7. One problem with using probability models to estimate
preference ranking results from the objective criteria.
Most algorithms for probability models maximize the
likelihood function appropriate to the model. This is not
the same as maximizing the degree of concordance,
although in most cases, it is a very close approximation.
It is possible, however, for the degree of concordance to
actually decrease as the maximum of the likelihood function
is approached. This apparently is a problem only when the
slope of the likelihood function in the area of the maxi-
mum is very flat with respect to some parameter. This is
indicated by large estimated variance for that parameter.
Our solution to this problem was a pragmatic one. We
simply examined the degree of concordance at each
iteration of the maximization process and stopped the
procedure when the maximum degree of concordance had
been obtained.
8. Other possible reasons include the non-uniqueness of
weights in ordinal preference functions, misspecification of
the preference function, and possible flaws in the ex-
perimental design. The non-uniqueness of weights,
however, should not be a problem when the substitution
between change in the level of an attribute and cost is
examined. The form of the preference equations used are
consistent with a maintained assumption of transitivity, and
it is possible that the attributes considered did not enter
into the respondents' decision-making function in a
transitive fashion. However, this is unlikely as all the
factors would affect profits. It is possible that some
respondents may not have really understood how the game
is played or may have intentionally given either wrong or
misleading answers. This is probably what happened with
broker number 16 in the first experiment. This broker's
responses were unexpected on the first and last questions,
and the responses to the second and third questions were
inconsistent with the reponses to the first.