Fairness Preferences. Suppose you can award exactly one person with a prize. Person A and person B both equally deserve the prize and you are indifferent between giving the prize to A or B. However, you strictly prefer to toss a fair coin to decide who gets the prize over giving the prize to either of the two individuals directly. What are three different lotteries for which a preference ranking is specied in the question? Write down the preference ranking between these three lotteries. Explain why such preferences are not compatible with expected utility representation