# comparing two lotteries

Suppose the prize space (in dollars) is $$\mathbb{Z}$$ = {1, 2, 3, 4, 5, 6, 7, 8} and consider choices by an agent whose preferences (over lotteries) satisfy the von Neumann-Morgenstern axioms.

A risk averse von Neumann-Morgenstern agent (with increasing utility) has to compare the following two gambles

p = ($$\frac{1}{8}$$, $$\frac{1}{8}$$, $$\frac{1}{8}$$,$$\frac{1}{8}$$,$$\frac{1}{8}$$,$$\frac{1}{8}$$,$$\frac{1}{8}$$,$$\frac{1}{8}$$)

q=($$\frac{2}{8}$$,$$0$$, $$\frac{1}{8}$$,$$\frac{1}{8}$$,$$\frac{1}{8}$$,$$\frac{1}{8}$$,$$0$$,$$\frac{2}{8}$$)

Question is: Can you say unambiguously which one she would prefer?

I am thinking that if I can show one gamble second order stochastically dominates the other I can find the answer but I could not do that. Any help will be appreciated thanks!

• Are you familiar with any of the definitions of risk aversion? How about applying one or the other? Oct 22 '21 at 21:46
• Can you give me a hint? Oct 22 '21 at 22:51
• Sure. Look up the definition in your textbook. Oct 23 '21 at 4:34
• I looked up the definition but still it didn't help enough. I know a risk averse individual has concave utility function but I couldn't adapt it here. Oct 23 '21 at 17:01
• The expected value is the same. What about variance? How is variance related to a risk-averse utility? Oct 25 '21 at 6:24