Logical Decisions - Classweb
Logical Decisions - Classweb Logical Decisions - Classweb
this truck B, and call the change from truck A to truck B change 1. Suppose in addition that tomorrow I find another truck that has 160 hp and the same levels on the other measures as trucks A and B. Call this truck C. Call the change from truck B to truck C change 2. Since all the other measures are equal, you should like truck C better than truck B better than truck A. But I want you to tell me which change is more important: change 1 where horsepower improves from 80 to 120 or change 2, where horsepower improves from 120 to 160? A: Well, 120 is halfway between 80 and 160, so I suppose I should feel that the changes are equally important, but I think that 120 hp is pretty adequate for the type of driving I do and that 80 hp is just barely acceptable, so even though I'd like the 160 hp truck, I think that change 1 is the most important. Q2: OK, that makes sense. Now let me change the question a little bit. Lets change the horsepower on truck B from 120 to 100 while keeping everything else the same. This means that change 1 is from 80 to 100 hp and change 2 is from 100 to 160. Now which change is more important? A: With truck B at 100 hp, its not that much better than truck A, so now I think that change 2, where I can improve all the way from 100 to 160 is more important. Q3: Good. You can see that I'm trying to find a horsepower for truck B that makes it so that change 1 and change 2 are equally important. Now, how would you feel if I change truck B's hp to 105? A: I still think that change 2 is more important if the midpoint is 105, but if you made it 110 I'd have a hard time choosing. The decision maker has discovered that 110 hp represents her mid-preference level in the range from 80 to 160 hp. 9-18 Section 9 -- In Depth
Since U(L0) = U(80) = 0 and U(L1) = U(160) = 1 by definition, we can use the equation above to see that U(L) = U(110) = 0.5. In other words, the mid-preference level is halfway in preferences between the most and least preferred levels. Thus it should get the utility that is half way in terms of utils between 0 and 1 -- 0.5. Defining a SUF from the Mid-preference Level. Once you have established the mid-preference level, you still need to define the SUF function for the evaluation measure. There are several ways to go. The simplest method is to draw a smooth curve that passes through the three points -- (level = 80 hp, Utility = 0.0), (110, 0.5) and (160, 1.0). LDW does this by estimating the parameters for an exponential curve of the form: U(x) = a + be (-cx) where a, b and c are scaling constants and e is the mathematical constant 2.718... whose natural logarithm is 1. The particular curve that would result from the example is U(x) = 1.543 - 4.384e (-0.01305x) Since LDW computes this curve automatically, understanding the details of the mathematics is not important. A graph of the resulting curve is shown in Figure 9-4. Section 9 -- In Depth 9-19
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Since U(L0) = U(80) = 0 and U(L1) = U(160) = 1 by definition, we<br />
can use the equation above to see that U(L) = U(110) = 0.5. In<br />
other words, the mid-preference level is halfway in preferences<br />
between the most and least preferred levels. Thus it should get<br />
the utility that is half way in terms of utils between 0 and 1 -- 0.5.<br />
Defining a SUF from the Mid-preference Level. Once you have<br />
established the mid-preference level, you still need to define the<br />
SUF function for the evaluation measure. There are several ways<br />
to go. The simplest method is to draw a smooth curve that passes<br />
through the three points -- (level = 80 hp, Utility = 0.0), (110, 0.5)<br />
and (160, 1.0). LDW does this by estimating the parameters for an<br />
exponential curve of the form:<br />
U(x) = a + be (-cx)<br />
where a, b and c are scaling constants and e is the mathematical<br />
constant 2.718... whose natural logarithm is 1. The particular<br />
curve that would result from the example is<br />
U(x) = 1.543 - 4.384e (-0.01305x)<br />
Since LDW computes this curve automatically, understanding the<br />
details of the mathematics is not important. A graph of the<br />
resulting curve is shown in Figure 9-4.<br />
Section 9 -- In Depth 9-19
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