2.5. SUMMARY
69
of choice-trials in Definition 2.4.1. It states that subsequent choice-trials be¬
long to the same point of view unless a shift of perspective has occurred. It
is stressed here that in contrast to assumptions about the sequence of choice¬
trials the independence of choice-trials is an implicit or explicit assumption
of all classical algebraic and probabilistic models as discussed in Chapter 1.
In the next chapter an experimental design is proposed which tests the
independence of choices in regard of intransitive choice behavior. If we can
show that inconsistent choice behavior systematically adapts to different ar¬
rangements of choice-trials then this would favor the ear decomposition by
sequence and reject classical algebraic or probabilistic models. Algebraic de¬
composition models are designed to study individual decision behavior. How¬
ever, experimental testing is usually based on group data. Because individual
choice varies additional qualitative information provided by the decomposi¬
tions had to be excluded. As a consequence, the experimental testing in the
next chapter focuses on a comparison of quantitative measures of inconsis¬
tency, that is Kendall's ( and r, with new measures derived from the algebraic
decompositions: the number of k-dicycles, ear dicycles, and the size of strong
components. A qualitative validation of the decomposition techniques is left
to future studies.