One thing this example illustrates is how the article style option is good for printing slides two-up, for distribution to a seminar audience or class, or just for proofreading.
Definition:
p (weakly) first-order stochastically dominates q if for every
∈Z,
)≤q(z≤)
| z | p(z) |
| $999 | .01 |
| $1,000,000 | .99 |
| z | q(z) |
| $1,000 | 1 |
Let Z be an arbitrary set of outcomes. Let u : Z→R be a utility representation of the DM's preferences over the elements of Z as certain outcomes. (I.e., u(y)≥u(z) iff y≥z.)
This can get around even St. Petersburg Paradox, because we don't require that utility be linear in money:
| Prize | $2 | $4 | $8 | $16 | … |
| u(z) = log2(z) | 1 | 2 | 3 | 4 | … |
| Prob. | 1/2 | 1/4 | 1/8 | 1/16 | … |
Expected utility is
k/2k = 2, and so lottery gives same
expected utility as getting $4 for sure.