Tutorial 1: Preferences, Utilities, and Decisions
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چکیده
Then, define u(xyz) = 100 ∗ U(x) + 10 ∗ U(y) + U(z), where x ∈ {red, blue, green}, y ∈ {electric, petrol, diesel}, and z ∈ {German, French,UK}. Observe that for all x, x′ ∈ {red, blue, green}with x 6= x′, and y, y′ ∈ {electric, petrol, diesel} with y 6= y′, and z ∈ {German, French,UK} we have that (i) |U(y)− U(y′)| > U(z), and (ii) |U(x)− U(x′)| > U(y) + U(z). Intuitively, this ensures that the difference in utility for higher ranked attributes can not be offset by higher utility values for the lower ranked attributes. This then yields a utility representation of lexicographic ordering specified. (A formal argument is rather tedious.)
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