Suppose, for example, that a decision maker can choose any probabilities , , that he or she wants for specified dollar outcomes
and that they have a given expected value
For example, if were the price of a lottery ticket with possible prizes and , then would define a “fair” lottery, while would afford the lottery organizer a profit. We may arbitrarily let the utilities of and be and ; then the utility of is . For a typical lottery, || is quite small as compared to and . With , this implies that feasible and are small, with well under , and therefore with well over .
1. If is the price of a lottery ticket, how could it possibly be less than zero?
2. Why include the price of a lottery ticket in an EV calculation? The prizes and have a probability associated with them, that makes sense when calculating expected value. But the price of a lottery ticket? What does it mean for a ticket price to have a probability "well over "
3. For , it only makes sense that must be negative, but again, how could the price of a lottery ticket be negative?