Logical Decisions - Classweb

other measures, including cost, and with 55
percent. Call this truck A. Now suppose I offer
you another truck, identical to A except for resale
value. Truck B has a 50% chance of having a 40
percent resale value and a 50% chance of having a
70 percent resale value.
Which of the two choices would you prefer, the
sure thing A or the uncertain alternative B?
A: Well, 55 percent is halfway between 40 and 70,
so I suppose I should feel that the two choices are
about equal, but I think that 55 percent is a pretty
adequate return and that 40 percent is just barely
acceptable, so even though I'd like the 70 percent
resale, I wouldn't be willing to risk the chance of
getting the 40 percent resale, so I'd pick A.
Q2: OK, that makes sense. Now let me change the
question a little bit. Lets change the resale value on
truck A from 55 to 45 percent while keeping
everything else the same. Now which choice
would you prefer?
A: With truck A at 45 percent resale value its not
that much better than truck B with 40 percent
resale value, so now I think that I might be
willing to gamble on getting the 70 percent resale
value. I guess this means I pick B.
Q3: Good. You can see that I'm trying to find a
resale value for truck A that makes it so choices A
and B are equally desirable. How about if I change
truck A's resale value to 50 percent?
A: Well, I think I'd have a hard time choosing.
Defining a SUF with the Probability Question. The rules of
decision analysis tell us that if alternatives A and B are equally
preferred, then the utility of alternative A is equal to the expected
utility of alternative B. The expected utility of B is the sum of the
utilities of the resale values multiplied by their probabilities
(P U(RV ) + P U(RV )).
1 1 2 2
The decision maker has told us that she prefers 50 percent for sure
and a lottery (the decision analysis term for this type of gamble)
9-24 Section 9 -- In Depth