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Loss-averse choice

Expected valueMedium

A gambler scores a gain or zero of $x$ dollars as $x$ , but scores a loss of $x$ dollars (with $x < 0$ ) as $2.5 x$ . Lottery A pays the face value of a fair $6$ -sided die minus $4$ dollars. Lottery B pays $+ 5$ or $- 3$ dollars with equal probability. The gambler picks the lottery with the higher expected score. What is that higher score?

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Hint

Convert each outcome to its score before averaging.

Solution

For A the outcomes are $- 3, - 2, - 1, 0, 1, 2$ with scores $- 7.5, - 5, - 2.5, 0, 1, 2$ , averaging $- \frac{12}{6} = - 2$ .
For B the scores are $5$ and $- 7.5$ , averaging $- \frac{5}{4}$ .
The higher score is that of B, which is $- \frac{5}{4}$ .

Answer: $- \frac{5}{4}$

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