1000 \oplus \frac{98}{100} \cdot 0 \right )$$
$$50\sim \left ( \frac{15}{100}\cdot1000 \oplus \frac{85}{100} \cdot 0 \right )$$
$$100\sim \left ( \frac{45}{100}\cdot1000 \oplus \frac{55}{100} \cdot 0 \right )$$
What does this notation mean? I figure that the direct sum is just showing that the percentage for winning $1000$ in the first equation is $2/100$ and $98/100$ for $0$. But what does the $20$ denote? Is this some utility and how would that be read with the indifference sign in front of it? Never seen the notation like this before.
$$
\left(\frac{2}{100} \cdot 1000 \oplus \frac{98}{100}\cdot 0\right)
$$
is the lottery where you get $1000$ with probability $2/100$ and $0$ with probability $98/100$.
The expression
$$
20 \sim \left(\frac{2}{100} \cdot 1000 \oplus \frac{98}{100}\cdot 0\right)
$$
usually says that the decision maker is indifferent (in terms of preferences) between taking the lottery and having $20$ for sure.