Game Development Reference
In-Depth Information
When we identify our personal preferences for the four potential dinner op-
tions and insert them into the above formula, we arrive at a combined utility value
for each one.
Selection
Dave
Laurie
Combined
Steak dinner
1.0
1.0
1.0
Chinese take-out
0.1
0.7
0.3
Microwave burritos
0.4
0.1
0.3
Frozen pizza
0.4
0.6
0.5
Examining the data above yields a few interesting observations. First, while I
look at the burritos and pizza with the same opinion, Laurie
really
doesn't like the
burritos. Therefore, her preference acts a tie-breaker. We can see this reflected in
the combined score where the pizza ranks higher than the burritos.
Additionally, despite the fact that she likes Chinese take-out quite a bit—more
than the frozen pizza, because I'm not in the mood for Chinese, the score suffers
significantly. Much to Laurie's dismay, the Chinese take-out option ends up with
the
same
score as the burritos. Her difference in preference between the two is very
large (0.6), whereas mine is relatively small (0.3). Because my opinion matters twice
as much, however, that 0.3 difference means as much as her 0.6.
The end result is less than surprising. With both of us preferring to go out for
steak, that option easily wins out. (And the agreement likely spares me the potential
of annoying my wife with my choice regardless of the fact that she
said
she didn't
care.
That
is a factor that carries a lot of utility value for me!)
Even after we have calculated or combined factors to arrive at a utility function, we
may not have enough information to process a decision. While weighted sums
allow us to combine (and even normalize) similar information, decisions often
take disparate pieces of information into account. It is usually simpler to combine
similar items together first to arrive at an aggregate value. For example, we com-
bined the two sets of dinner preferences into
one
combined dinner preference
value. Once we have arrived at these combined figures, we can combine them with
other figures in another step of the process. By doing this, we are creating a
layered
weighting model
. In essence, we are building our decision in tiers.
