Notes for Session 1, Dominance and Book, Summer School 2011 T.Seidenfeld 1 Session 1: Dominance and de Finetti's "Book" argument Summary: Notes for Session 1, Dominance and Book, Summer School 2011 T.Seidenfeld 1 Session 1: Dominance and de Finetti's "Book" argument Partition circumstances with a finite set of pairwise exclusive and mutually exhaustive situations. A partition with n-states {state1, state2, ....., staten} is written as: = { 1, 2, ...., n}. Suppose that YOU, the decision maker, can compare two acts, state by state, according to the desirability of their outcomes, oij. 1 2 ... k ... n Act1 o11 o12 ... o1k ... o1n Act2 o21 o22 ... o2k ... o2n Strict dominance · If YOU judge each outcome o1j is strictly preferable to the outcome o2j (j = 1,..., n), then you strictly prefer Act1 over Act2 in a pairwise choice between them. Notes for Session 1, Dominance and Book, Summer School 2011 T.Seidenfeld 2 Example 1: Suppose that you prefer more money to less. Consider the binary state decision problem where the payoffs are: 1 2 Act1 \$300 \$100 Act2 \$400 \$200 Collections: Mathematics