Information Technology Reference
In-Depth Information
Ta b l e 1 .
Satisfaction of issues and interests
a.
Issues
b.
Interests
high high full-
salary position time
a
✓✓✓
b
✓✓✗
c
✓✗ ✓
d
✓✗
family
wealth status time
a
✓✓✗
b
✓✓✓
c
✓✓✗
d
✓✓✓
e
✗✓✗
f
✗✓✓
g
✗✗✗
h
✗✗✓
✗
e
✗ ✓✓
f
✗ ✓✗
g
✗
✗ ✓
h
✗
✗
✗
outcome satisfying criterion
G
but not
H
cannot be compared to an outcome satisfying
H
but not
G
.
Another well-known approach is the
lexicographic
preference ordering (see e.g. [2],
where it is denoted #). Here, preferences over outcomes are based on a set of relevant
criteria, which are ranked according to their importance. The importance ranking of
criteria is defined by a total preorder
, which yields a stratification of the set of cri-
teria into importance levels. Each importance level consists of criteria that are equally
important. The lexicographic preference ordering first considers the highest importance
level. If some outcome satisfies more criteria on that level than another, then the first
is preferred over the second. If two outcomes satisfy the same number of criteria on
this level, the next importance level is considered, and so on. Two outcomes are equally
preferred if they satisfy the same number of criteria on every level.
We use a slightly more abstract definition of preference that covers both ceteris
paribus and lexicographic preferences. Let
C
be a set of binary criteria, ordered ac-
cording to importance by a preorder
.If
P
Q
and not
Q
P
, we say that
P
is strictly
more important than
Q
and write
P
Q
.If
P
Q
and
Q
P
, we say that
P
is equally
important as
Q
and write
P
≈
Q
.
C
can be divided into equivalence classes induced by
≈
, which we call importance levels. An importance level
L
is said to be more important
than
L
iff the criteria in
L
are more important than the criteria in
L
.Let
O
beasetof
2
C
.If
outcomes, and
sat
a function that maps outcomes
a
∈O
to sets of criteria
C
a
∈
P
∈
sat
(
a
)
, we say that
a
satisfies
P
.
Definition 1. (Preference).
An outcome
a
is
strictly preferred
to another outcome
b
if
it satisfies more criteria on some importance level
L
, and for any importance level
L
on which
b
satisfies more criteria than
a
, there is a more important level on which
a
satisfies more criteria than
b
. An outcome
a
is
equally preferred
as another outcome
b
if both satisfy the same number of criteria on every importance level.
The least specific importance order possible is the identity relation, in which case the
importance levels are all singletons and no importance level is more important than any
other. In this case, the preference definition is equivalent to ceteris paribus preference
(if
a
is preferred to
b
ceteris paribus, there are no criteria that
b
satisfies but
a
does not).
If the importance order is a total preorder, the definition is equivalent to lexicographic
