
The Basics of Measurement ◾ 35
is statement means that:
• Whenever Joe is taller than Fred, then M(Joe) must be a bigger num-
ber than M(Fred).
• We can map Jill to a higher number than Jack only if Jill is taller than
Jack.
EXAMPLE 2.5
In Section 2.1.1, we noted that there can be many relations on a given
set, and we mentioned several for the attribute height. The representa-
tion condition has implications for each of these relations. Consider these
examples:
For the (binary) empirical relation taller than, we can have the numerical
relation
x > y
Then, the representation condition requires that for any measure M,
A taller than B if and ...