By Michael D. Resnik
An creation to what's known as "Choice Theory" in Economics.
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But for any b, au(x) > au(y) if and only if au(x) + b > au(y) + b. Putting this together yields u(x) > u(y) if and only if u'(x) > u' (y), which is the condition for «' to be an ordinal transformation of u. Not every ordinal transformation is a positive linear transformation. Not every ordinal transformation preserves the ordering of the acts given by the minimax regret rule, but positive linear transformations do. The last example illustrated this, but let us see why it holds in general. When we form a regret table we calculate the numbers R = MAX — U, where MAX is the largest number in the column containing U.
Then your smoking will not affect your chances of being in one state rather than another. In the original formulation, you saw smoking as actually determining whether you entered a state leading to your death from lung cancer; thus you saw smoking as affecting the probability of being in that state. On the new formulation, you are already in a state that can lead to your death from lung cancer or you are not. If you are in the unlucky state, your not smoking cannot alter that; but if you smoke you are certain to die, since you lack the protective factor.
Each day resolving her dilemma becomes more urgent. Should she have her children now and postpone her career? Or should she capitalize now on her brilliant start in order to establish herself as a physicist and raise her family later? As Kathryn sees her decision, the relevant states concern her ability seven years from now to establish a career or to be a good mother. ) We can thus represent her problem as choosing between two acts: have children now and postpone career and pursue career now and postpone children.