CHAPTER 3. EXPERIMENTS 
Figure 3.1: Complete graph of order 12 
alternatives in the domain of lotteries, and the fifth and sixth experiment 
investigate psychophysical discrimination between disks varying in bright¬ 
ness contrast. The aim of the experiments is to decide in which of the three 
domains algebraic decomposition models offer an alternative to classical alge¬ 
braic and probabilistic decision models. In particular, the ear decomposition 
by sequence is expected to trace adapting intransitive decision behavior pro¬ 
viding a better measure of inconsistency. The completion by cuts as outlined 
in Section 2.4 was not applied to the data sets because a computerized im¬ 
plementation has yet to be developed. 
3.1 General Method 
In the following experiments subjects chose in two or three sessions between 
the same set of alternatives. In a single session subjects chose in an incomplete 
pair comparison between 12 alternatives comprising 66 choice-trials. The 
sequence of trials was arranged in different block designs which are explained 
below. In Figure 3.1 a complete graph of order 12 is depicted that also 
describes a pair comparison. Each of the 66 lines connecting two vertices 
refer to a single pair comparison or binary choice. If an orientation is assigned 
to each connecting line a tournament of order 12 results, which completely 
describes the preference relations in a pair comparison. 
The block designs were constructed so that in each block of six choice-trials