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Theoretical considerations 49
should also accept the preference rankings indicated by the method. Let
us now consider the axioms:
(1) Decidability: We assumed that the owner was able to decide which
of two options he preferred. For example, we assumed that he could
state whether the improvement in image between Carlisle Walk and
Gorton Square was greater than the improvement between Carlisle
Walk and Bilton Village. It may have been that the owner was very
unsure about making this comparison or he may have refused to
make it at all.
(2) Transitivity: The owner preferred the image of Addison Square to
Bilton Village (i.e. A to B). He also preferred the image of Bilton
Village to Carlisle Walk (i.e. B to C). If transitivity applies then the
owner must therefore also prefer the image of Addison Square to
Carlisle Walk (i.e. A to C).
(3) Summation: This implies that if the owner prefers A to B and B to C,
then the strength of preference of A over C must be greater than the
strength of preference of A over B (or B over C).
(4) Solvability: This assumption was necessary for the bisection method
of obtaining a value function. Here the owner was asked to identify a
distance from the center of town which had a value halfway between
the worst and best distances. It was implicitly assumed that such a
distance existed. In some circumstances there may be ‘gaps’ in the
values which an attribute can assume. For example, the existence
of a zone of planning restrictions between the center of the town
and certain possible locations might mean that siting an office at
a distance which has a value halfway between the worst and best
distances is not a possibility which the decision maker can envisage.
(5) Finite upper and lower bounds for value: In assessing values we had
to assume that the best option was not so wonderful and the worst
option was not so awful that values of plus and minus infinity would
be assigned to these options.
Assumptions made when aggregating values
In our analysis we used the additive model to aggregate the values
for the different attributes. As we pointed out, the use of this model is
not appropriate where there is an interaction between the scores on the
attributes. In technical terms, in order to apply the model we need to
assume that mutual preference independence exists between the attributes.