Sean and Luce are asked to assign their probability ofrain this coming Thursday night based on their true belief. After meeting the clarity test on a binary distinction Rain and Sun, they assign their...

Sean and Luce are asked to assign their probability ofrain this coming Thursday night based on their true belief. After meeting the clarity test on a binary distinction Rain and Sun, they assign their probabilities as

and are given the deals shown in the figure.

Given the low range of monetary prospects involved in these deals, we can assume that both Sean and Luce are risk neutral. Circle the statements that are true:

I. Both Sean and Luce value their deals at $2.70.

II. Even if Sean's probability of rain were 0.33 (more than three times the probability he stated), he would still prefer the deal he got to 0.

III. If Luce had stated a lower probability than his true belief, he would have gotten a deal with a higher certain equivalent.

IV. Uncertain deals should not be valued based on their outcome, but rather on their certain equivalent.