Roger reports:
- I ascribe probability 0.3 to "the Philadelphia Phillies will win the World Series next year, Chris ascribes probability 0.4 to their winning the World Series and to me ascribing probability 0.4 that they will win the World Series, and Chris ascribes probability 0.6 to the Philadelphia Phillies not winning the World Series and to me ascribing probability 0.2 that they will win the World Series."
- I ascribe probability 0.2 to "the Philadelphia Phillies will win the World Series next year, Chris ascribes probability 0.4 to their winning the World Series and to me ascribing probability 0.5 that they will win the World Series, and Chris ascribes probability 0.6 to the Philadelphia Phillies not winning the World Series and to me ascribing probability 0.8 that they will win the World Series."
- I ascribe probability 0.4 to "the Philadelphia Phillies will win the World Series next year, Chris ascribes probability 0.2 to their winning the World Series and to me ascribing probability 0.1 that they will win the World Series, and Chris ascribes probability 0.8 to the Philadelphia Phillies not winning the World Series and to me ascribing probability 0.3 that they will win the World Series."
- I ascribe probability 0.1 to "the Philadelphia Phillies will win the World Series next year, Chris ascribes probability 0.6 to their winning the World Series and to me ascribing probability 0.4 that they will win the World Series, and Chris ascribes probability 0.4 to the Philadelphia Phillies not winning the World Series and to me ascribing probability 0.7 that they will win the World Series."
Answer the following questions:
(a) Construct a space of states of nature corresponding to the above description.
(b) What is Roger's first-order belief? What is his second-order belief? What is his third-order belief?