Uncovering and Displaying the Coherent Groups of Rank Data by Exploratory Riffle Shuffling ()
ABSTRACT
Let
n respondents rank order d items, and suppose that 
. Our main task is to
uncover and display the structure of the observed rank data by an exploratory
riffle shuffling procedure which sequentially decomposes the n voters into a
finite number of coherent groups plus a noisy group: where the noisy group
represents the outlier voters and each coherent group is composed of a finite
number of coherent clusters. We consider exploratory riffle shuffling of a set
of items to be equivalent to optimal two blocks seriation of the items with
crossing of some scores between the two blocks. A riffle shuffled coherent
cluster of voters within its coherent group is essentially characterized by the
following facts: 1) Voters have identical first TCA factor score, where TCA
designates taxicab correspondence analysis, an L1 variant of
correspondence analysis; 2) Any preference
is easily interpreted as riffle shuffling of its items; 3) The nature of
different riffle shuffling of items can be seen in the structure of the
contingency table of the first-order marginals constructed from the Borda
scorings of the voters; 4) The first TCA factor scores of the items of a
coherent cluster are interpreted as Borda scale of the items. We also introduce
a crossing index, which measures the extent of crossing of scores of voters
between the two blocks seriation of the items. The novel approach is explained
on the benchmarking SUSHI data set, where we show that this data set has a very
simple structure, which can also be communicated in a tabular form.
Share and Cite:
Choulakian, V. and Allard, J. (2021) Uncovering and Displaying the Coherent Groups of Rank Data by Exploratory Riffle Shuffling.
Open Journal of Statistics,
11, 178-212. doi:
10.4236/ojs.2021.111010.
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