Game Development Reference
In-Depth Information
Or (if you are like me and the big
E
sign scares you)
Deciding on Dinner
If my wife, Laurie, and I were to decide what we were going to eat for dinner (I
really have to stop working on this topic when I'm hungry), we may have a conver-
sation about what we are interested in eating. Naturally, we both have preferences,
and, just as naturally, those preferences may differ. We may not, however, always
put equal weight on our preferences. In a typical example, Laurie may say that she
really doesn't care what we have. (Whether or not I can believe that she
really
doesn't
care what we eat or whether I am supposed to guess is a topic for a book on under-
standing women, however, and beyond the scope of this chapter.) While I don't
want to entirely disregard her preferences, I can assume at this point that she wants
my
preference to have more weight than her own. To reflect this, we can weight
my
utility for varying dinner selections more than we do
her
utility for those same
selections.
Let's assume that our four options for the evening are a steak dinner at a restau-
rant (I'm just
not
firing up my grill when it's freezing out!), Chinese take-out, nuking
some burritos, and cooking a frozen pizza. First, we would establish the coefficients
that we will use in the formula so that our preferences are proportional to how
much consideration we put on our respective preferences. From those coefficients,
we can calculate a
combined
utility that reflects our joint decision.
Because I don't want to completely disregard my wife's desires, we will estab-
lish the coefficients as:
Dave
2
Laurie
1
This means my desires are worth twice as much as hers. Put another way, instead
of splitting the decision 50/50, my preferences are worth 67% and hers are worth
33%.
Put into a utility formula, this gives us:
Assuming that we have normalized the two personal utilities on a scale from 0
to 1, we can normalize the combined score by dividing by the sum of the coefficients.
